Volume 8, Issue 2, June 2019, Page: 70-93
Effects of Zn Substitution on Structure Factors, Debye-Waller Factors and Related Structural Properties of the Mg1-xZnxFeNiO4 Spinels
Kadhim Ahmed Khalaf, Department of Mathematical and Physical Sciences, College of Arts and Sciences, University of Nizwa, Nizwa, Oman
Ahmed Al-Rawas, Department of Physics, College of Science, Sultan Qaboos University, Al-koud, Oman
Abbasher Gismelseed, Department of Physics, College of Science, Sultan Qaboos University, Al-koud, Oman
Majid Al-Ruqeishi, Department of Physics, College of Science, Sultan Qaboos University, Al-koud, Oman
Salwan Al-Ani, Department of Physics, College of Science, University of Baghdad, Baghdad, Iraq
Ahmad Al-Jubouri, Department of Mathematical and Physical Sciences, College of Arts and Sciences, University of Nizwa, Nizwa, Oman
Khamis Al-Ryami, Department of Mathematical and Physical Sciences, College of Arts and Sciences, University of Nizwa, Nizwa, Oman
Bushra Al-Jaddedi, Department of Mathematical and Physical Sciences, College of Arts and Sciences, University of Nizwa, Nizwa, Oman
Received: Jan. 7, 2019;       Accepted: May 24, 2019;       Published: Jun. 10, 2019
DOI: 10.11648/j.am.20190802.15      View  97      Downloads  36
Abstract
The effects of Zn2+ ions substitutions on the Debye-Waller Factors, structure factor and other related structural properties of the Mg1-xZnxNiFeO4 (where 0.0≤x≤1.0) spinels have been investigated using the XRD, TEM, SEM and FT-IR tools. The Mg1-xZnxNiFeO4 samples were prepared using the conventional ceramic solid state sintering techniques at temperatures around 1100°C. The Mg1-xZnxNiFeO4 spinels have predominantly inverse type structure with inversion factor, λ in the range 0.69 to 0.36. The X-ray diffraction (XRD) patterns of all compositions showed the formation of cubic spinel structure. The lattice constant “a” increases from 8.3397Å for MgFeNiO4 to 8.3855Å for ZnFeNiO4 spinels. The increases in lattice parameters have been attributed to the replacement of small Mg2+ ions (0.66 Å) with the Zn2+ (0.74 Å) ions of a larger ionic radius. The IR spectra confirm the existence of two main absorption bands υ1 and υ2 in the frequency range of (400–1000 cm-1), arising due to the tetrahedral (A) and octahedral (B) stretching vibrations respectively. Values of both υ1 and υ2 decrease as Zn content increases. The scanning electron microscope (SEM) and transmission electron microscope (TEM) images showed aggregates of stacked grains. The normalized XRD intensities of the main (hkl) planes were used in the estimation of the Debye-Waller factor. Values of the Debye-Waller factors were estimated to be in the range (0.77-1.44A2). The calculated and observed relative intensities and areas of the most related plains to cation distributions (i.e.: the (220), (311), (222), (400), (422), (511) and (440) plains) were obtained by normalizing with respect to the most intensive reflection from the (311) plane. An inverse relation between the ordering, Q and inversion, λ factors exists in these partially inverse spinels. Both Q and λ decrease as Zn content (x) increases in the sample. The cation distributions indicate that the sample, MgFeNiO4 with x=0, λ=2/3 and maximum configurational entropy Sc(=15.876 J/mol, K) should represents the sample of the complete randomness of cation distributions in these spinels and can be written as (Mg1/3Fe2/3)[Mg2/3Fe1/3Ni3/3)O4. In general the variation of the different structural parameters with Zn content lie on two different regions, the first region for x values (0.0-0.6) the “highly normal” and the second region for x values (0.6-1.0) the “highly inverse” type structure.
Keywords
XRD, TEM, SEM, FTIR, Structure Factor, Debye Waller Factor, Order Parameter
To cite this article
Kadhim Ahmed Khalaf, Ahmed Al-Rawas, Abbasher Gismelseed, Majid Al-Ruqeishi, Salwan Al-Ani, Ahmad Al-Jubouri, Khamis Al-Ryami, Bushra Al-Jaddedi, Effects of Zn Substitution on Structure Factors, Debye-Waller Factors and Related Structural Properties of the Mg1-xZnxFeNiO4 Spinels, Advances in Materials. Vol. 8, No. 2, 2019, pp. 70-93. doi: 10.11648/j.am.20190802.15
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This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Reference
[1]
Alex Golden (2006) “Applications and Functions of Ferrites”. In: Modern Ferrite Technology. Springer, Boston, MA. USA
[2]
K. K. Kefeni, T. A. M. Msagati and B. B. Mamba “Ferrite nanoparticles: Synthesis, characterization and applications in electronic device” materials Science and Engineering Vol. 215 (2017) 37-55. https://doi.org/10.1016/j.mseb. 2016.11.002
[3]
J. M. Hastings and L. M. Corliss “Neutron Diffraction Studies of Zinc Ferrite and Nickel Ferrite” Rev. Mod. Phys. Vol. 25 (1953) 114-118 https://doi.org/ 10.1103/RevModPhys.25.114
[4]
P. K. Nayak “Synthesis and characterization of cadmium ferrite” Mater. Chem. Phys. Vol. 112 (2008) 24–26 http://doi:10.1016/j.matchemphys 2008.05.018
[5]
C. P. Marshall, W. A. Dollase “Cation arrangement in iron-zinc-chromium spinel oxides”Ameri. Miner. Vol. 69 (1984) 928-936.
[6]
L. M. Corliss, J. M. Hastings, and F. G. Brockman “A Neutron Diffraction Study of Magnesium Ferrite” Phys. Rev. Vol. 90 (1953) 1013 –1018 https://doi.org/10.1103/ PhysRev.90.1013
[7]
H. Knoch, H. Dannheim “Temperature dependence of the cation distribution in magnesium ferrite” Phys. Status. Solidi A 37 (1976) K135-K137.
[8]
https://doi.org/10.1002/pssa.2210370251
[9]
D. Carta, M. F. Casula, A. Falqui, D. Loche, G. Mountjoy, C. Sangregorio and A. Corrias “A structural and magnetic investigation of the inversion degree in ferrite nanocrystals MFe2O4 (M) Mn, Co, Ni)” J. Phys. Chem. C 113 ((2009) 8606–8615. https://doi:10.1021/jp901077c
[10]
C. Angelettfir, F. Pepe and P. Porta “Structure and catalytic activity of CoMgl -xA12O4 spinel solid solutions. Part 1: cation distribution of Co2+ ions” J. Chem. Soc., Faraday Trans. 1, Vol. 73 (1977) 1972-1982. https://www.doi0.1039/F19777301972
[11]
P. Porta, A. Anichini, U. Buccciarelli “Distribution of nickel ions among octahedral and tetrahedral sites in NixZn1-xAl2O4 spinel solid solutions”. J. Chem. Soc. Faraday Trans. Vol. 1 (1979) 1876-1887. https://doi.10.1039/ F19797501876
[12]
Hugh St. C. O'Neill and Alexandra Navarotsky “Simple spinels: crystallographic parameters, cation radii, lattice energies, and cation distribution” Amer. Miner. Vol. 68 (1983) 181-194
[13]
A. M. Gismelseed, K. A. Mohammed, F. N. Al-Mabsali, M. S. Al-Maashani, A. D. Al-Rawas, A. A. Yousif, H. M. Widatallah, M. E. Elzain. “The effect of Zn substitution on the structure and magnetic properties of magnesium nickel ferrite” Hyperfine Interact Vol. 239: 16 (2018). https://doi.org/10.1007/s10751-018-1492-4
[14]
Y. Waseda, E. Matsubara, K. Shinoda, X-ray Diffraction Crystallography, Springer-Verlag Berlin, Heidelberg, 2011
[15]
A. R. Jani and V. B. Gohel “Temperature variation of Debye-Waller factor for alkali and nobel metals” Z. Naturforsch Vol. 38 a (1983) 503-508
[16]
N. Singh and P. K. Sharma “Debye-Waller Factors of Cubic Metals” Phys. Rev. B 3 Vol. 1141 (1971). https://doi.org/10.1103/ PhysRevB.3.1141
[17]
H. L. Kharoo, O. P. Gupta, M. P. Hemkar, “Debye Waller factors in bcc metals. I” J. Phys. Soc. Jap. Vol. 43 (1977) 797-799. https://doi.org/10.1143 /JPSJ.43.2030
[18]
H. L. Kharoo, O. P. Gupta, M. P. Hemkar, Debye Waller factors of fcc metals by the modified angular force model, Z. Naturforsch. 32 a (1977) 570-576. ISSN 0932-0784
[19]
O. P. Gupta “Debye-Waller Factors of Nickel, Aluminium and Sodium” J. Phys. Soc. Jpn. 38 (1975) 1451-1454 https://doi.org/10.1143/JPSJ.38.1451
[20]
J. Prakash, L. P. Pathak and M. P. Hemkar “Debye-Waller factor of α-Iron and Sodium” Aust. J. Phys. Vol. 28 (1975) 63-68
[21]
J. Bashir, N. M. Buit, M. NasirKhan and Q. H. Khan “Determination of the Debye-Waller Factor of Molybdenum by Powder Neutron Diffraction” J. Appl. Cryst.Vol. 25 (1992) 797-799. https://doi.org/10.1107/S0021889892007416
[22]
K. A. Mohammed, A. D. Al Rawas, A. M. Gismelseed, A. Sellai, H. M. Widatallah, A. Yousif, M. E. Elzain, M. Shongwe, Infrared and structural studies of Mg1-xZnxFe2O4 ferrites, Physica B 407 (2012) 795-804. 10.1016/j.physb.2011.12.097
[23]
Kadhim A. M. Khalaf, A. D. Al Rawas, A. M. Gismelssed, Ahmed Al Jamel, Salwan K. J. Al Ani, M. S. Shongwe, K. O. Al Riyami and S. R. Al Alawi Influence of Cr substitution on Debye-Waller factor and relatedstructural parameters of ZnFe2-xCrxO4 spinels” J. Alloy Comp. Vol. 701 (2016) 474-486 https://doi.org/ 10.1016/ j.jallcom.2017.01.083
[24]
B. D. Cullity “Elements of X-ray Diffraction” Addison-Wesley Publishing Company, Inc. 1959.
[25]
K. Sabri, R. Rais, K. Taibi, M. Moreau, B. Ouddane, A. Addou, Structural Rietveld refinement and vibrational study of MgCrxFe2-xO4 spinel ferrites, Phys. B 501 (2016) 38-44. https://doi.org/10.1016/j.physb. 2016.08.011
[26]
A. Baykal, S. Eryigit, M. Sertkol, S. Unlu, A. Yildiz and S. E. Shirsath, “ The effect of Cr3+‏ substitution on magnetic properties of CoFe2O4 nanoparticles synthesized by microwave combustion route” J. Supercond. Nov. Magn. Vol. 29 (2016) 2395-2400. https://doi.org/10.1007/s10948-016-3533-z
[27]
P. P. Hankare, U. B. Sankpal, R. P. Patil, I. S. Mulla, R. Sasikala, A. K. Tripathi, K. M. Garadkar “Synthesis and characterization of nickel substituted cobalt ferrite nanoparticles by sol–gel auto-combustion method” J. Alloy. Comp. Vol. 553 (2013) 383–388. https://dx.doi.org/10.1016/j.jallcom.2012.11.181
[28]
T. R. Tatarchuk, M. Bououdina, W. Macyk, O. Shyichuk, N. Paliychuk, I. Yaremiy, B. Al-NajarandM. Pacia “Structural, optical and magnetic properties of Zn-doped CoFe2O4 nanoparticles” Nano.Resea. Lett. Vol. 12 (141) (2017) 1-11. https://doi.org/10.1186/s11671-017-1899-x
[29]
N. Murali, S. J. Margarette, G. P. Kumar, B. Sailaja, S. Y. Mulushoa, P. Himakar, B. K. Babu, V. Veeraiah “Effect of Al substitution on the structural and magnetic properties of Co-Zn ferrites” Physica B: Cond. Matt. Vol. 522 (2017) 1-6 https://doi.org/10.1016/j.physb.2017.07.043
[30]
A. Globus, H. Pascard, V. Cagan “Distance between magnetic ions and fundamental properties in ferrites” J. Phys. Colloq. 38 C1 (1977) 163-168. https://hal.archives-ouvertes.fr/jpa-00216992
[31]
R. D. Shannon “Revised Effective Ionic Radii and Systematic Studies of Interatomie Distances in Halides and Chaleogenides” Acta Cryst. A32 (1976), 751-767 https://doi.org/10.1107/S0567739476001551
[32]
K. A. M. Khalaf, A. D. Al-Rawas, H. M. Widatallah, K. S. Al-Rashdi, A. Sellai, A. M. Gismelseed, Mohd. Hashim, S. K. Jameel, M. S. Al-Ruqeishi, K. O. Al-Riyami, M. Shongwe, A. H. Al-Rajhi “Influence of Zn2+‏ ions on the structural and electrical properties of Mg1-xZnxFeCrO4 spinels” J. Alloy. Comp. Vol. 657 (2016) 733-747. https://dx.doi.org/10.1016/j.jallcom.2015.10.157
[33]
M. C. Chhantbar, U. N. Trivedi, P. V. Tanna, H. J. Shah, R. P. Vara, H. H. Joshi, K. B. Modi “Infrared spectral studies of Zn-substituted CuFeCrO4 spinel ferrite system” Indian J. Phys. 78A (2004) 321-326. https://core.ac.uk/download/pdf/49286685.pdf
[34]
H. M. Zaki, H. A. Dawoud “Far-infrared spectra for copper–zinc mixed ferrites” Physica B Vol. 405 (2010) 4476–4479. https://doi:10.1016/j.physb.2010.08.018
[35]
S. Singhal, S. Bhukal, J. Singh, K. Chandra, S. Bansal “Optical, X-ray diffraction, and magnetic properties of the cobalt-substituted nickel chromium ferrites CrCoxNi1-xFeO4 (x=0, 0.2, 0.4, 0.6, 0.8, 1.0) synthesized using sol-gel autocombustion method” J. Nano. Technol. 2011 (2011) 1-6. https://dx.doi.org/10.1155/2011/930243
[36]
A. K. M. Zakaria, M. A. Asgar, S.-G. Eriksson, F. U. Ahmed, S. M. Yunus, A. K. Azad, H. Rundlof “Preparation of Zn substituted Ni-Fe-Cr ferrites and study of the crystal structure by neutron diffraction” Mater. Lett.Vol.(57) (2003) 4243-4250. https://doi.org/10.1016/S0167-577X(03)00298-2
[37]
K. J. Standley, Oxide Magnetic Materials, Claredon Press, Oxford, 1990. ISBN 10: 0198513186 / ISBN 13: 9780198513186.
[38]
R. J. Hill, J. R. Craig and G. V. Gibbs “Systematic of the spinel structure type” Phys. Chem. Miner. 4 (1979) 317-339. https://doi.10.1007/BF00307535
[39]
B. F. Levine, “d-Electron effects on bond susceptibilities and ionicities” Phys. Rev. B Vol. 7 (1973) 2591-2599. https://doi.org/10.1103/PhysRevB.7.2591
[40]
K. Kugimitu and H. Steikfink “The Influence of crystal radii and electronegativities on the crystallization of AB2X4 stoichiometries” Inorg. Chem. Vol. 7 (1968) 1762-1770. https://doi:10.1021/ic50067a015
[41]
S. M. Patange, S. E. Shirsath, K. S. Lohar, S. G. Algude, S. R. Kamble, N. Kulkarni, D. R. Mane and K. M. Jadhav, “Infrared spectral and elastic moduli study of NiFe2-xCrxO4 nanocrystalline ferrites” J. Magn. Magn. Mater. Vol. 325 (2013) 107-111. https://doi.org/10.1016/j.jmmm.2012.08.022
[42]
A. T. Raghavender, D. Pajic, K. Zadro, T. Milekovic, P. V. Rao, K. M. Jadhav and D. Ravinder “Synthesis and magnetic properties of NiFe2-xAlxO4 nanoparticles” J. Magn. Magn. Mater. Vol. 316 (2007) 1-7. https://doi.org/10.1016/j.jmmm.2007.03.204
[43]
Q. Lina, Y. Hea, J. Lina, F. Yang, L. Wang and J. Dong “Structural and magnetic studies of Mg substituted cobalt composite oxide catalyst Co1−xMgxFe2O4” J. Magn. Magn. Mater. Vol. 469 (2019) 89–94. https://doi.org/10.1016/j.jmmm.2018.08.050
[44]
S. Khanam, A. K. M. Zakaria, M. H. Ahsan, T. K. Datta, S. Aktar, S. I. Liba, S. Hossain, A. K. Das, I. Kamal, S. M. Yunus, D. K. Saha, S.-G. Eriksson “Study of the Crystallographic and Magnetic Structure in the Nickel Substituted Cobalt Ferrites by Neutron Diffraction” Mater. Sci. Appl. Vol. 6 (2015) Article ID: 55841, 10 pages. 10.4236/msa.2015.64038
[45]
T. R. Tatarchuk, N. D. Paliychuk, M. Bououdina, B. Al-Najar, M. Pacia, W. Macyk and A. Shyichuk “Effect of cobalt substitution on structural, elastic, magnetic and optical properties of zinc ferrite nanoparticles” J. Alloys and Comp. Vol. 731 (2018) 1256-1266. https://doi.org/10.1016/j.jallcom.2017.10.103
[46]
G. K. Williamsonand W. H. Hall “X-ray line broadening from filed aluminum and wolfram” Acta Metall, 1 (1953) 22-31. https://doi.org/10.1016/ 0001-6160(53)90006-6
[47]
Gh. H. Khorrami, A. Khorsand Zak, A. Kompany and R. Yousefi “Optical and structural properties of X-doped (X=Mn, Mg, and Zn) PZT nanoparticles by Kramers–Kronig and size strain plot methods” Ceramic Inter. Vol. 38 (2012) 5683-5690. https://doi.org/10.1016/j.ceramint.2012.04.012
[48]
A. Khorsand Zak and W. H. Abd. Majid “Characterization and X-ray peak broadening analysis in PZT nanoparticles prepared by modified sol-gel method” Ceramics Intern. Vol. 36 (2010) 1905-1910. https://doi.org/10.1016/j.ceramint. 2010.03.022
[49]
M. Chakrabarti, D. Sanyal, A. Chakrabarti “Preparation of Zn1-xCdxFe2O4 (x = 0.0, 0.1, 0.3, 0.5, 0.7 and 1.0) ferrite samples and their characterization by Mossbauer and positron annihilation techniques” J. Phys. Cond. Matter. 19 (2007) 236210 (11 pp). https://doi.org/10.1088/0953-8984/19/23/236210
[50]
M. A. Tagliente and M. Massaro “Strain-driven (0 0 2) preferred orientation of ZnO nanoparticles in ion-implanted silica” Nuc.Instrum.methods in phys. Res. B 266 (2008) 1055–1061. https://doi:10.1016/j.nimb. 2008.02.036
[51]
A. Khorsand Zak, W. H. Abd. Majid, M. E. Abrishami, RaminYousefi “X-ray analysis of ZnO nanoparticles by WilliamsoneHall and sizestrain plot methods” Solid State Sciences 13 (2011) 251-256. https://doi:10.1016/j.solidstatesciences. 2010.11.024
[52]
M. Jalaly, M. H. Enayati, P. Kameli, F. Karimzadeh “Effect of composition on structural and magnetic properties of nanocrystalline ball milled Ni1-xZnxFe2O4 ferrite” Physica B 405 (2010) 507–512 http://doi: 10.1016/j.physb.2009.09.044
[53]
V. Sepelal, K. Tkacova, V. V. Boldyerv, S. Wissmann, K. D. Becke “Mechanically induced cation redistribution in ZnFe2O4 and its thermal stability” Physica B Vol. 234-236 (1997) 617-619. https://doi.org/10.1016/S09214526 (96)01061-7.
[54]
M. H. Mahmoud, H. H. Hamdeh, A. I. Abdel-Mageed, A. M. Abdallah, M. K. Fayek “Effect of HEBM on the cation distribution of Mn-ferrite” Physica B Vol. 291 (2000) 49-53. https://doi.org/10.1016/S0921-4526(99)01381-2
[55]
A. I. Borhan, T. Slatineanu, A. R. Iordan and M. N. Palamaru “Influence of chromium ion substitution on the structure and properties of zinc ferrite synthesized by sol-gel auto-combustion method” Polyhedron Vol. 56 (2013) 82-89 http://dx.doi.org/10.1016/j.poly.2013.03.058
[56]
H. ST. C. O’Neill and A. Navrotsky “Simple spinels: crystallographic parameters, cation radii, lattice energies, and cation distribution” J. Am. Mineral., Vol. 68 (1983) 181–194.
[57]
H. ST. C. O’Neill, M. James, W. A. Dollase and S. A. T. Redfern, “Temperature dependence of the cation distribution in CuAl2O4 spinel” Eur. J. Min. Vol. 17 (2005) 581-586.https://doi:10.1127/0935-1221/2005/0017-0581
[58]
H. ST. C. O’Neill and W. A. Dollase “Crystal-structures and cation distributionsin simple spinels from powder XRD structural refinement -MgCr2O4, ZnCr2O4, Fe3O4 and the temperature-dependence of the cation distribution in ZnAl2O4” J. Phys. Chem. Miner. Vol. 20 (1994) 541-555. https://doi:10.1007%2FBF00211850
[59]
S. M. Antao, I. S. Hassan, W. A. Crichton and J. B. Parise “Effects of high pressure and high temperature on cation ordering in magnesioferrite, MgFe2O4, using in situ synchrotron X-ray powder diffraction up to 1430 K and 6 GPa” Amer. Miner. Vol. 90 (2005) 1500 – 1505.
[60]
A. Navrotsky and O. J. Kleppa “The thermodynamics of cation distributions in simple spinels” J. Inorg, Nucl. Chem. Vol. 29 (1967) 2701-2714 https://doi.org/10.1016/0022-1902(67)80008-3
[61]
K. I. Lilova, C. I. Pearce, C. Gorski, K. M. Rosso and A. Navrotsky “Thermodynamics of the magnetite-ulvospinel (Fe3O4-Fe2TiO4) solid solution” Amer. Mineral. Vol. 97 (2012) 1330-1338. https://dx.doi:10.2138/am.2012.4076
[62]
L. Schwarz, Z. Galazka, T. M. Gesing and D. Klimm, “On the influence of inversion on thermal properties of magnesium gallium spinel” Cryst. Res. Technol. Vol. 50 (2015) 961-966. https://doi:10.1002/cras.201500275
[63]
V. Stevanovic, M. d’Avezac and A. Zunger “universal electrostatic origion of cation ordering in A2BO4 spinel oxide” J. Ameri. Chem. Soc. Vol. 133 (2011) 11649- 11654. https://dx.doi.org/10.1021/ja2034602
[64]
(n.d.). Retrieved from http://shodhganga.inflibnet.ac.in/bitstream. 10603/ 151666/9/08_appendix.pdf
[65]
H. Furuhashi, M. Inagaki, S. Naka “Determination of cation distribution in spinels by X- ray diffraction method” J. Inorh. Nucl. Chem. Vol. 35 (1973) 3009-3014. https://doi.org/10.1016/0022-1902(73)80531-7
[66]
V. K. Lakhani, T. K. Pathak, N. H. Vasoya, K. B. Modi “Structural parameters and X-ray Debye temperature determination study on copper-ferrite-aluminate” Solid State Sci. Vol. 13 (2011) 539-547. https://doi.org/10.1016/j.solidstatesciences.2010.12.023
[67]
E. F. Westrum Jr., D. M. Grimes “Low temperature heat capacity and thermodynamic properties of zinc ferrite” J. Phys. Chem. Solids Vol. 3 (1957) 44-49. https://doi.org/10.1016/0022-3697(57)90046-X
[68]
G. C. Bensin and E. K. Gile, Tables of integral functions related to Debye-Waller factors (National Research Council of Canada, Ottawa) 1966.
[69]
K. A. M. Khalaf, A. D. Al-Rawas, H. M. Widatallah, K. S. Al-Rashdi, A. Sellai, A. M. Gismelseed, Mohd. Hashim, S. K. Jameel, M. S. Al-Ruqeishi, K. O. Al-Riyami, M. Shongwe, A. H. Al-Rajhi “Influence of Zn2+ ions on the structural and electrical properties of Mg1-xZnxFeCrO4 spinels” J. Alloy Comp. 657 (2016) 733-747 https://doi.org/10.1016/j.jallcom.2015.10.157
[70]
O. V. Lounassmaa and L. J. Sundstrom “Specific heat of Gadolinium, Terbium, Dysprosium, Holmium, and Thulium metalsbetween 3 and 25 K” Phys. Rev. Vol. 150 (1966) 399-412. https://doi.org/10.1103/PhysRev.150.399
[71]
K. B. Modi, T. K. Pathak, N. H. Vasoya, V. K. Lakhani, G. J. Baldha, P. K. J ha “X-ray Debye temperature of mechanically milled Ni0.5Zn0.5Fe2O4 spinel ferrite” Indian J. Phys. Vol. 85 (2011) 411-420. https://doi.org/10.1007/s12648-011-0051-5
[72]
B. Bridge and A. A. Higazy “Acoustic and optical Debye temperatures of thevitreous system CoO-Co203-P2O5” J. Mater. Sci. Vol. 21 (1986) 2385-2390.
[73]
https://doi.org/10.1007%2FBF01114282
[74]
D. C. Gupta and M. N. Sharma “Infrared eigen frequency and characteristic Debye temperature of a few heavier halides” Indian journal of Physics Vol. 43 (1969) 201-204
[75]
R. D. Waldron, Infrared spectra of ferrites, Phys. Rev. 99 (1955) 1727-1735. https://doi.org/10.1103/PhysRev.99.1727
[76]
C. M. Srivastava and T. T. Srinivasan ‘Effect of Jahn-Teller distortion on the lattice vibration frequencies of nickel ferrite” J. Appl. Phys. 53 (1982) 8148-8150. http://dx.doi.org/10.1063/1.330276
[77]
S. A. Patil, V. C. Mahajan, A. K. Ghatage and S. D. Lotke “Structure and magnetic properties of Cd and Ti/Si substituted cobalt ferrites” Mater. Chem. Phys. Vol. 57 (1998) 86-91. https://doi.org/10.1016/S0254-0584(98)00202-8
[78]
T. Satoh, T. Tsushima, K. Kudo, A classification of normal spinel type compounds by “Ionic packing factor” Mater. Res. Bull. 9 (1974) 1297-1300. https://doi.org/10.1016/0025-5408(74)90051-8
[79]
R. L. Williams “The relation of force constant to electronegativity and covalent radius” J. Phys. Chem. Vol. 60 (1956) 1016–1017. https://doi:10.1021/j150541a050
[80]
W. Gordy “A Relation between Bond Force Constants, Bond Orders, Bond Lengths, and the Electronegativities of the Bonded Atoms” J. Chem. Phys. Vol. 14 (1946) 305-320. https://doi.org/10.1063/1.1724138
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