Raman and Mossbauer Spectroscopy and X-ray Diffractometry

Article pubs.acs.org/IC

Raman and Mossbauer Spectroscopy and X‑ray Diffractometry Studies on Quenched Copper−Ferri−Aluminates Kunal B. Modi,*,† Pooja Y. Raval,‡ Suraj J. Shah,§ Chetan R. Kathad,† Sonal V. Dulera,† Mansi V. Popat,† Kiritsinh B. Zankat,∥ Kiran G. Saija,⊥ Tushar K. Pathak,# Nimish H. Vasoya,⊗ Vinay K. Lakhani,○ Usha Chandra,▽ and Prafulla K. Jha⧫ †

Department of Physics, Saurashtra University, Rajkot 360005, India Department of Physics, SVNIT, Surat 395007, India § Darshan Institute of Engineering and Technology, Morvi Road, Rajkot 363650, India ∥ Department of Physics, Government Science College, Gandhinagar 382015, India ⊥ Smt. R. P. Bhalodiya Mahila College, Upleta 360490, India # Government Engineering College, Kalawad Road, Rajkot 360005, India ⊗ Sanjaybhai Rajguru College of Engineering, Morvi Road, Rajkot 360030, India ○ Department of Physics, M. D. Science College, Porbandar 360575, India ▽ High Pressure Physics Laboratory, Department of Physics, University of Rajasthan, Jaipur 302004, India ⧫ Department of Physics, Faculty of Science, M. S. University of Baroda, Vadodara 390002, India ‡

ABSTRACT: Four spinel ferrite compositions of the CuAlxFe2−xO4, x = 0.0, 0.2, 0.4, 0.6, system prepared by usual double-sintering ceramic route and quenched (rapid thermal cooling) from final sintering temperature (1373 K) to liquid nitrogen temperature (80 K) were investigated by employing X-ray powder diffractometry, 57Fe Mossbauer spectroscopy, and micro-Raman spectroscopy at 300 K. The Raman spectra collected in the wavenumber range of 100−1000 cm−1 were analyzed in a systematic manner and showed five predicted modes for the spinel structure and splitting of A1g Raman mode into two/three energy values, attributed to peaks belonging to each ion (Cu2+, Fe3+, and Al3+) in the tetrahedral positions. The suppression of lower-frequency peaks was explained on the basis of weakening in magnetic coupling and reduction in ferrimagnetic behavior as well as increase in stress induced by square bond formation on Al3+ substitution. The enhancement in intensity, random variation of line width, and blue shift for highest frequency peak corresponding to A1g mode were observed. The ferric ion (Fe3+) concentration for different compositions determined from Raman spectral analysis agrees well with that deduced by means of X-ray diffraction line-intensity calculations and Mossbauer spectral analysis. An attempt was made to determine elastic and thermodynamic properties from Raman spectral analysis and elastic constants from cation distribution.

1. INTRODUCTION The strong dependence of structural, microstructural, vibrational, magnetic, electrical, and dielectric characteristics of spinel ferrites on the way metallic cations occupy the available interstices is the most remarkable effect.1 The spinel structure possesses two different crystal lattice sites, namely, tetrahedral (A-) sites and octahedral (B-) sites, coordinated with four and six oxygen anions, respectively. The general formula for spinel 2− ferrite is M2+Fe3+ 2 O4 . Full occupation of A-sites by divalent metallic cations and B-sites by Fe3+ ions produce the normal spinel structure. If M2+ ions are exclusively bound at the B-sites and Fe3+ ions equally fill the available A- and B-sites of the spinel structure, an inverse spinel structure is produced. In partially inverse spinel structure, M2+ ions reside at both the lattice sites.2 © XXXX American Chemical Society

Vibrational Raman spectroscopy has been proven a nondestructive and highly efficient experimental technique for a straightaway detection of lattice dynamics in various types of materials.3 The peak positions, line widths, and intensities provide the information regarding the composition, chemical environment, bonding, and confinement details of phonon.4,5 It is widely used to study stress, strain, substitution effects, porosity, nonstoichiometry, microinhomogeneties, and primary phases of nucleation and growth of different kinds of nanometric materials. The high spectral resolution and allowance of micron-sized samples make Raman spectroscopy a more powerful and suitable technique to study the phase Received: October 18, 2014

A

DOI: 10.1021/ic502497a Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry

Figure 1. Rietveld-fitted XRD patterns for the typical compositions with x = 0.2 and 0.6 of CuAlxFe2−xO4 spinel ferrite system recorded at 300 K (* reflections due to the tetragonal distortion).

transformations in high-pressure fields.6 The popularity of this technique in the investigation of oxides (in bulk, nanoparticles, and thin film) and for characterization of the corrosion products as ex situ and in situ7 methods is growing by virtue of its ability to detect local disorder.8 Recent research reports available on Raman spectroscopic study of spinel-structured ferrite systems deal with commonly encountered pure and substituted cobalt ferrite, CoFe2O4,6,9−12 nickel ferrite, NiFe2O4,7,8 and magnetite, Fe3O4, including maghemite and hematite,1,7,13−15 zinc ferrite, ZnFe2O4,3,16,18 and aluminates like NiAl2O4, MgAl2O4, and CaAl2O4.19,20 Other experimental methods like X-ray absorption, Mossbauer spectroscopy, neutron diffraction, and X-ray diffractometry have also been employed to determine distribution of cations among the unoccupied interstices of the spinel structure.3 Limitation of 57Fe (57Co/Rh) Mossbauer spectroscopy and Xray diffractometry puts Raman spectroscopy as a supplementary technique to determine cation distribution in quaternary spinels. Another conventional experimental method to deduce elastic wave velocities and elastic moduli is the ultrasonic pulse transmission technique.21,22 Despite limitations of sample size and sample quality (presence, shape, size, and distribution of pores, microcracks, etc.) for specially treated materials, infrared spectral study has been proved suitable to ascertain force constants and elastic moduli.23 A comparative study has been carried out recently on elastic properties of slowly cooled and quenched spinel ferrite composition CuAl0.4Fe1.6O424 and on the effect of thermal history on Mossbauer signature and hyperfine interaction parameters of copper ferrite,25 besides earlier studied the structural,26 elastic,21 transport,27 and magnetic28 properties of slowly cooled system, CuAlxFe2−xO4 (x = 0.0−0.6). Surprisingly, systematic studies on vibrational spectra of pure and substituted CuFe 2 O 4 systems are scarce. In this communication, we report a room-temperature Raman spectroscopic study on quenched spinel ferrite system CuAlxFe2−xO4, (x = 0.0−0.6). Since the difference of energy between Cu2+ ions residing at the A- and B-sites is relatively small, rearrangement of metallic ions is mainly governed by sintering temperature and rate of cooling. The possible causes for peak intensity suppression in the region of 150−600 cm−1, enhancement in intensity, shoulder-like structure, blue shift, and random variation of line width for highest frequency mode

are also mentioned. The intensities of peaks corresponding to different cations on the A-sites were used to estimate the cation distribution. An attempt was made for the first time to employ Raman spectroscopy as a tool to determine force constants and elastic constants including Debye temperature, lattice energy, and molar heat capacity determination.

2. EXPERIMENTAL DETAILS Aluminum (Al3+)-modified CuFe 2O4 (copper ferrite) system, CuAlxFe2−xO4, with x = 0.0, 0.2, 0.4, and 0.6, was prepared using AR grade (99.9% pure) ingredients CuO, Al2O3, and Fe2O3, procured from Sigma-Aldrich India, Mumbai. The stoichiometric proportions of the oxides were mixed thoroughly, well-ground for 4 h in an agate mortar and pestle using acetone as wet medium. After drying ceramic powders were pressed into cylindrical-shaped pellets to ensure better solid-state reaction. In the pre-sintering process the pelletized samples were kept at 1100 °C for 24 h and slowly furnace-cooled to room temperature at the rate of 120 °C/hr. In the final sintering process, reground and repelletized samples were kept at 1100 °C (1373 K) for 24 h and then quenched at the liquid nitrogen temperature (80 K). The synthesized ferrite samples were characterized for crystalline phase identification, lattice constants, and cation distribution determination by X-ray diffractometry using a Philips, Holland, Xpert MPD automated X-ray powder diffractometer using Cu Kα radiation (λ = 1.5405 Å), graphite monochromator, and Xe-filled proportional counter. The diffractograms were recorded in the 2θ range from 5° to 80° with a scan speed of 2° min−1 at 300 K. The Raman spectra were recorded using the 514.5 nm line of Ar ion laser at a power of ∼40 mW in the backscattering geometry using a highthroughput micro-Raman spectrometer (Renishaw model Invia). Unpolarized and polarized scattered light from the samples were dispersed using a double monochromator (Spex, model 14018) and detected using a photomultiplier tube ITT FW-130 operating in the photon-counting mode. Scanning of the spectra and data acquisition was performed with the help of microprocessor-based data acquisitioncum-control system in the wavenumber range of 100−1000 cm−1 step with 10 s integration times. Figure 2 shows the fitted patterns after exponential background subtraction from the observed data to remove the Rayleigh background followed by a straight line subtraction. The fitting is done by using PEAKFIT software deconvoluting by Lorentzian contours with an appropriate goodness of fit. Ambient Mossbauer measurements on the samples with the thickness (∼0.15 mg 57Fe/cm2) were done using 10 mCi 57Co isotope in a (Rh)-matrix at constant acceleration mode in transmission geometry using a Si-PIN solid-state detector XR-100 CR (Amptek), CMCA-550 Data Acquisition Module (Wissel). The data were analyzed using B


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Inorganic Chemistry Mossbauer spectral analysis program29 with an appreciable goodnessof-fit parameter.

axial ratio (c/a) remains almost constant (1.03−1.05).37 The axial ratio (c/a = 1.046) found in the present case lies in the expected range (Table 1(b)). Tailoring of the axial ratio is possible by changing the concentration of Jahn−Teller (JT) Cu2+ ions at the B-sites or by controlling synthesis temperature and rate of cooling.38 The structure of pure CuFe2O4 and Al3+substituted CuFe2O4 (x = 0.2−0.6) is a tetragonally deformed spinel stretched along the ⟨011⟩ direction. According to JT theorem, molecules in which electronic ground state is orbitally degenerated are not so stable in the symmetric arrangement. These molecules always find one or more vibrational coordinates responsible for breaking the symmetry and lower the system’s energy. The transition metal ions with one, two, four, six, seven, and nine 3d electrons possess an orbitally degenerate ground state, but in the case of Cr2+, Mn3+, Fe4+(3d4), and Cu2+(3d9) arrangements, the degeneracy appears in the strongly antibonding orbits. The distortions are large, but there is long-range elastic coupling between the sites.39 The prolate tetragonal-type distortions are usually seen in which octahedron is stretched such that four ligands sit near the cation, while two others are further detached. Goodenough and Loeb40 explained the transfer of Cu ions to the tetrahedral sites considering their square-bond formation even if Cu ions are more stable at the octahedral sites of the spinel lattice. In the octahedral crystal field the ground state of Cu2+ ion is an orbital doublet 2Eg (t62ge3g) that resulted in JT effect responsible for the removal of the ground-state degeneracy. Thus, the presence of Cu2+ ions at the octahedral sublattice tend to suffer from a tetragonal distortion.41 According to Kim et al.,41 for an octahedral Cu2+ compound (C4X6) with a d6εd3γ configuration, a severe JT distortion (Oh− D4h) is likely due to its 2Eg ground state. With dγ electron articulated in terms of dz2 and dx2−y2, two configurations, namely, (dz2)2(dx2−y2)1 and (dz2)1(dx2−y2)2, are possible. A distortion to a compressed tetragonal structure (c/a < 1) is expected. For the first type of configuration, four ligand ions in the xy plane are attracted by the central ions on the z axis, resulting in a distortion of the octahedron to an elongated tetragonal structure (c/a > 1), while for second type of configuration a distortion to a compressed tetragonal structure (c/a < 1) is anticipated. In general, the elongated distortion instead of the compressed distortion is taking place.42 A precise knowledge of cationic distribution among the crystal lattice sites of the spinel structure helps to understand the various physical properties of ferrite materials. The atomic scattering factor of Al3+ ions is appreciably low compared to the atomic scattering factors of other constituent cations, Fe3+ and Cu2+. Scattering factor of Cu2+ ions is close to that of Fe3+ ions.43 Thus, the distribution of Al3+ ions among the two

3. RESULTS AND DISCUSSION 3.1. X-ray Diffraction Pattern Analysis and Determination of Structural Parameters, Cation Distribution, and Elastic Constants. Indexing and refinement of X-ray powder diffraction (XRD) patterns carried out using powder-X software30 by fitting a single-phase fcc spinel structure (space group O7hFd3̅m), as well as single-phase tetragonal spinel with a space group I41/amd, failed to large extent. In contrast to earlier reports where quenching resulted in cubic-structured copper ferrite material,31−33 present analysis confirmed that the quenched samples of CuAlxFe2−xO4 (where x = 0.0, 0.2, 0.4, and 0.6) possess a tetragonally distorted spinel structure with nonstandard face-centered space group F41/ddm. Figure 1 displays Rietveld-fitted (using general scattering analysis software (GSAS))34 X-ray diffraction patterns for the samples with x = 0.2 and 0.6. The degree of matching between observed and calculated data can also be evaluated numerically using the weighted profile R-factor, Rwp, the expected R-factor, Rexp, and the goodness-of-fit, χ2 = (Rwp/Rexp)2, paramter.35 The Rietveld refinement factors are summarized in Table 1(a). The Table 1(a). Rietveld Discrepancy Values for Quenched CuAlxFe2−xO4 System at 300 K Rwp (%) Al content (x) 0.0 0.2 0.4 0.6

Rexp (%) (±0.2)

6.00 6.29 6.85 7.20

χ2 (±0.1)

5.25 5.26 5.50 5.64

1.31 1.43 1.55 1.63

Rwp for laboratory X-ray data is larger (e.g., ∼10%)23 in comparison to that for neutron time-of-flight data. The χ2 values obtained between 1.3−1.6 are quite satisfactory for the refinement. The samples showed a dominant cubic phase with a minor tetragonal component. The substitution of smaller Al3+ ions (0.535 Å) for larger Fe3+ ions (0.645 Å) in the system result in the observed reduction in lattice parameters (Table 1(b)). The axial ratio (c/a) = 1.046 for CuFe2O4 (x = 0.0) increases to 1.063 for x = 0.6 composition (in concurrence to JCPDS c/a ratio = 1.06 for CuFe2O4), suggesting enhancement of tetragonal distortion with increasing Al content (x). Naik et al.36 reported that for CuFe2O4 c/a ratio lies between 1.01 and 1.06. It was also suggested that, although crystal cell parameters may vary from a = b = 8.20 to 8.30 Å and c = 8.544 to 8.692 Å,

Table 1(b). Molar Mass (Mw), Lattice Parameters, Unit Cell Volume (Vo), Axial Ratio, X-ray Density (ρx), Stress, and Strain for Quenched CuAlxFe2−xO4 System lattice constants (Å)

a* a = (a2c)1/3 (Å)

Vo = a2c (Å)3

±0.002 Å Al3+ content (x)

Mw (kg) 1 × 10−3

a=b

c

0.0 0.2 0.4 0.6

239.29 233.46 227.69 221.92

8.288 8.202 8.135 8.067

8.669 8.588 8.582 8.575

a

8.413 8.329 8.281 8.233

595.48 577.74 567.94 558.03

c/a

ρx (kg/m3) 1 × 103

λ

stress

strain

1.046 1.047 1.055 1.063

5.339 5.369 5.328 5.285

0.398 0.400 0.425 0.450

0.138 0.140 0.165 0.190

0.046 0.047 0.055 0.063

The values of a* were used for elastic parameters determination. C


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The value of K0 and the characteristic value of Poisson’s ratio,47 σo ≈ 0.33, are further used to compute other elastic moduli using the standard relations48

different sublattices can be determined precisely, but the determination of Fe3+ and Cu2+ ion distribution among the Aand B-sites from X-ray diffraction line-intensity calculations may not be reliable. The temperature dependence of lattice parameters and cation ordering parameter, λ, for CuFe2O4 has been studied by Bertaut et al.44 The parameter λ is the fraction of octahedral interstices occupied by JT ions (Cu2+). A well-established correlation between the axial ratio (c/a) and the concentration of Cu2+ ions at the B-sites is given by the relation (λ − 0.26) = 3[(c − a)/a] for λ ≥ 0.26, where (λ − 0.26) represents the square bond formation induced stress, and (c − a)/a represents corresponding strain (Table 1(b)). The c/a ratio was utilized to determine the concentration of Cu2+ ions (= 2λ) on the B-sites using the simple relation44 λ = 3(c/a) − 2.74. After fixing the concentration of Cu 2+ ions on the B-sites and the corresponding concentration of Cu2+ ions on the A-sites, the distribution of Al3+ and Fe3+ ions were determined from X-ray diffraction line-intensity calculations using a computer-based program45 whose details are given elsewhere.26 The final cation distributions thus deduced for various ferrite samples are given as

Young’s modulus, E0 = 3K 0(1 − 2σ0) rigidity modulus, G0 = E0 /2(1 + σ0) longitudinal modulus, L0 = K 0 + (4/3)G0 Lame’s constant, λLo = Lo − 2Go

The elastic moduli thus determined for various compositions are shown in Table 2. The elastic moduli evaluated for Table 2. Elastic Constants Determined from Cation Distribution for Quenched CuAlxFe2−xO4 System Ko

Eo

Al3+ content (x) 0.0 0.2 0.4 0.6

+ + A + 3+ B 2− x = 0.0, (Cu 20.20 Fe30.80 ) [Cu 20.80 Fe1.20 ] O4

Go

Lo

λLo

290.75 291.18 283.52 286.92

143.21 143.42 139.64 141.32

(GPa) 192.39 192.67 187.60 189.85

196.24 196.52 191.35 193.65

73.77 73.88 71.94 72.80

CuFe2O4 (x = 0.0) are in good agreement, but the magnitude of elastic constants is much higher for the substituted ferrites (x = 0.2−0.6) as compared to the elastic constant values determine from ultrasonic pulse transmission technique for slowly cooled and quenched CuAlxFe2−xO4 systems.21,24 3.2. Raman Spectral Analysis and Determination of Force Constants, Elastic Moduli, Lattice Energy, and Thermodynamic Parameters. The different compositions of ferrite system, CuAlxFe2−xO4, x = 0.0, 0.2, 0.4, and 0.6, possess tetragonally distorted face-centered cubic (fcc) spinel structure. A spinel unit cell consists 56 atoms (Z = 8). The smallest Bravais cell consists of only 14 atoms (Z = 2); consequently, the factor group study suggests vibrational modes given by

+ + + A + 3+ + B 2− x = 0.2, (Cu 20.20 Fe30.71 Al 30.09 ) [Cu 20.80 Fe1.09 Al 30.11 ] O4 + + + A + + + B 2− x = 0.4, (Cu 20.15 Fe30.67 Al 30.18 ) [Cu 20.85 Fe30.93 Al 30.22 ] O4 + + + A + + + B 2− x = 0.6, (Cu 20.10 Fe30.62 Al 30.28 ) [Cu 20.90 Fe30.78 Al 30.32 ] O4

(1)

Increasing concentration of JT Cu2+ ions at the octahedral sites seems to be responsible for the observed increase in tetragonal distortion (c/a) (Table 1(b)). It has been reported earlier that the critical number of B-site Cu2+ ions per spinel formula unit for a cooperative JT distortion to tetragonal symmetry (c/a > 1) in copper ferrospinel is ∼0.8.38 The B-site Cu2+ ions per formula unit in the range of 0.8−0.9 (eq 1) is in agreement with this limiting concentration value of ∼0.8. It is possible to determine bulk modulus (Ko) in particular as well as other elastic constants, by taking into account cation distribution, ionic radii of constituent cations, and unit cell volume of ferrite composition under study, using the normalized average cationic sphere volume (Å3) given by the formula46 SN =

(3)

Γ = A1g + Eg + F1g + 3F2g + 2A 2u + 2E u + 4F1u + 2F2u (4)

where A, E, and F notations show one, two, and threedimensional representations, whereas g indicates the symmetry with reference to the center of inversion.49,50 Here, A1g + Eg + 3F2g, five optical modes are Raman-active, 4F1u are infrared active modes, while 2A2u + 2Eu + 2F2u + F1g are inactive modes. Group theoretical and lattice-vibration studies based on the quasi-molecular description of the spinel structure have led to the following description of normal mode motions of the FeO4 tetrahedron.15 The A1g mode is due to the symmetric stretch of oxygen atoms along Fe−O bonds, Eg and F2g(3) modes are due to the symmetric and asymmetric bending of oxygen with respect to Fe, respectively, F2g (2) mode belongs to asymmetric stretch of Fe and O, while F2g(1) mode involves the translatory movement of the whole FeO4 unit.15,51 Figure 2 presents the Raman spectra for quenched CuAlxFe2−xO4 (x = 0.0−0.6) spinel ferrite system in the spectral region of 100 to 1000 cm−1, recorded at 300 K. As the copper−ferri−aluminate powders are in polycrystalline form, polarized measurements could not be carried out; therefore, the assignments of all degenerate irreducible representations to each of the Raman active modes were also not performed. The common features observed for x = 0.0−0.6 compositions are (i) a strong peak at ∼698 ± 5 cm−1 and group of bands between 150 and 600 cm−1 and (ii) the effect of higher content of Al3+ is

[x(rB ‐ t)3 + (1 − x)(rA ‐ t)3 + x(rA ‐ O)3 + (2 − x)(rB ‐ O)3 ]Vs 3VO

(2)

where x is the degree of inversion, and Vs and V0 are the unit cell volume of mineral spinel, MgAl2O4 (a = 8.084 Å and Vs = 528.55 Å3), and ferrite sample under study (Table 1(b)), 2− respectively. Considering general formula A2+B3+ 2 O4 for spinel structured ferrites, rA‑t, rA‑O, rB‑t, and rB‑O are referred to as cationic radii of the A and B cations at the tetrahedral sites and octahedral sites, respectively. According to Greenberg et al.,46 the spinel ferrites and ringwoodite spinels show a linear relationship of K0 = (60 + 490 × SN) GPa, with uncertainties of 7% and 3%, respectively. This relationship is established based on the assumption that the Ko is greatly dependent on the space occupied by the constituent metallic cations. D


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Figure 2. Raman spectra for quenched CuAlxFe2−xO4 system recorded at 300 K.

Table 3. Saturation Magnetization (σs), Magneton Number (nB), Neel Temperature (TN), Raman Shift, Line Width, and Intensity (I) for Quenched Copper−Ferri−Aluminates System σs (emu/g) Al3+ concentration (x) 0.0 0.2 0.4 0.6

nB (μB)

TN ± 2 K (K)

Raman shift (A1g) × 102 ± 1 (m−1)

line width (A1g) × 102 ± 1 (m−1)

I (a.u.) (A1g) ± 3 (a.u.)

Raman shift (F2g (2)) × 102 ± 1 (m−1)

650 620 580 515

702.8 692.0 700.0 706.0

95.5 100.1 86.6 97.8

102.2 257.8 509.8 634.5

494.4 481.1 475.6 481.2

ref 57 71.34 57.04 39.34 29.13

3.06 2.38 1.60 1.16

to suppress the peaks in the region of 150−600 cm−1 and to enhance the intensity of highest frequency peak. Referring to the Raman spectrum of pure CuFe2O4, a strong peak centered at 702.8 cm−1 corresponds to A1g mode and is due to the vibration of oxygen ion in the tetrahedral complex (T-site mode). The A1g vibrations are expected to be dominated by the oxygen atoms, and the bands corresponding to such vibrations are known to be very intense52 as observed for the mode at 698 ± 5 cm−1 for the different ferrite samples (Figure 2). It has been found that A1g mode in the Raman spectrum of normal spinels occurs in the 600−620 cm−1 region3 (e.g., for ZnFe2O4, A1g at 664.8 cm−1,16 at 647 cm−1,53 for MnFe2O4, A1g at 625 cm−1 16), while for inverse spinel ferrites the value lies in

the 670−710 cm−1 region3 (e.g., for NiFe2O4, A1g at 700 cm−1, for Fe3O4, A1g at 706 cm−1,8 at 670 cm−1,14 for CoFe2O4, A1g at 693 cm−1,10 at 695 cm−1,11 and for MgFe2O4, A1g at 710 cm−1,3 at 715 cm−1 54). Thus, the occurrence of A1g mode for pure and Al3+-substituted copper ferrites at ∼700 cm−1 suggests partially inverse spinel structure for all the compositions as reflected in cation distribution formulas (eq 1). It has been reported that the integral intensity and frequency shift of Raman modes are related to the magnetic ordering and are observed to be influenced by the mechanochemical polishing-induced residual stress.55 In general, the intensity of various modes in Raman spectra of Mn−Zn ferrite is found to decrease with increase in temperature and the residual stress. E


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Inorganic Chemistry According to Yamashita et al.,55 increase in residual stress is correlated with increasing temperature. On the other hand, increase in temperature results in increase in frustration and disorder in ferrimagnetic long-range ordering by transferring the system into paramagnetic short-range ordering,56 that is, decreases in ferrimagnetic behavior and weakening in magnetic coupling. In the present case both these effects are observed with increase in Al3+ substitution (x) in the system. For the system under investigation, CuAlxFe2−xO4 with x = 0.0−0.6, saturation magnetization (σs (emu/g)), magneton number (nB(μB)) determined from high-field magnetization measurement and the Neel temperature (TN (K)) determined from low-field alternating current susceptibility measurement decreases on Al3+ substitution (x) (Table 3)57 attributed to the weakening in ferrimagnetic ordering due to substitution of nonmagnetic Al3+ for magnetic Fe3+ ions. Furthermore, the stress induced by square bond formation increases with Al3+ content (x) (Table 1(b)). Thus, as discussed above, observed reduction in the integral Raman intensity in the region of 150− 600 cm−1 may be correlated with decrease in ferrimagnetic behavior and increase in stress on Al3+ substitution. It is important here to note that stress induced by square bond formation is dominant at the B-sites, while intensity of A1g mode belonging to the vibration of oxygen ion in the tetrahedral complex is not affected at all. Now it is possible to explain the observed change in intensity of peaks corresponding to different modes in Raman spectra in the light of the change in electric dipole moment. The observed change in intensity of various vibrational modes reflects corresponding change in electric dipole moment as a function of change in interatomic distances and ionic charge. On the basis of the infrared reflectivity measurements on ZnFe2O4 and NiFe2O4, it has been shown that the effective ionic charge on different cations is different from the actual ionic valence at the A- and B-sites. The radial spread of the electron orbital restricts such change in ionic charge such that it remains very close to the ionic valence of the respective ion.58 In the absence of reflectivity data if we consider that all the cations involved in the system are in the normal charge state, namely, +2, +3, and +3 for Cu, Fe, and Al ions, respectively, at 300 K, then based on the cation distribution formulas (eq 1), for x = 0.0 to 0.6 compositions, it is found that the effective average ionic charge for the A-site increases from +2.8 to +2.9, while it decreases from +5.2 to +5.1 for the octahedral site. Considering the above findings, it is conjectured that, on Al3+ substitution, the magnitude of electric dipole moment (pi = qi × di), where di is the relative displacement of the atoms and qi is the effective ionic charge of metallic cations, change such that the intensity of the peak that corresponds to the A1g vibrational mode increases and the intensity of peaks that correspond to the (Eg + 3T2g) modes decreases, as observed (Figure 2 and Table 3). A shoulder (broad hump) at the lower wavenumber side of A1g mode is clearly visible for x = 0.0 and 0.4 compositions but completely absent for x = 0.6 composition. Such doublet-like feature has been reported for CoFe2O4,10 NiFe2O4,8 and mixed Mn−Zn ferrite,16 in contrast to sharp and well-defined Raman bands observed for Fe3O4.7 These results are explained in the light of the fact that while in Fe3O4, both the A- and B-sites are occupied by Fe ions, while in NiFe2O4 and CoFe2O4, due to differences in ionic radii of Ni and Fe as well as Co and Fe, the Fe/Ni−O and Fe/Co−O bond lengths show a significant distribution. Raman spectroscopy is referred to as a powerful microscopic technique to study any local structural changes and

thereby efficiently detect such microstructural changes in the system. Thus, the difference in local structure between Fe3O4 and CoFe2O4/NiFe2O4 results in the doublet-like feature. These arguments are rather not convincing based on the facts that (i) A1g mode corresponds to only the vibrations of the oxygen ions, which form a tetrahedron without the vibrations of the octahedral sites ions at all15 and (ii) referring to the cation 3+ A 2+ 3+ B 2− distribution of Fe3O4, (Fe2+Fe3+ 2 O4), (Fe1.0) [Fe1.0Fe1.0] O4 , 3+ the A-sites contain Fe ions only, while the B-sites contain an equal amount of Fe2+ and Fe3+ ions. This situation is similar to that of NiFe2O4 and CoFe2O4 being an inverse spinel; the Asites are fully filled by Fe3+ ions, while the B-sites are filled by trivalent Fe3+ ions and divalent Ni2+/Co2+ ions, respectively. Furthermore, the ionic radii of Ni2+ (0.72 Å) and Co2+ (0.72 Å) are comparable with the ionic radius of Fe2+ (0.74 Å) and as a result, comparable bond lengths, Fe2+−O2−, Ni2+−O2−, Co2+− O2−, and strengths are expected. Thus, the argument regarding the difference in bond-distance distribution8,10,16 responsible for shoulder-like structure in Raman spectrum is not valid. The observed shoulder-like structure for NiFe2O4, CoFe2O4, and Mn−Zn ferrites and in the present case of the CuAlxFe2−xO4 system may be caused by the disparity in atomic masses of metallic cations residing at the tetrahedral sites.23,59 For the pristine ferrite composition (x = 0.0) of the system, CuAlxFe2−xO4, both the cations, Cu2+ (63.55 amu) and Fe3+ (55.85 amu), and for substituted ferrites (x = 0.2−0.6) all the three metallic cations, Cu2+, Fe3+, and Al3+ (26.98 amu), are present on the A-sites with large disparity in their atomic masses. Similarly, for mixed Mn−Zn ferrite, large amount Zn2+ (65.37 amu), small amount of Mn2+ (54.94 amu) and Fe3+ are expected to reside at the tetrahedral sites.55 On the other hand, presence of small amount of Co2+ (58.93 amu) and Ni2+ (58.71 amu) along with Fe3+ ions on the A-sites10,60 cannot be neglected. These two/three cations with different atomic masses at the same atomic crystal site vibrate with different frequencies that result in a shoulder-like structure. The position of A1g mode is found to shift toward higher wavenumbers for substituted ferrites, 691 cm−1 for x = 0.2 to 706 cm−1; for x = 0.6 composition (Table 3), this blue shift is attributed to the replacement of heavier (55.85 amu) and larger (0.645 Å) Fe3+ ions by lighter (26.98 amu) and smaller (0.535 Å) Al3+ ions in the system. On the other hand, the line width shows the random variation with Al3+ substitution (x) and suggests random distribution of different cations at the A-sites for the different compositions that randomly affect electron− phonon interaction and electronic disorder.10 Furthermore, the intensity of A1g mode increases with increasing Al3+ content (x) in the system (Table 3), which may be due to the decrease in disparity of cationic masses on increasing Al3+ substitution. The low-frequency intense mode centered at 300 cm−1 is assigned to Eg mode, while modes at 200, 492, and 550 cm−1 correspond to F2g (1), F2g (2), and F2g (3) modes, respectively. The Eg mode, like A1g mode, involves vibration of oxygen ion only, which forms a tetrahedron.55 In fact there exists a large controversy regarding the occurrence of Raman vibrational modes for cubic-structured ferrite materials. According to some authors,15,55 observed Raman modes are mainly due to the tetrahedral-like sublattice without vibrations of cations at the Bsites, which are not involved at all. If it be so, then the signature of Raman spectra and the position of various vibrational modes 2+ 3+ for purely normal spinels, Zn2+Fe3+ 2 O4 and Zn Cr2 O4, as well as purely inverse spinel ferrites, NiFe2O4 and Fe3O4, should be identical by all means. In the first case, A-sites are exclusively F


Article

Inorganic Chemistry

Figure 3. Solid line through data points represents total fitted peak corresponding to A1g mode, and dashed lines correspond to individual fitted peaks.

occupied by Zn2+ ions, and the B-sites are filled with Fe3+ or Cr3+ ions, having a very small difference in their ionic radii, 0.64 and 0.63 Å, and atomic masses, 55.85 and 52.0 amu, respectively. Similarly, in the second case, based on the normal cation distribution formulas, namely, (Fe3+)A [Ni2+Fe3+]B O2− 4 and (Fe3+)A [Fe2+Fe3+]B O2− 4 , tetrahedral (A-) sites are fully occupied by Fe3+ ions. However, a completely different set of band positions and signature8,14,55 suggest that B-site cations play a role in influencing the Raman modes, which is consistent with the claim that the Raman modes observed in the lowerfrequency region (460−640 cm−1) are dominated by the stretching vibration associated with the octahedral Fe3+O6 sublattice.52 On the contrary, it is well-established and accepted that the highest-frequency A1g mode is assigned to the tetrahedral sublattice. On the basis of the extensive literature survey,9,11,12,18,51−53,55 F2g(2) mode (∼492 cm−1 for x = 0.0 composition) is assigned to the octahedral site mode, which reflects the local lattice effect in the octahedral sublattice, or else it corresponds to the local symmetry vibrations of metal ions in octahedron (BO6) (O-site mode). Because of the atomic mass differences between the three metallic cations (Cu (63.55 amu), Fe (55.85 amu), and Al (26.98 amu)) involved in the system, the A1g mode splits into two (for x = 0.0 composition) and three (for x = 0.2, 0.4, and 0.6 compositions) different energy values3,17 (Figure 3). According to Seong et al.61 the integrated intensity of the

Raman mode is proportional to the number of corresponding oscillations. The lightest ion (Al3+) (Al−O vibrations) corresponds to the Raman mode peaking at 699 cm−1, whereas the heaviest one (Cu2+) (Cu−O vibrations) corresponds to the 618 cm−1 mode. Because the iron ion (Fe3+) possesses an intermediate mass, we associated the 668 cm−1 mode for the Fe3+ ion in the tetrahedral sublattice for x = 0.2 composition. It is clearly observed that the relative intensities of the peaks belonging to each ion change with Al3+ concentration (x) in the system (Figure 3). This suggests change in the cation distribution at the A-sites and corresponding changes in distribution of cations at the B-sites on Al3+ substitution. According to the above discussion, for pristine composition with x = 0.0, the Raman mode at ∼650 cm−1, A1g(Cu2+), is associated with Cu2+ ions located on the A-sites, which are surrounded by 12 nearest metal ions located on the B-sites (1) (Cu−O4−M(1,2) = Cu and M(2) = Fe). Likewise, the 12 , with M −1 A1g(Fe) mode (∼703 cm ) is claimed to be associated with (1,2) Fe3+ ions residing at the A-sites (Fe−O4−M12 ). The integrated intensities, I(Cu) and I(Fe), are proportional to the number of Cu−O4−M(1,2) and Fe−O4−M(1,2) bonds, 12 12 respectively. Following the work by Silva et al.,3 I(Cu) and I(Fe) can be used to estimate the concentration of Cu2+ and Fe3+ ions at the tetrahedral (A-) site, as follows: A x(Raman) (Fe) = αIFe/(αIFe + βICu)

G

(5) DOI: 10.1021/ic502497a Inorg. Chem. XXXX, XXX, XXX−XXX

Article

Inorganic Chemistry

Table 4(a). Elastic Parameters for Quenched CuAlxFe2−xO4 System Determined from Raman Spectral Analysis Recorded at 300 K kt content (x) 0.0 0.2 0.4 0.6

ko

k

Lo

Go

363.0 350.9 353.8 357.4

92.1 89.0 89.8 90.7

× 10 ± 0.01 (N/m) 3.66 3.52 3.55 3.56

1.82 1.72 1.69 1.70

3.05 2.92 2.93 2.94

Ko

Eo

λLo

Vlo

245.0 236.8 238.9 241.3

178.8 172.9 174.2 176.0

8245.7 8084.8 8148.9 8223.7

±1 (GPa)

2

240.2 232.2 234.1 236.5

Vso

Vmo

θR ± 1 (K)

VΔ × 10−6 ± 0.002 (m−3)

4657.4 4566.6 4603.5 4645.4

631.6 625.3 634.0 643.5

6.401 6.212 6.105 5.999

±10 (m/s)

where α and β are the oscillator strength corresponding to the (1,2) Fe−O4−M(1,2) 12 and Cu−O4−M12 bonds, respectively. According to Nakagomi et al.1, while studying cation distribution using Raman spectroscopy in the case of MgxFe3−xO4 system, the oscillator strength involving Fe−O4−M(1,2) 12 bonds is two times as compared to the oscillator strength that involves Mg−O4− M(1,2) 12 bonds. Thus, the relative oscillator strength, R = β/α, is found to be 0.5. Considering (i) MgFe2O4 and CuFe2O4 are partially inverse spinels, approximately 85−90% of Mg2+ and Cu2+ ions occupy the octahedral site, and the remaining 10− 15% of Mg2+ and Cu2+ ions reside at the A-site and (ii) ionic radius of Cu2+ (0.73 Å) is comparable with the ionic radius of Mg2+ (0.71 Å),17 it is appropriate to use R = 0.5 value for A A A x(Raman) (Fe) and x(Raman) (Cu) = 1 − x(Raman) (Fe) determination using eq 2 for unsubstituted CuFe2O4 sample. We found I(Fe) = 367 au and I(Cu) = 166 au for x = 0.0 composition. On the basis of the above calculations it is found that the concentration of Fe3+ ions is ∼0.81 and corresponding concentration of Cu2+ ions at the A-sites is ∼0.19. An attempt was made to determine the concentration of Fe3+ ions on the A-sites for substituted compositions (x = 0.2−0.6) also. For the system ZnxMg1−xFe2O4, (x = 0.0−1.0), it is quite reasonable to take R = 0.5 throughout the system3 because Fe3+ ion concentration remains constant, that is, 2, and nonmagnetic Mg2+ ion is replaced by another nonmagnetic Zn2+ ion in the system. In the present case, magnetic Fe3+ ion concentration decreases by an amount of (2 − x) by nonmagnetic Al3+ substitution (x) in the system, CuAlxFe2−xO4. Therefore, the relative oscillator strength for substituted compositions (x = 0.2−0.6) is expected to change by 1/(2 − x) instead of (1/2) = 0.5 = R as taken for unsubstituted (x = 0.0) ferrite. The Fe3+ ion concentration at the A-sites, xA(Raman) (Fe), for x = 0.2 is found to be 0.67 (I(Cu) = 290 au and I(Fe) = 330 au), for x = 0.4, xA(Raman) (Fe) = 0.83 (I(Cu) = 101 au and I(Fe) = 307 au), and for x = 0.6, xA(Raman) (Fe) = 0.67 (I(Cu) = 220 au and I(Fe) = 405 au), taking into account R = 0.56, 0.625, 0.714, for x = 0.2, 0.4, and 0.6 compositions, respectively. Thus, the resultant cation distributions for the different compositions may be presented as

4153.6 4072.4 4105.4 4142.7

Raman spectroscopy as a tool to determine cation site occupancies in quaternary cubic ferrite system. Raman shifts are nearly the same as the infrared band frequencies, as they are associated with the same vibration mode for a given molecule. This prompted us to employ Raman spectroscopy as a tool to evaluate force constants23,51 and elastic constants, including Debye temperature23 and thermodynamic properties.20 Second derivative of the potential energy with respect to internuclear separation is referred to as force constant, (k), while the other independent parameters are kept constant. The elastic moduli are of great significance as they can explain the binding forces in solids and hence the thermal properties. The knowledge of mechanical properties is inevitable for enabling the material as a functional device.62 The force constant, k (N/m), in terms of frequency of vibrating atoms, υ (m−1), and their reduced mass, μ (kg), is given by k = 4π2c2υ2μ, where c is the velocity of light. The tetrahedral site force constant, kt, is determined by the position of high-frequency vibrational mode, A1g (T-mode), and reduced mass of the cations and anions that form the tetrahedral site, μt. In the same way, for the octahedral site, the force constant, ko, is calculated by considering the position of low-frequency vibrational mode, F2g(2) (O-mode), and reduced mass of the cations and anions that form the octahedral site (μo). The force constants kt and ko for different compositions of the system are summarized in Table 4(a). The lattice constant (a) for the spinel ferrite materials varies according to the relation, 0.33rA + 0.67rB,63 where rA and rB are the ionic radii of the tetrahedral and octahedral sites, respectively. As mentioned before, force constant varies inversely with the site radius. Thus, resultant force constant (k) for the given ferrite composition was calculated using k = (0.67kt + 0.33ko) and are given in Table 4(a). The average force constant (k) and kt increase with increasing Al3+ substitution (x = 0.2−0.6), while ko decreases with increase in (x) for x = 0.0− 0.4 compositions (Table 4(a)). One can expect a decrease in force constant for either site if the mean ionic charge for such a site gets decreased. The decreased electrostatic energy would result in increase in metal ion−oxygen bond length at the octahedral sites, and a decrease of repulsive forces between ions leads to decrease in force constant. As discussed earlier, the average ionic charge for the B-sites decreases with (x); on the other hand, the formation of ferrous (Fe2+) ions (which is quite probable in such ferrite systems23) at the octahedral sites decreases the mean ionic charge further, which results in increase in interatomic bond length. Thus, ko decreases on Al3+ substitution (x). In other words, k and kt follow a trend opposite to that of variation of lattice constant with Al content (x), as expected. For the materials with cubic crystal structure, the force constant (k) is a product of stiffness constant (C11 = Lo; longitudinal modulus) and lattice constant (a).64 The value of

+ + A + 3+ B 2− x = 0.0, (Cu 20.19 Fe30.81 ) [Cu 20.81 Fe1.19 ] O4 + A 3+ B 2− x = 0.2, (Cu 2 + + Al3 +)0.33 Fe30.67 ) [(Cu 2 + + Al3 +)0.87 Fe1.13 ] O4 + A + B 2− x = 0.4, (Cu 2 + + Al3 +)0.17 Fe30.83 ) [(Cu 2 + + Al3 +)1.23 Fe30.77 ] O4 + A + B 2− x = 0.6, (Cu 2 + + Al3 +)0.33 Fe30.67 ) [(Cu 2 + + Al3 +)1.27 Fe30.73 ] O4

(6)

where no precise concentration of divalent (Cu2+) and trivalent (Al3+) cations on either site is given. Thus, the Fe3+ ion distribution obtained from X-ray diffraction line-intensity calculations, Mossbauer spectroscopy (Section 3.3), and Raman spectroscopy agree reasonably well, indicating the robustness of the approach as well as successful employment of H


Article

Inorganic Chemistry longitudinal modulus (Lo) and the characteristic value of Poisson’s ratio, σo ≈ 1/3,47 were further used to compute different elastic parameters: rigidity modulus (Go), Young’s modulus (Eo), bulk modulus (Ko), longitudinal (Vlo), transverse (Vso), and mean (Vmo) elastic wave velocities, Lame’s constant (λLo), and Debye characteristic temperature (θR), with the help of standard formulas available in the literature.23 It is found that the values of elastic moduli for x = 0.2−0.6 compositions increase with Al3+ concentration (x) (Table 4(a)). This indicates that the generation of strain in the solid is difficult and that the solid has a strong tendency to retain its original equilibrium position. According to Wooster,65 the variation observed in various elastic constants as a function of Al content (x) may be attributed to the change in interatomic bond strength. In the system under investigation, CuAlxFe2−xO4, lattice constants and as a result interionic distances decrease with increasing Al3+ substitution (x) (Table 1(b)). The decrease in interionic separation strengthens the interionic bonding, which is responsible for the increased magnitude of elastic constants. At the other side, it is quite obvious that cations with a completely filled outermost orbit are more stable than those of with incomplete outermost orbit. In the system, CuAlxFe2−xO4, the Fe3+ ions with incomplete outermost orbit (3d5) are substituted by Al3+ ions having completely filled outermost orbit, which do not involve in active bond formation. Thus, the bond strength and magnitude of elastic moduli are expected to decrease with increase in Al3+ substitution. We feel that initially for x = 0.0−0.2 compositions, second effect is dominant, and as a result the magnitude of elastic constants decreases; however, for higher concentration of (x), the first effect overcomes the second one, and elastic constants increase with increasing Al3+ substitution (x) (Table 4(a)). The Debye temperature increases with increasing Al3+ substitution (x) (x = 0.2−0.6) in the system indicate that lattice vibrations are impeded by Al3+ substitution. Overall, the variation in elastic moduli and Debye characteristic temperature shows opposite behavior than that of lattice constant as a function of Al3+ content (x). In the case of oxides and silicates with same atomic weight, (Mw/q), Brich66 proposes that the longitudinal velocity (Vlo) varies linearly with the X-ray density (ρx). Simmons67 afterward approved these findings and further extended them to shear wave velocity (Vso). Anderson68 has further shown that with the change in Vlo/ρx values, there is a variation in the values of mean atomic weight because the products Mw/q × Vlo/ρx and Mw/q × Vso/ρx should remain unchanged. Similarly, for mixed ferrite systems, such relationships were observed by many researchers69−71 and were also found applicable for manganite perovskites.72 In recent times, it has been observed that such relationships are not valid for slow-cooled Al3+-substituted CuFe2O4 spinel ferrite system21 and Fe3+-modified yttrium iron garnet system.22 In the present study, we attempted to establish a relationship between Mw/q and Vlo/ρx, Vso/ρx for quenched CuAlxFe2−xO4 system. The results are shown in Table 4(b). It is found that the products (Mw/q × Vlo/ρx and Mw/q × Vso/ρx) do not remain unchanged. This indicates that these ferrites do not act like the materials discussed in the literature. In ionic solids, the bond strength is referred to as lattice energy. The lattice energy values for polycrystalline compositions of CuAlxFe2−xO4 system are computed by Kadriavtsev’s approach.73 The velocity of sound wave (V) in liquid and solid media, assuming the additive of internal energy and using standard thermodynamic equation, is given by

Table 4(b). Experimental Data for Quenched CuAlxFe2−xO4 Spinel Ferrite Compositions at 300 K Mw/q × Vlo/ρx Al3+ content (x)

Mw /q × 10−3 (kg)

0.0 0.2 0.4 0.6

34.18 33.25 32.53 31.70

V2 = −

Mw/q × Vso/ρx

±0.1 × 10−3 (m4/s) 52.79 50.22 49.75 49.33

26.59 25.30 25.07 24.85

nmγ γRT + Uo Mw

(7)

where n and m are constants of potential energy function, γ is the ratio of molar heat capacity, (Cp/Cv), R is the gas constant, T is absolute temperature, Mw is the molar mass, and Uo is the potential energy of the substance possessing an equilibrium volume at the particular temperature. In the above-mentioned expression, (i) in the case of ionic solids the lattice energy of polycrystalline solid, ULp can be taken as Uo, (ii) for most of the ionic solids, γ ≈ 1 (Table 4(d)), and (iii) the value of n = 3 is found pertinent to many spinel ferrites, garnets, and many ionic solids.74−76 By taking into account the above points the expression for lattice energy can be simplified as ULp = −3.108(M w Vm 0 2) × 10−3 eV

(8)

where Vmo (mean sound velocity corrected to zero porosity) (Table 4(a)) replaces V. The ULp values for the various compositions are depicted in Table 4(c). Table 4(c). Lattice Energy for Quenched CuAlxFe2−xO4 Spinel Ferrite System UL (eV) Al3+ content (x)

ULp ± 0.5 (eV)

ULs (eV)

compound

present work

Catlow78 et al.

0.0 0.2 0.4 0.6

(−161.3) (−151.3) (−150.0) (−148.8)

(−191.1) (−191.7) (−192.2) (−192.8)

YFeO3 Y4Fe4O12

(−149.8) (−599.3)

(−142.5) (−567.6)

An attempt was made to compute the lattice energy (ULs) for all the compositions of CuAlxFe2−xO4 spinel ferrite system using Kapustiskii equation,77 specifically used for singlecrystalline materials. This was one of the most successful approaches to calculate lattice energies for a broad range of crystals. ULs = −1202.5 × q ×

|Z +||Z −| ⎡ 0.345 ⎤ 1− + ⎥ + − × ⎢ ⎣ r +r r + r− ⎦

(9)

where q is the total number (7) of ions in the general chemical formula AB2O4 of the spinel ferrites, Z+ and Z− are cationic and anionic charge, respectively, while r+ and r− are the ionic radii (Å) of the cation and anion, respectively. Here, it is notable that the lattice energy values thus obtained are in kJ/mol but are given in eV for the purpose of comparison (Table 4(c)). The ionic radius (r−) and ionic charge (Z−) of oxygen anion are taken to be 1.32 Å and (2−), respectively, and to determine r+ and Z+ values, weighted average of ionic radii and ionic charges of the cations present in the system were considered. The values of lattice energy computed for other types of I


Article

Inorganic Chemistry Table 4(d). Thermodynamic Parameters for Spinel Ferrites at 300 K σmax

fmax ̅

Al3+ content (x)

× 109 ± 0.002 (m−1)

× 1013 ± 0.002 (sec−1)

υ̅max × 102 ± 1 (m−1)

θI ± 1 (K)

0.0 0.2 0.4 0.6

2.460 2.485 2.500 2.514

2.029 2.009 2.037 2.067

676.3 669.7 679.0 689.2

974.5 965.0 978.4 993.1

Cv

Cp

±0.2 (J/mol·K) 96.3 97.2 95.9 94.3

96.6 97.5 96.2 94.3

Figure 4. 57Mossbauer spectra for x = 0.0 and 0.4 compositions of quenched CuAlxFe2−xO4 system recorded at 300 K. The velocity scale is with respect to metallic iron.

calculated for magnetite, Fe2+Fe3+ 2 O4, by infrared spectral analysis.81 The value of Cp = 120.5 J/mol·K for CaAl2O4, obtained from Raman spectral analysis at 295 K,20 is in agreement with the present results. The Debye temperature is an essential parameter to study lattice vibrations in solid-state physics. According to Salter et al.,81 Debye temperatures measured using various experimental techniques like ultrasonic pulse transmission technique of elastic constants determination, specific heat, and infrared spectroscopy, will not be in concordance. The Debye temperatures determined in the present investigation from Waldron’s approach are in excellent agreement with those reported for MgAl2O4 (θ = 933 K) and CaAl2O4 (θ = 831 K) obtained from Raman spectroscopy using the Kieffer model at 298 K,20 thus validating the present approach. According to Dulong and Petit law,47 theoretically expected value of heat capacity at constant volume, Cv, can be deduced using the relation Cv = 3pR, where p is the number of atoms per chemical formula, and R is the gas constant. In the case of spinel ferrite materials of the type A2+B3+ 2 O4, the number of atoms p per chemical formula is 7. Thus, Cv = 174.5 J/K·mol, which is the limiting value of heat capacity at T ≈ θ. Finally, by using Einstein’s theory of the heat capacity of solids,47 the Cv value at T = 300 K for all the samples of CuAlxFe2−xO4 spinel ferrite system was calculated.

ferrites, yttrium orthoferrite (YFeO3), and yttrium-substituted yttrium iron garnet (Y4Fe4O12), by using weighted average of ionic radii and ionic charge, are given in Table 4(c). The values calculated by this approach show excellent agreement with those computed from atomistic computer simulation.78 The lattice energy values for polycrystalline spinel ferrite compositions (ULp) are found less compared to their singlecrystalline counterparts (ULs). This may be due to the presence of grains and grain boundaries in the polycrystalline material. At the grain boundary, which is a region several atomic distances wide, there are many degrees of crystallographic disorientation between adjacent grains present. The atoms along the grain boundaries are less bonded than those at the inner one, and the bond angles are larger, which results in grain boundary energy, which can be represented as a function of degree of disorientation at the grain boundaries.79 Prevention of longdistance interactions by the grain boundaries reduces the overall lattice energy of polycrystalline solids compared to single-crystalline materials (Table 4(c)). Following Waldron’s approach,80 we can calculate the highfrequency cutoff of the elastic waves using the equation f max = Vl × σmax. Considering the shortest wave corresponds to onehalf wave per mean interatomic distance, d̅, and since d̅ is given by d̅ = 1/4 (3r0 + rt) = 7.732 (a/32), we obtain σmax = 2.07 × 10−2/a (m). The high-frequency cutoff, f max, thus computed for different ferrites are presented in Table 4(d). The approximate mean between the cutoff frequencies of the oxide and metal ion vibrations, υ1 and υ3, respectively, is given by the relation υmax = f max/c (m/sec). The characteristic Debye temperature is defined by θI = hcυmax/kB. The Debye temperature, θI, values thus determined for the different ferrite compositions are shown in Table 4(d). The value of θI is further used to compute molar heat capacity at constant volume, Cv, by the equation Cv = 21Rf(T/θI), where R is the gas constant (8.31 J/mol·K), f is Debye function, and T is temperature. The calculated values of molar heat capacity at constant pressure (Cp) assuming Cp − Cv = 0.0011 T(K),80 for different compositions of CuAlxFe2−xO4 spinel ferrite system are summarized in Table 4(d). The different parameter values are in agreement with those

⎛ θ ⎞2 exp(θR /T ) Cv = 3pR ⎜ R ⎟ ⎝ T ⎠ [exp(θR /T ) − 1]2

(10)

We found Cv = 122.1, 122.9, 122.0, and 120.5 J/K·mol for x = 0.0, 0.2, 0.4, and 0.6 compositions, respectively. These values of Cv and those calculated based on Waldron’s approach81 (Table 4(d)) are in good agreement with this limiting value as derived from Dulong and Petit law. 3.3. Mossbauer Spectral Analysis and Determination of Hyperfine Interaction Parameters. 57Fe Mossbauer spectroscopy is a versatile microscopic tool for different types of ferrites to investigate magnetic ordering, hyperfine interaction parameters, to deduce concentration of ferric J


Article

Inorganic Chemistry (Fe3+) ions among the antiferromagnetically coupled sublattices, to determine presence/absence of iron ion in other oxidation states, and the evolution of magnetic phases in the system.82,83 Mossbauer spectra for the ferrite samples with x = 0.0 and 0.4 obtained at 300 K are shown in Figure 4. Fitting of the spectra was done assuming equal line width for the A- and Bsites of the spinel structure. All the compositions display two well-resolved Zeeman split sextets, one due to Fe3+ ions at the octahedral sites and other due to Fe3+ ions at tetrahedral sites, suggesting ferrimagnetic behavior of the samples. The refinements of hyperfine interaction parameters using computer software based on nonlinear least-squares minimization method are shown in Table 5. The chemical shifts or Table 5. Mossbauer Hyperfine Interaction Parameters for the Spinel System, CuAlxFe2−xO4, with Typical Compositions, x = 0.0 and 0.4, at 300 K

a

parametera

x = 0.0

x = 0.4

IS(A) ± 0.02 (mm/s) IS(B) ± 0.02 (mm/s) Γ(A) ± 0.03(mm/s) Γ(B) ± 0.03 (mm/s) QS(A) ± 0.02 (mm/s) QS(B) ± 0.02 (mm/s) δ (Moss) δ (X-ray)

0.23 0.33 0.65 0.69 (−0.01) (−0.27) 0.64 0.67

0.22 0.23 0.68 0.83 (−0.11) (−0.16) 0.72 0.70

Figure 5. Hyperfine fields vs Al3+ concentration (x) for CuAlxFe2−xO4 system at 300 K.

It is noticeable that the line width for the octahedral sites is larger than that for the tetrahedral sites for all the compositions (Table 5). This is because of increase in distribution values of hyperfine field for the octahedral sites as compared to the tetrahedral sites, resulting from A- sites magnetic dilution by nonmagnetic Al3+ substitution. Since only nonmagnetic Al3+ ions (0 μB) are in the system, when they enter into the A- sites, the internal hyperfine field at the B-sites is also greatly influenced; that is, super-transferred hyperfine interaction gives rise to more distribution values to the octahedral sites hyperfine field. The QS values sof the tetrahedral and octahedral sites vary arbitrarily with concentration (x) suggesting a chemical disorder as a result of arbitrary distribution of Al3+ ions around Fe3+ ions at the tetrahedral and octahedral sites. The negative signs of QS (Table 5) suggest the orientation of direction of hyperfine field relative to the principle axis of the electric field gradient tensor. The distribution of ferric ion (Fe3+) among the available tetrahedral (A-) and octahedral (B-) sites deduced from Mössbauer spectral analysis for the different compositions may be summarized as

IS with respect to Fe metal.

isomer shifts (IS) are used to identify the ionic state of Fe ions in the system. IS and quadrupole splitting (QS) for ferrous ions (Fe2+) lie between 0.90 and 1.06 mm/s and 1.75−2.10 mm/s, respectively, while IS for ferric ion (Fe3+) varies in the range of ∼0.22−0.33 mm/s. IS is governed by s-electron density at the Fe nucleus.84 The IS values for iron (Fe) ion at the A- and Bsites are found to be on the order of 0.22−0.33 mm/s with regard to Fe-metal for all the compositions, suggesting presence of Fe3+ ions in the system. As anticipated, the IS value for Fe ions at the octahedral sites is more positive than that for the tetrahedral sites Fe3+ ions because of larger Fe3+−O2− bond separation in the previous one. The concentration dependence of mean hyperfine field values acting on the A- and B-site 57Fe nuclei is as shown in Figure 5. Apparently, there is a gradual reduction in the internal hyperfine field values on Al3+ substitution (x) in the system. This occurs due to the substitution of nonmagnetic Al3+ ions for magnetic Fe3+ ions, which alters the internal hyperfine field at the nearest Fe3+ sites through super transferred hyperfine fields. This also shows a decrease in ferrimagnetic behavior and magnetic coupling, JAB, with increase in Al content (x), which is consistent with magnetization results.57 The lower values of hyperfine field for the tetrahedral sites compared to the octahedral sites are because Fe3+−O2− bonds at the tetrahedral sites are of more covalent nature than they are at the octahedral sites.85 As the magnetic Fe3+ ions are replaced by nonmagnetic Al3+ ions at the octahedral sites and by the dominant super exchange interaction, the supertransferred hyperfine field, HSTHF, is greatly affected at the tetrahedral sites. The faster decrease in average internal hyperfine field for Fe3+ ions at the octahedral sites compared to that at the tetrahedral (A-) sites can also be accounted for by the same reasons discussed above (Figure 5).

3+ B 2− + + A + x = 0.0, (Cu 20.22 Fe30.78 ) [Cu 20.78 Fe1.22 ] O4 + A 3+ B 2− x = 0.2, (Cu 2 + + Al3 +)0.28 Fe30.72 ) [(Cu 2 + + Al3 +)0.92 Fe1.08 ] O4 + A + B 2− x = 0.4, (Cu 2 + + Al3 +)0.36 Fe30.64 ) [(Cu 2 + + Al3 +)1.04 Fe30.96 ] O4 + A + B 2− x = 0.6, (Cu 2 + + Al3 +)0.40 Fe30.60 ) [(Cu 2 + + Al3 +)1.20 Fe30.80 ] O4

(11)

The values of ferric ion distribution parameter, δ = Fe3+ A / Fe3+ B , determined from Mossbauer spectral analysis for the different compositions are consistent with the δ values obtained from cation distribution formulas (eq 1) (Table 5).

4. CONCLUSIONS Rietveld refinement of X-ray powder diffraction data confirms that tetragonally distorted spinel structure due to rapid thermal cooling induced large B-site occupancy of JT ions (Cu2+) in the CuAlxFe2−xO4 system. The axial ratio (c/a) can be used to determine concentration of Cu2+ ions at the octahedral sites and square bond formation induced stress and strain. The K


Article

Inorganic Chemistry relation Ko = (60 + 490 × SN) GPa provides a simple approach to compute bulk modulus of the spinel structured materials using cation distribution. Besides structural analysis using X-ray diffractometry, Raman spectral analysis also confirms five first-order Raman active modes corresponding to spinel-structured materials. The A1g vibrational mode splits into two/three energy values due to the large disparity in atomic masses of constituent metallic cations residing at the tetrahedral sites, which allows us to determine the distribution of Fe3+ ions based on Raman spectral analysis. This is also responsible for the shoulder-like structure, enhancement in intensity, and random variation of line width of peak corresponding to the A1g mode. On the other hand, decrease in ferrimagnetic behavior, weakening in magnetic coupling, and square bond formation induced stress at the Bsites are responsible for observed reduction in integral intensity of Raman modes in the wavenumber range of 150−600 cm−1. The force constants and various elastic moduli were determined from Raman data. The compositional dependence of elastic constants can be explained on the basis of reduction in interionic distances and noncontribution to the active bond formation by substitution of nonmagnetic Al3+ ions having completely filled outermost orbit for magnetic Fe3+ ions with half-filled outermost orbit in the system CuAlxFe2−xO4. The presence of grains and grain boundaries in the polycrystalline materials is responsible for the lower lattice energy values as compared to their single-crystalline counterparts. The Debye temperature and molar heat capacity values determined from Raman spectral analysis are in agreement with the reported ones, validating the present approach. 57 Fe Mossbauer spectra show six-line patterns for all the compositions, and decreases in hyperfine field values indicate ferrimagnetic behavior that decreases with increase in Al3+ concentration (x). Mossbauer hyperfine interaction parameters are found to be influenced by replacement of Al3+ ions for Fe3+ ions in the system. The X-ray powder diffractometry, micro-Raman spectroscopy, and 57Fe Mossbauer spectroscopy techniques are employed successfully in a complementary manner for the determination of Fe3+ ion concentration at the A-sites and B-sites of the spinel structure.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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Raman and Mossbauer Spectroscopy and X-ray Diffractometry

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