Cation Distribution and Magnetic Properties of Nanocrystalline Mixed Spinel Ferrites

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CATION DISTRIBUTION AND MAGNETIC PROPERTIES OF NANOCRYSTALLINE MIXED

SPINEL FERRITES

BRAJESH NANDAN

DEPARTMENT OF PHYSICS

INDIAN INSTITUTE OF TECHNOLOGY DELHI-INDIA

SEPTEMBER 2019

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© Indian Institute of Technology Delhi (IITD), New Delhi, 2019

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CATION DISTRIBUTION AND MAGNETIC PROPERTIES OF NANOCRYSTALLINE MIXED

SPINEL FERRITES

by

BRAJESH NANDAN Department of Physics

Submitted

in the fulfilment of the requirements for the degree of Doctor of Philosophy

to the

INDIAN INSTITUTE OF TECHNOLOGY DELHI-INDIA

SEPTEMBER 2019

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DEDICATED TO

MY PARENTS AND TEACHERS

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Certificate

This is to certify that the thesis entitled “Cation Distribution and Magnetic Properties of Nanocrystalline Mixed Spinel Ferrites” being submitted by Mr. Brajesh Nandan to Indian Institute of Technology Delhi for the award of the degree of Doctor of Philosophy is a record of bonafide research work carried out by him. He has worked under my guidance and supervision and has fulfilled the requirements which to my knowledge have reached the requisite standard for the submission of the thesis.

The results contained in this thesis have not been submitted in part or full to any other University or Institute for the award of any degree or diploma.

Date: Sep. 30, 2019 Prof. Mukesh C. Bhatnagar

New Delhi Department of Physics

Indian Institute of Technology Delhi New Delhi- 110016

India

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Acknowledgements

This is a memorable moment in my life to complete the writing of my doctoral thesis.

I take this opportunity to thank all individuals who have directly or indirectly made the present thesis possible.

It is an honour for me to express a deep sense of gratitude to my supervisor Prof.

Mukesh C. Bhatnagar for his guidance and invaluable support to carry out research work during this programme. I would like to thank Prof. Subhash C. Kashyap for the invaluable discussions and encouragement which helped me a lot during my Ph. D. programme. I would also thank to Prof. P. Thangadurai (M. Tech. supervisor), Pondicherry University who had guided and prepared me to face and easily overcome the hurdles during my Ph.D.

programme.

I would like to thank the Head, Department of Physics for providing me all the facilities in the Department. Also I would like to thank Prof. Sujeet Choudhary, Prof. Pankaj Srivastava and Prof. Santanu Ghosh for advising me time to time. My thanks are due to Prof.

G. V. Prakash and Dr. P. K. Muduli for helping me to learn Raman spectroscopy and X-ray diffraction techniques respectively. Thanks are also due to Mr. D. S. Rawat for helping me in my experiments.

I would like to thank my seniors Dr. Parul Yadav, Dr. Gyanendra Prakash Shukla and Mr. Sourav Sarkar from whom I learnt the necessary skills in solving problems related to the research work. Though, it is difficult to mention the name of all colleagues and friends who contributed directly or indirectly in this persuit, I would like to mention my friends and lab-mates Mr. Prabhat Kumar, Ms. Megha Singh, Mr. Sreekanth Maddaka, Dr. Samir Kumar, Dr. Raghav Sharma, Dr. Sajid Hussain, Dr. Simrjit Singh, Mr. Deshraj Meena, Ms.

Mukesh Kumari, Mr. Abhishek Anand, Mr. Srinivas Pandit, Ms. Hemlata, Mr. Arun Kumar, Dr. Gavendra Pandey, Mr. Sandip Karmakar, Mr. Partik Kumar Jaysinghani, Mr. Supriya

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Chakraborty, Mr. Saurav Pandey and Mr. Kamal Kumar for the joyful company and support provided by them.

I am feeling happy for fulfiling the dream of my father (Late) to be a doctoral student of an intitute like IIT Delhi. I am grateful to my mother and maternal grand mother for their blessings and continuous emotional support. My special thanks to my wife Ms. Rachna who has always supported me morally in paper and thesis writing and creating a pleasant work environment at home. I would also acknowledge my little angel Tarunya Nandan (daughter) and Lakshyavendra Nandan (nephew) to come in the family and adding happiness in my life. I place on record my love for Mr. Rajdeep Nandan, Ms. Reema, Mamta Nandan and Osin Nandan for handling and carrying out the family responsibilities during my absence at home. Also, I would say thanks to Mr. Mahipal Singh and Mr. Balbir Singh who always encouraged me for higher studies

I gratefully acknowledge Indian Institute of Technology Delhi, India for providing Senior Research Fellowship during Ph. D. Programme.

Finally, I thank all those who have directly or indirectly contributed in this endeavour.

Brajesh Nandan

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Abstract

In the present work_, three sets comprising of nanocrystalline Ni1-xCoxFe2O4 (x=0.0, 0.4, 0.5, 0.6 and1.0), Ni0.5Co0.5CrxFe2-xO4 (x= 0.0, 0.2, 0.4, 0.6 and 0.8) and sintered Ni0.5Co0.5Fe2O4 (500, 700, 900 and 1100 °C) samples are successfully synthesized using sol-gel method and investigated for their structural and magnetic properties. The cation distribution among different sites in a unit cell is estimated by X-ray diffraction and Raman spectroscopy methods. Magnetization data too is employed for this estimation.

The Rietveld refined X-ray diffraction (XRD) and selected area electron diffraction (SAED) patterns reveal that Ni1-xCoxFe2O4, (NCFO) and Ni0.5Co0.5CrxFe2-xO4 samples possess single cubic spinel phase. The lattice parameter of the substituted Ni1-xCoxFe2O4

samples increases from 8.344 to 8.392 Å whereas it decreases monotonically from 8.368 to 8.338 Å for Ni0.5Co0.5CrxFe2-xO4 with an increase in the concentration of substituents in the samples. The lattice parameter of Ni0.5Co0.5Fe2O4 samples sintered at different temperatures is nearly 8.37 Å. The crystallite size of Ni1-xCoxFe2O4 samples are estimated to be 51 to 64 nm (Scherrer formula) and 67 to 76 nm (Williamson-Hall plot). The crystallite size in Ni0.5Co0.5CrxFe2-xO4 samples are estimated to be in the range of 58 – 75 nm (Williamson- Hall plot). The crystallite size of sintered Ni0.5Co0.5Fe2O4 samples understandably increases from 16 to 57 nm with an increase in the sintering temperature up to 1100 ° C. The average particle size, as estimated by electron microscopic analysis, in Ni1-xCoxFe2O4 and Ni0.5Co0.5CrxFe2-xO4 lie in the range of 350 - 750 nm and 200- 400 nm respectively.

The fraction of cations occupying tetrahedral (A-) and octahedral [B-] sites in Ni1-xCoxFe2O4, estimated from both Rietveld refinement and XRD peaks intensity ratio

methods, are in good agreement. The pristine nanocrystalline NiFe2O4 (NFO) is established to possess nearly inverse spinel structure with approximately 4% Ni occupying A-sites. The occupancy of A-site by Co²⁺ in NFO increases to a maximum of 25% when total cobalt concentration increases to x = 1.0. Rest of the cobalt (75%) in nanocrystalline CoFe2O4

(CFO) occupies B-sites, and the spinel structure is transformed from nearly inverse to partially inverse (a mixed ferrite). In Cr³⁺ substituted Ni0.5Co0.5Fe2O4 samples, Cr³⁺ ions replace Fe³⁺ ions from B-sites and induce no change in the occupation of the divalent cations. In the Ni0.5Co0.5Fe2O4 samples sintered at different temperatures, it is estimated that

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the concentration of Ni²⁺ and Co²⁺ at A-site increases from 2 to 4% and 12 to 18%

respectively with an increase in sintering temperature from 500 to 1100 °C. The ratio of Fe³⁺

occupyingA- and B-sites remains nearly unchanged in these samples.

The infrared (IR) and Raman measurements have reconfirmed that the prepared nanocrystalline Ni1-xCoxFe2O4 and Ni0.5Co0.5CrxFe2-xO4 samples exhibit cubic spinel single phase. The fraction of cations between A- and B-sites in Ni1-xCoxFe2O4, and Ni0.5Co0.5CrxFe2-xO4 estimated from both Raman spectra and Rietveld refinement of XRD data are in agreement.

The magnetization vs temperature zero field cooled (ZFC) curve of pristine NFO shows a magnetization of ~3 emu/g at 10 K while the corresponding curves for Co²⁺ substituted samples reveal nearly zero magnetization. The observed magnetization in ZFC mode (MZFC) at low temperature is correlated with anisotropy of the prepared samples. The two anomalies, observed in the temperature derivative of MZFC vs. temperature curves of Co²⁺

substituted NiFe2O4, around 160 K (T1) and 340 K ((T2)), are reported to be associated with Verwey transition (T1) and reorientation of anisotropic vacancies (T2). Nearly constant MFC

of Cr³⁺ substituted Ni0.5Co0.5Fe2O4 samples with x=0.0 and 0.2 is attributed to the strong inter-particle interaction. At low temperature (10 K), the increment in MFC in Cr³⁺

substituted samples (x  0.4) is correlated with anisotropy/weak inter-particle interaction.

Temperature derivatives of MZFC vs temperature curves of these samples also reveal two anomalies. The Ni0.5Co0.5Fe2O4 sample sintered only at 1100 °C exhibited two anomalies at 160 and 340 K. Surface defects are responsible for masking the 160 K anomaly in lower temperature sintered samples.

The substitution of Co²⁺in NFO enhances saturation magnetization from 51.6 to 82.2 emu/g. Large increase (~60 times) in the coercivity of these samples is attributed to the changes in microstructure (grain size, porosity, and micro-strain) and induced magnetocrystalline anisotropy. The NCFO with improved magnetic properties may be useful for magnetic recording applications. The MS values of Cr³⁺ substituted Ni0.5Co0.5Fe2O4 decrease from 65.2 to 26.8 emu/g due to substitution of a higher magnetic moment cation (Fe³⁺, 5µB) with the lower one (Cr³⁺, 3µB) thereby inducing reduction in A-B exchange interaction. The decreased coercivity values (from 357 to 122 Oe) of the samples makes them suitable for high-frequency applications. The MS of Ni0.5Co0.5Fe2O4

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increases with an increase in sintering temperature while HC decreases (down to 357 Oe) due to change in grain size and surface defects. The sintering converts the resulting ferrites into soft one, which may be useful for microwave applications.

The cation distribution, estimated from the calculated magnetic moment, and the lattice parameter calculated therefrom match well with the distribution of the substituents estimated from XRD and Raman techniques and the lattice parameter calculated from XRD in all the samples.

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साराांश

इस शोध कार्य में, तीन समूह जिसमें नैनोक्रिस्टलाइन Ni^१-xCoxFe२O४ (x = ०.० ०.४ ,०.५ ०.६ और १.०), Ni०.५Co०.५CrxFe२-xO४ (x = ०.०, ०.२, ०.४, ०.६ और 0.८) और विभिन्न तापों पर तपार्े Ni०.५Co०.५Fe२O४ (५००, ७००, ९००, और ११०० °C) नमूनों को

सॉल-िेल विधध का उपर्ोग करके सफलतापूियक बनार्ा गर्ा है ि उनके संरचनात्मक और चुंबकीर् गुणों के भलए अनुसन्धान क्रकर्ा गर्ा है। एक र्ूननट सेल में विभिन्न साइटों के

बीच धनार्न वितरण का आकलन एक्स-रे विितयन और रमन स्पेक्रोस्कोपी विधधर्ों द्िारा

क्रकर्ा गर्ा है। इस आकलन के भलए चुंबकीकरण डेटा िी ननर्ोजित क्रकर्ा गर्ा है।

Rietveld पररष्कृत एक्स-रे विितयन (XRD) और चर्ननत क्षेत्र इलेक्रॉन विितयन (SAED) पैटनय से पता चलता है क्रक Ni१-xCoxFe२O४, (NCFO) और Ni०.५Co०.५CrxFe२- xO४ के नमूने एकल क्र्ूबबकल स्पीनल अिस्था में हैं। प्रनतस्थावपत Ni^१-xCoxFe२O४ नमूनों

की लैटटस पैरामीटर ८.३४४ से बढ़कर ८.३९२ Å हो िाती है, िबक्रक र्ह Ni०.५Co०.५CrxFe२- xO४ नमूनों में प्रनतस्थापन्न की सांद्रता में िृवधि के साथ ८.३६८ से ८.३३८ Å तक एकात्मक रूप से घटती है। अलग-अलग तापमानों पर तपार्े गए Ni०.५Co०.५Fe२O४ नमूनों के लैटटस पैरामीटर लगिग ८.३७० Å है। Ni१-xCoxFe२O४ के नमूनों का क्रिस्टलीर् आकार ५१ से ६४ nm (Scherrer सूत्र) और ६७ से ७६ nm (Williamson – Hall प्लॉट) आंकी गर्ी है।

Ni०.५Co०.५CrxFe२-xO४ नमूनों में क्रिस्टलीर् आकार ५८ - ७५ nm (विभलर्मसन हॉल प्लॉट) की सीमा में आका गर्ा है। बढ़ते हुए तापमान पर ११०० °C तक तपार्े Ni^०.५Co०.५Fe२O४

नमूनों का क्रिस्टलीर् आकार १६ से ५७ nm तक बढ़ता है। Ni^१-xCoxFe२O४ और Ni०.५Co०.५CrxFe२-xO४ में इलेक्रॉन सूक्ष्म विश्लेषण द्िारा अनुमाननत औसत कण आकार

िमशः ३५० - ७५० nm और २००- ४०० nm की सीमा में है।

Ni१-xCoxFe२O४ में टेराहेड्रल (A-) और ऑक्टाहेड्रल [B-] साइट्स पर जस्थत धनार्नों

का अंश, िो क्रक ररटिल्ड शोधन और एक्सआरडी चोटटर्ों की तीव्रता अनुपात विधधर्ों से

अनुमाननत है, अच्छे समझौते में हैं। वप्रस्टाइन नैनोक्रकस्टलाइन NiFe^२O४ (NFO) लगिग ४% Ni A- साइट्स पर कब्िा करने के साथ लगिग उल्टे जस्पनेल संरचना बनाता है।

NFO में Co^२+ द्िारा ए-स्थलों का अधधिोग अधधकतम २५% तक बढ़ िाता है िब कुल कोबाल्ट सांद्रता x = १.० तक बढ़ िाती है। बाकी का कोबाल्ट (७५%) नैनोक्रिस्टलाइन CoFe२O४ (CFO) में B-साइट्स पर िाता है, और जस्पनेल संरचना लगिग उलटे से आंभशक रूप से उलटे (एक भमधित फेराइट) में पररिनतयत हो िाती है। Cr^३+ स्थानापन्न Ni०.५Co०.५Fe२O४ नमूने में, Cr^३+ आर्नों द्िारा Fe^३+ आर्नों को B-साइटों से प्रनतस्थावपत करते हैं और द्विसंर्ोिक धनार्नों की जस्थनत में कोई पररितयन नहीं करते हैं। अलग-अलग तापमान पर तपार्े गए Ni०.५Co०.५Fe२O४ नमूनों में र्ह पार्ा गर्ा क्रक िब ५०० से ११००

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°C तक भसंटररंग तापमान में िृवधि होती है तब A-साइट पर Ni^२+ और Co^२+ की सांद्रता

िमशः २ से ४% और १२ से १८% तक बढ़ िाती है। A- और B- साइटों पर Fe^३+ के

कब्िे का अनुपात इन नमूनों में लगिग अपररिनतयत रहता है।

अिरक्त (IR) और रमन मापों ने पुन: पुजष्ट की है क्रक तैर्ार क्रकए गए नैनोक्रिस्टलाइन Ni१-xCoxFe२O४ और Ni०.५Co०.५CrxFe२-xO४ नमूने घनीर् एकल अिस्था प्रदभशयत प्रदशयन करते हैं। Ni१-xCoxFe२O४ और Ni०.५Co०.५CrxFe२-xO४ में A- और B-साइटों के बीच धनार्नों

के अंशों की गणना, रमन स्पेक्रा और XRD डेटा के Rietveld शोधन दोनों की गणना में

सहमनत है।

चुम्बकीर् बनाम तापमान शून्र् क्षेत्र पर ठंडा (ZFC) क्रकर्ा हुआ मौभलक NFO का िि

१० K पर  ३ emu/g चुम्बकीर्करण को दशायता है िबक्रक Co^२+ प्रनतस्थावपत नमूनों के

भलए संगत िि लगिग शून्र् चुंबकत्ि को प्रकट करता है। कम तापमान पर ZFC प्रणाली

(MZFC) में देखे गए मैग्नेटाइिेशन को तैर्ार क्रकए गए नमूनों के एननसोरॉपी से संबधि क्रकर्ा

गर्ा है।

Co^२+ के प्रनतस्थावपत NiFe२O४ के तापमान अिकभलत MZFC ग्राफ में देखी गई दो

विसंगनतर्ां, लगिग १६० K (T१) और ३४० K ((T२)) तापमान पर, को Verwey transition (T१) और अनआइसोरोवपक पुनसंर्ोिन ररजक्तर्ों (T^२) से संबंधधत बतार्ा गर्ा है। Cr^३+

प्रनतस्थावपत Ni०.५Co०.५Fe२O४ (x = ०.० और ०.२) नमूनों के लगिग ननर्त M^FC के भलए मिबूत अंतर-कण संपकय को जिम्मेदार माना गर्ा है। कम तापमान (१० K) पर, Cr^३+

प्रनतस्थावपत नमूनों में MFC में िृवधि (x  ०.४) को अनआइसोरोपी / कमिोर अंतर-कण इंटरैक्शन के साथ सहसंबधि क्रकर्ा िाता है। इन नमूनों के तापमान अिकभलत M^ZFC ग्राफ

िी दो विसंगनतर्ों को प्रदभशयत करतें हैं। केिल ११०० °C पर तपार्ा Ni०.५Co०.५Fe२O४

नमूना दो विसंगनतर्ां १६० और ३४० K पर को प्रदभशयत क्रकर्ा। कम तापमान तपार्े नमूनों

में लुप्त हुई १६० K विसंगनत के भलए सतह के दोष जिम्मेदार हैं।

NFO में Co^२+ का प्रनतस्थापन संतृजप्त चुंबकत्ि को ५१.६ से ८२.२ emu/g तक बढ़ाता

है। इन नमूनों की कोभसयविटी में बडी िृवधि (६० गुना) को माइिोस्रक्चर (ग्रेन साइज़, पोरोभसटी और माइिो-स्रेन) और प्रेररत मैग्नेटोक्रिस्टलाइन एननसोरॉपी में पररितयन को

जिम्मेदार ठहरार्ा गर्ा है। बेहतर चुंबकीर् गुणों िाला NCFO चुंबकीर् ररकॉर्डंग अनुप्रर्ोग के भलए उपर्ोगी हो सकता है। Cr^३+ प्रनतस्थावपत Ni_०.५Co_०.५Fe_२O_४में चुम्बकीर्करण का मान ६५.२ से २६.८ emu/g घटना, कम चुम्बकीर् मूमेंट (Cr^३+, ३ µB) द्िारा अधधक चुम्बकीर्

मूमेंट (Fe^३+, ५ µB) का प्रनतस्थापन्न है िोक्रक A-B एक्सचेंि इंटरैक्शन में कमी को प्रेररत करते है।

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Cr³⁺ के प्रनतस्थापन्न के द्िारा कोभसयविटी के मानों का ३५७ से १२२ Oe का घटना

नमूनों को उच्च-आिृजत्त अनुप्रर्ोगों के भलए उपर्ुक्त बनाती है। ग्रेन साइज़ और सतह के

दोषों में पररितयन कारण Ni०.५Co०.५Fe२O४ के चुम्बकीर्करण का मान तपार्े तापमान के

बढ़ने के साथ बढ़ता है िबक्रक कोभसयविटी ३५७ Oe तक घटती है। भसंटररंग पररणामी को

सॉफ्ट फेराइट्स में पररिनतयत करती है, िो माइिोिेि अनुप्रर्ोगों के भलए उपर्ोगी हो सकता

है।

चुंबकीर् मूमेंट से अनुमाननत धनार्न वितरण की गणना, और उससे लैटटस पैरामीटर क्रक गणना का XRD और रमन तकनीकों से अनुमाननत प्रनतस्थापन के धनार्न वितरण और सिी नमूनों में XRD से गणना क्रकए गए लैटटस पैरामीटर की गणना का भमलान सिी

नमूनों में अच्छी तरह से भमलान क्रकर्े हुए है।

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3.3.1 Microscopic Analysis of Nanocrystalline Ni1-xCoxFe2O4 62 3.3.2 Compositional Analysis of Nanocrystalline Ni1-xCoxFe2O4 64 3.3.3 Microscopic Analysis of Nanocrystalline Ni0.5Co0.5CrxFe2-xO4 65 3.3.4 Compositional Analysis of Nanocrystalline Ni0.5Co0.5CrxFe2-xO4 67 3.3.5 Microscopic Analysis of Sintered Nanocrystalline Ni0.5Co0.5Fe2O4 68

3.4 Conclusions 69

Chapter 4: Cation Distribution in Substituted Ferrites

4.1 Introduction 71

4.2 X-ray Diffraction Intensity Ratio Method 71

4.3 Rietveld Refinement Method 75

4.4 Estimation of Cation Distribution in Ferrites 76

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4.4.2 Nanocrystalline Ni0.5Co0.5CrxFe2-xO4 80

4.4.3 Sintered Nanocrystalline Ni0.5Co0.5Fe2O4 81

4.5 Conclusions 82

Chapter 5: Vibrational Spectroscopy of Substituted Ferrites 5.1 Introduction 84

5.2 FTIR Spectroscopy of Nanocrystalline Ni1-xCoxFe2O4 85 5.3 Raman Spectroscopy of Cubic Spinel Ferrites 87 5.3.1 Nanocrystalline Ni1-xCoxFe2O4 89 5.3.2 Nanocrystalline Ni0.5Co0.5CrxFe2-xO4 94 5.3.3 Sintered Nanocrystalline Ni0.5Co0.5Fe2O4 96

5.4 Conclusions 98

Chapter 6: Thermomagnetic Study of Substituted Ferrites 6.1 Introduction 100

6.2 Thermomagnetic Analysis of Substituted Ferrites 100

6.2.2 Nanocrystalline Ni0.5Co0.5CrxFe2O4 105

6.3 Conclusions 110

Chapter 7: Static Magnetic Properties of Different Spinel Ferrites 7.1 Introduction 111

7.2 Static Magnetic Properties of Substituted Ferrites 111

7.2.2 Nanocrystalline Ni0.5Co0.5CrxFe2-xO4 117

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7.3 Conclusions 124

Chapter 8: Major Outcomes and Scope of the Work 8.1 Major Outcomes 126

8.2 Scope of the Work 128

References 130

List of Publications 142

Author’s Biography 144

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List of Figures

Number Figure Caption Page

No.

Figure 1.1 Schematic representation of (a) orbital magnetic moment and (b) spin magnetic moment of an electron.

2 Figure 1.2 Ordering of spins in the domains of Ferro-, Antiferro- and Ferri-

magnetic materials.

5 Figure 1.3 Typical magnetization curves of (a) diamagnetic, (b)

paramagnetic or antiferromagnetic, and (c) ferromagnetic or ferrimagnetic materials [3].

6 Figure 1.4 Orientation of the spins in tetrahedral and octahedral sites in Fe3O4

spinel arrangement resulting in a net magnetic moment of 4 μB.

9 Figure 1.5 A unit cell of normal cubic (spinel) ferrite, exhibiting ionic

occupation [2M (A-site), 4Fe (B-site), and 8O ions] in the 1/4 of the cell [6].

11 Figure 1.6 Splitting of d orbitals in octahedral and tetrahedral crystal field. 15 Figure 1.7 The Fe³⁺ cation in octahedral and tetrahedral crystal field with low

and high-spin configurations.

16 Figure 1.8 The distribution of different d orbital spins of cations in the

octahedral and tetrahedral crystal fields in high spin configuration.

17 Figure 1.9 (A) Schematic representation of domain motion/growth during

magnetization and (B) Magnetization (M-H) curve of ferrimagnetic material indicating various static magnetic parameters.

19

Figure 1.10 Typical magnetization vs temperature curves (M-T) in Zero field cooled (ZFC) and field cooled (FC) mode of the magnetic samples.

21

Figure 2.1 Typical steps generally followed in the sol-gel method. 33 Figure 2.2 A schematic flow chart followed for the synthesis of

nanocrystalline NiFe2O4 sample.

34 Figure 2.3 (a) Schematic representation of X-ray diffraction from a

crystalline sample and (b) Schematic diagram of Phillips X’ Pert Pro X-ray diffractometer.

36

Figure 2.4 Schematic diagram of a scanning electron microscope. 39 Figure 2.5 Interaction an of electron beam with a specimen. 40 Figure 2.6 Schematic diagram of a high resolution transmission electron

microscope.

41 Figure 2.7 Characteristic X-ray generation by an energetic electron due to

inter-orbital electron transfer in an atom.

43 Figure 2.8 Schematic diagram of an interferometer unit of a Fourier

Transform spectrometer.

45 Figure 2.9 Energy levels involved in the scattering of the radiation

giving rise to Rayleigh and Raman line.

47 Figure 2.10 Schematic diagram of a vibrating sample magnetometer. 49 Figure 3.1 Room temperature Rietveld refined powder diffraction patterns of

nanocrystalline Ni1-xCoxFe2O4 (x=0.0, 0.4, 0.5, 0.6 and 1.0) 51

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samples: As observed data is shown as black curves, Rietveld refined as red curves and difference between these two is shown as blue curves. Bragg’s positions are shown as small lines in pink colour below each peak.

Figure 3.2 (a) Enlarged view of peak (311) to exhibit the shift in diffraction pattern (b) variation in lattice parameter calculated from Rietveld refined of nanocrystalline Ni1-xCoxFe2O4 (x= 0.0, 0.4, 0.5, 0.6 and 1.0) samples.

53

Figure 3.3 (a) Williamson Hall plot, (b) crystallite size (D) and (c) microstrain (є) of nanocrystalline Ni1-xCoxFe2O4 (x= 0.0, 0.4, 0.5, 0.6 and 1.0) samples.

54

Figure 3.4 Rietveld refined X-ray diffractograms of nanocrystalline Ni0.5Co0.5CrxFe2-xO4 (0.0, 0.2, 0.4, 0.6 and 0.8) samples. As observed data is shown as black curves, Rietveld refined as red curves and difference between these two is shown as blue curves.

Bragg’s positions are shown as small lines in pink colour below each peak.

56

Figure 3.5 (a) An enlarged view of (311) diffraction peaks showing shift in them and (b) variation in lattice parameter ‘a’ with Cr³⁺

concentration (x).

57 Figure 3.6 Williamson Hall plots of nanocrystalline Ni0.5Co0.5CrxFe2-xO4

(0.0, 0.2, 0.4, 0.6 and 0.8) samples.

58 Figure 3.7 Rietveld refined X-ray diffractograms of nanocrystalline

Ni0.5Co0.5Fe2O4 samples sintered at different temperatures. As observed data is shown as black curves, Rietveld refined as red curves and difference between these two is shown as blue curves.

Bragg’s positions are shown as small lines in pink colour below each peak.

59

Figure 3.8 Estimated crystallite size (DSch andDWH) of the Ni0.5Co0.5Fe2O4

samples using Scherrer formula and Willianson-Hall plot analysis.

61 Figure 3.9 Williamson-Hall plots for nanocrystalline Ni0.5Co0.5Fe2O4 samples

sintered at different temperatures.

62 Figure 3.10 Scanning electron micrographs of Ni1-xCoxFe2O4 (x=0.0, 0.4, 0.5,

0.6 and 1.0) ferrites.

63 Figure 3.11 HRTEM images of Ni1-xCoxFe2O4 (x=0.0, 0.5 and 1.0) ferrites. (a)

Distribution of particles with average particle size histogram as in inset, (b) Moire fringes and (c) SAED patterns.

64

Figure 3.12 Compositional analysis of nanocrystalline Ni1-xCoxFe2O4 (x=0.0, 0.4, 0.5, 0.6 and 1.0) samples using EDX spectroscopy.

65 Figure 3.13 Scanning electron micrographs of Ni0.5Co0.5Fe2-xCrxO4 samples

with Cr concentration (x) as (a) x=0.0, (b) 0.4 and (c) 0.8).

65 Figure 3.14 (a) High resolution transmission electron micrographs with

histogram (inset), (b) Moire patterns and (c) SAED patterns for Ni0.5Co0.5Fe2-xCrxO4 (x=0.0, 0.4 and 0.8) samples.

66

Figure 3.15 Compositional analysis of nanocrystalline Ni0.5Co0.5Fe2-xCrxO4

(x=0.0, 0.4, 0.5, 0.6 and 1.0) samples using EDX spectroscopy.

67 Figure 3.15 Scanning electron micrographs of Ni0.5Co0.5Fe2O4 samples

sintered at different temperatures.

68

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Figure 4.1 Variation in atomic scattering factor with scattering angle for different transition metals [58].

73 Figure 5.1 FTIR spectra of nanocrystalline Ni1-xCoxFe2O4 (x=0.0, 0.4, 0.5,

0.6 and 1.0) samples. The inset shows the shift in the peak position (605 cm^-1 for x=0) with an increase in Co²⁺ concentration in the samples.

86

Figure 5.2 Room temperature deconvoluted Raman spectra of nanocrystalline Ni1-xCoxFe2O4 (x= 0.0, 0.4, 0.5, 0.6 and 1.0) samples.

89

Figure 5.3 (a) Shift in most prominent Raman peaks (A1g and T2g (2)) and (b) change in peak intensity ratio of T2g (2) and A1g peaks for nanocrystalline Ni1-xCoxFe2O4 (x= 0.0, 0.4, 0.5, 0.6 and 1.0) samples.

90

Figure 5.4 Room temperature deconvoluted Raman spectra of nanocrystalline Ni0.5Co0.5CrxFe2-xO4 samples.

95 Figure 5.5 Room temperature deconvoluted Raman spectra of

nanocrystalline Ni0.5Co0.5Fe2O4 samples sintered at different temperature.

97

Figure 6.1 Zero field cooled (ZFC) and field cooled (FC) magnetization vs temperature curves of Ni1-xCoxFe2O4 samples. Black (Red) color is corresponding to ZFC (FC) data.

101

Figure 6.2 Temperature derivative of MZFC vs. temperature curves of Ni1- xCoxFe2O4 samples.

103 Figure 6.3 Zero field cooled (ZFC) and field cooled (FC) magnetization vs

temperature curves of Ni0.5Co0.5CrxFe2-xO4 samples. Black (Red) color is corresponding to ZFC (FC) data.

105

Figure 6.4 Temperature derivative of MZFC vs. temperature curves of Ni0.5Co0.5CrxFe2-xO4 samples.

106 Figure 6.5 Zero field cooled (ZFC) and field cooled (FC) magnetization vs

temperature curves of Ni0.5Co0.5Fe2O4 samples. Black (Red) color is corresponding to ZFC (FC) data.

108

Figure 6.6 Temperature derivative of MZFC vs. temperature curves of Ni0.5Co0.5Fe2O4 samples.

109 Figure 7.1 Magnetic hysteresis curves of Ni1-xCoxFe2O4 (x=0.0, 0.4, 0.5, 0.6

and 1.0) samples recorded at room temperature. The inset (second quadrant) shows the enlarged view of the M-H curves close to the origin and the second inset (fourth quadrant) shows even further enlarged M-H curve revealing coercivity of nearly 10 Oe for the pristine (x=0.0) sample.

112

Figure 7.2 Coercivity (HC) and saturation magnetization (MS) of Ni1-xCoxFe2O4 (x= 0.0, 0.4, 0.5, 0.6 and 1.0) samples. The inset

shows magnetocrystalline anisotropy of these samples.

114

Figure 7.3 Room temperature recorded M-H loops of Ni0.5Co0.5CrxFe2-xO4

(0.0, 0.2, 0.4, 0.6 and 0.8) samples. The inset in second quadrant shows the variation of saturation magnetization and coercivity with Cr³⁺ concentration and (b) enlarged view of M-H loops.

117

Figure 7.4 Variation in magnetocrystalline anisotropy (K1) of Ni0.5Co0.5CrxFe2-xO4 (x=0.0, 0.2, 0.4, 0.6 and 0.8) samples with Cr³⁺concentration.

119

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Figure 7.5 M-H loops of Ni0.5Co0.5Fe2O4 samples recorded at room temperature. The inset (a) shows the enlarged view of M-H curves close to the origin, and the inset (b) shows changes in MS and HC

with sintering temperature.

121

Figure 7.6 (a) Neel model (collinear structure) and (b) Yafet and Kittel model (noncollinear structure) in spinel ferrite.

124

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List of Tables

Number Table caption Page

No.

Table 1.1 Characteristics of different magnetic materials. 7 Table 1.2 Electronic configuration, orbital splitting and theoretically estimated

crystal field stabilization energy (CFSE) of different transition metal cations.

18

Table 1.3 Magnetic and electrical properties of Ni- and Co-ferrites. 20 Table 3.1 Structural and Rietveld refinement parameters [Weighted profile

factor (Rwp), expected R factor (Rexp) and goodness of fit (χ²)] of Ni1-xCoxFe2O4 (x= 0.0, 0.4, 0.5, 0.6 and 1.0) samples.

52

Table 3.2 Rietveld refinement parameters [Weighted profile R factor (Rwp), expected R factor (Rexp) and goodness of fit (χ²)], lattice parameter ‘a’

oxygen positional parameter (u), crystallite size and presence of microstrain in Ni0.5Co0.5CrxFe2-xO4 (x= 0.0, 0.2, 0.4, 0.6 and 0.8) samples.

57

Table 3.3 Rietveld refinement parameters [Weighted profile R factor (Rwp), expected R factor (Rexp) and goodness of fit (χ²)], lattice parameter

‘a’, and oxygen positional parameter (u) of Ni0.5Co0.5Fe2O4 sample sintered at different temperature.

60

Table 4.1 The planes (hkl), Bragg angle (θ), atomic scattering factor (f), structure factor (Fhkl), Lorentz-polarization factor (Lp) and multiplicity factor (P) along with calculated intensity ((Ihkl)cal) of different peaks in the XRD pattern of Ni0.6Co0.4Fe2O4.

77

Table 4.2 Cation distribution in Ni1-xCoxFe2O4 (x=0.0, 0.4, 0.5, 0.6 and 1.0) samples estimated by X-ray diffraction intensity ratio method.

78 Table 4.3 Cation distribution in (A-) and [B-] sites and inversion parameter (δ)

of Ni1-xCoxFe2O4 (x= 0.0, 0.4, 0.5, 0.6 and 1.0) samples estimated by Rietveld refinement method.

79

Table 4.4 The estimated cation distribution and inversion parameter of Ni0.5Co0.5CrxFe2-xO4 samples estimated by Rietveld refinement method.

80

Table 4.5 Cation distribution in (A-) and [B-] sites and inversion parameter (δ) of Ni0.5Co0.5Fe2O4 samples sintered at different temperature using Rietveld refinement method.

81

Table 5.1 Peak positions in the infra-red spectra of some spinel ferrites. 85 Table 5.2 Reported and observed Raman peaks (in cm^-1) for various spinel

ferrites.

88 Table 5.3 Variation in Raman peak positions of nanocrystalline Ni1-xCoxFe2O4

(x= 0.0, 0.4, 0.5, 0.6 and 1.0) ferrites recorded at room temperature.

Lower numbers in each row represent the fraction of cations in tetrahedral sites as calculated from the integrated area of the peaks.

92

Table 5.4 Cation distribution and inversion parameter () of Ni1-xCoxFe2O4

samples as obtained by Raman spectroscopy.

94 Table 5.5 Cation distribution and inversion parameter () of Ni0.5Co0.5CrxFe2-

xO4 samples.

96

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Table 5.6 Cation distribution and inversion parameter () of Ni0.5Co0.5Fe2O4

samples sintered at different temperatures.

98 Table 7.1 The static magnetic parameters of Ni1-xCoxFe2O4 (x= 0.0, 0.4, 0.5, 0.6

and 1.0) samples as estimated from M-H curves. The cation distribution corresponds to the calculated magnetic moment µnet of the spinel per formula unit

113

Table 7.2 Room temperature saturation magnetization (MSobs), coercivity (HC) and calculated magnetic moment (μobs), along with the estimated magnetic moment (μnet) for the proposed cation distribution in the Ni0.5Co0.5CrxFe2-xO4 samples.

118

Table 7.3 Room temperature recorded saturation magnetization (MSobs), coercivity (HC) calculated magnetic moment (μobs), estimated magnetic moment (μnet) for the proposed cation distribution and canting angle (θC) associated with the spin in sintered Ni0.5Co0.5Fe2O4

samples.

122

Cation Distribution and Magnetic Properties of Nanocrystalline Mixed Spinel Ferrites

CATION DISTRIBUTION AND MAGNETIC PROPERTIES OF NANOCRYSTALLINE MIXED

SPINEL FERRITES

BRAJESH NANDAN

DEPARTMENT OF PHYSICS

INDIAN INSTITUTE OF TECHNOLOGY DELHI-INDIA

SEPTEMBER 2019

© Indian Institute of Technology Delhi (IITD), New Delhi, 2019

CATION DISTRIBUTION AND MAGNETIC PROPERTIES OF NANOCRYSTALLINE MIXED

SPINEL FERRITES

by

BRAJESH NANDAN Department of Physics

Submitted

in the fulfilment of the requirements for the degree of Doctor of Philosophy

to the

INDIAN INSTITUTE OF TECHNOLOGY DELHI-INDIA

SEPTEMBER 2019

DEDICATED TO

MY PARENTS AND TEACHERS

Certificate

Acknowledgements

Abstract

साराांश

Contents

List of Figures

List of Tables