DESIGN AND DEVELOPMENT OF NI-BASED HEUSLER ALLOYS …

DESIGN AND DEVELOPMENT OF NI-BASED HEUSLER ALLOYS FORMAGNETIC REFRIGERATION

A THESIS SUBMITTED TOTHE GRADUATE SCHOOL OF NATURAL AND APPLIED SCIENCES

OFMIDDLE EAST TECHNICAL UNIVERSITY

BY

SEDANUR TORAMAN

IN PARTIAL FULFILLMENT OF THE REQUIREMENTSFOR

THE DEGREE OF MASTER OF SCIENCEIN

METALLURGICAL AND MATERIALS ENGINEERING

NOVEMBER 2018

Approval of the thesis:


submitted by SEDANUR TORAMAN in partial fulfillment of the requirements forthe degree of Master of Science in Metallurgical and Materials Engineering De-partment, Middle East Technical University by,

Prof. Dr. Halil KalıpçılarDean, Graduate School of Natural and Applied Sciences

Prof. Dr. Cemil Hakan GürHead of Department, Metallurgical and Materials Engineering

Prof. Dr. Amdulla O. MekhrabovSupervisor, Metallurgical and Materials Eng. Dept., METU

Prof. Dr. M. Vedat AkdenizCo-supervisor, Metallurgical and Materials Eng.Dept., METU

Examining Committee Members:

Prof. Dr. Tayfur ÖztürkMetallurgical and Materials Eng. Dept., METU

Prof. Dr. Amdulla O. MekhrabovMetallurgical and Materials Eng. Dept., METU

Prof. Dr. M. Vedat AkdenizMetallurgical and Materials Eng. Dept., METU

Prof. Dr. Nizami M. GasanlyPhyscics Department, METU

Prof. Dr. Sükrü TalasMetallurgical and Materials Eng. Dept., AKU

Date: 20.11.2018

I hereby declare that all information in this document has been obtained andpresented in accordance with academic rules and ethical conduct. I also declarethat, as required by these rules and conduct, I have fully cited and referenced allmaterial and results that are not original to this work.

Name, Last Name: Sedanur Toraman

Signature :

iv

ABSTRACT


Toraman, SedanurM.S., Department of Metallurgical and Materials Engineering

Supervisor : Prof. Dr. Amdulla O. Mekhrabov

Co-Supervisor : Prof. Dr. M. Vedat Akdeniz

November 2018, 101 pages

Magnetic refrigeration has attracted increasing interest in the materials research com-

munities because of its higher cooling efficiency and environmentally friendliness. In

this thesis study, it is aimed to develop Ni-based Heusler alloys for use in magnetic

refrigeration systems, which consists of two parts; the theoretical and experimental

part.

In the theoretical part of this thesis, in order to characterize the order-order (L21 ↔B2) and order-disorder (B2 ↔ A2) phase transitions in A2BC type full Heusler

alloys, statisco-thermodynamical theory of ordering by means of Bragg-Williams-

Gorsky (BWG) method combined with electronic theory in the pseudopotential ap-

proximation were employed. The effect on ternary alloy element addition on ordering

characteristics in Ni-Mn-C (C=Ga, In, Sb, Sn) Heusler alloys were studied and the

L21 ↔ B2 and B2 ↔ A2 critical transformation temperatures were determined by

calculating the partial ordering energies using the electronic theory of alloys in pseu-

dopotential approximation. The results of these calculations were utilized to predict

the most suitable potential alloying element (C) and its composition for the develop-

v

ment of Ni-Mn-C magnetocaloric materials.

In the experimental part of this thesis, by using the results obtained from the theoreti-

cal predictions, Ni-Mn-In alloy system was chosen and structural and magnetic anal-

yses of Ni51Mn34In15 alloy were performed. Within this context, the effect of heat

treatment processes on structural and magnetic properties of Ni-rich Ni51Mn34In15

Heusler alloy have been analysed by means of XRD, SEM, EDS and VSM tech-

niques. While L21-type ordered crystal structure could not be detected in the as-cast

alloy, however, after applying a proper heat treatment processes, formation of stable

L21-type ordered structure in Ni51Mn34In15 alloy was achieved, which is most de-

sirable structure for magnetocaloric applications. To determine the magnetocaloric

effect (MCE), the magnetic entropy changes (∆SM) of the samples were calculated

from the magnetic field dependent magnetization measurements. It was shown that

the maximum of ∆SM reaches the magnitudes of 4.8 J/kg ·K, 5.6 J/kg ·K and 12.8

J/kg ·K at 271 K, 294 K and 305 K temperatures at magnetic field change of ∆H=18

kOe for the as-cast, 24 hours-aged and 48 hours-aged Ni51Mn34In15 alloy, respec-

tively. Consequently, large magnetic entropy changes with positive sign were ob-

served in wide temperature ranges and these positive ∆SM values indicate that this

alloy exhibits inverse MCE around the martensitic transformation temperature (TM).

In addition to that, the relative cooling power (RCP) of the magnetocaloric material

was calculated according to the magnetic entropy change. Results of the calculations

reveal that application of heat treatment processes tends to increase magnitude of

RCP parameter of Ni51Mn34In15 Heusler alloy.

Keywords: Ni-based Heusler Alloys, Ordering Characteristics, Electronic Theory,

Magnetocaloric Effect, Magnetic Refrigeration, Relative Cooling Power

vi

ÖZ

MANYETIK SOGUTUCULAR IÇIN NI-TABANLI HEUSLERALASIMLARININ TASARLANMASI VE GELISTIRILMESI

Toraman, SedanurYüksek Lisans, Metalurji ve Malzeme Mühendisligi Bölümü

Tez Yöneticisi : Prof. Dr. Amdulla O. Mekhrabov

Ortak Tez Yöneticisi : Prof. Dr. M. Vedat Akdeniz

Kasım 2018 , 101 sayfa

Manyetik sogutma, daha yüksek sogutma verimi ve çevre dostu olması sebebiyle mal-

zeme arastırma komunitelerince giderek artan bir ilgi çekmektedir. Teorik ve deney-

sel olmak üzere iki bölümden olusan bu tez çalısmasında manyetik sogutma sistemle-

rinde kullanılmak üzere Ni-tabanlı Heusler alasımlarının gelistirilmesi amaçlanmıstır.

Bu tezin teorik kısmında, A2BC tipi tam Heusler alasımlarında düzen-düzen (L21 ↔B2) ve düzen-düzensizlik (B2 ↔ A2) faz dönüsümlerini karakterize etmek için,

istatiksel-termodinamik teorinin Bragg-Williams-Gorsky (BWG) metodu ile elekt-

ronik teorinin psödopotensiyel yaklasımı kullanılmıstır. Psödopotensiyel yaklasım

içinde alasımların elektronik teorisini kullanarak kısmi düzenleme enerjileri hesap-

lanmıs, Ni-Mn-C (C=Ga, In, Sb, Sn) Heusler alasımlarındaki düzen karakteristikle-

rine göre üçlü alasım elementi incelenmis ve L21 ↔ B2 ve B2 ↔ A2 kritik dö-

nüsüm sıcaklıkları etkileri belirlenmistir. Hesaplama sonuçları Ni-Mn-C manyetoka-

lorik malzemelerin gelistirilmesi için en uygun potansiyel alasım elementini (C) ve

kompozisyonunu belirlemek için kullanılmıstır.

vii

Bu tezin deneysel bölümünde, teorik çalısmalardan elde edilen sonuçlar kullanılarak,

Ni-Mn-In alasım sistemi seçilmis ve Ni51Mn34In15 alasımının yapısal ve manyetik

analizleri yapılmıstır. Bu kapsamda, ısıl islem süreçlerinin Ni-zengin Ni51Mn34In15

Heusler alasımının yapısal ve manyetik özelliklerine etkisi XRD, SEM, EDS ve VSM

teknikleri ile analiz edilmistir. L21 tipi düzenli kristal yapı ham döküm alasımında tes-

pit edilemese de uygun bir ısıl islem prosesi uygulandıktan sonra Ni51Mn34In15 He-

usler alasımında kararlı L21 tipi düzenli yapının olusumu basarılmıstır, ki bu da man-

yetokalorik uygulamalar için en çok istenen yapıdır. Manyetokalorik etkiyi (MCE)

belirlemek için, manyetik alan bagımlı mıknatıslanma ölçümlerinden manyetik ent-

ropi degisimleri (∆SM) hesaplanmıstır. Maksimum ∆SM degerlerinin ∆H=18 kOe

manyetik alan degisiminde ham döküm, 24 saat yaslandırılmıs ve 48 saat yaslandırıl-

mıs Ni51Mn34In15 alasımı için sırasıyla, 4.8 J/kg ·K, 5.6 J/kg ·K ve 12.8 J/kg ·K271 K, 294 K ve 305 K’de ulastıgı gözlenmistir. Sonuç olarak, genis sıcaklık aralıkla-

rında pozitif isaretli büyük manyetik entropi degisimleri gözlemlenmistir ve bu pozitif

∆SM degerleri, bu alasımın martensitik dönüsüm sıcaklıgı (TM) etrafında ters MCE

sergiledigini göstermektedir. Buna ek olarak, manyetokalorik malzemenin bagıl so-

gutma gücü (RCP) manyetik entropi degisimine göre hesaplanmıstır. Hesaplamaların

sonuçları, ısıl islem proseslerinin uygulanmasının Ni51Mn34In15 Heusler alasımının

RCP parametresinin büyüklügünü artırdıgını göstermektedir.

Anahtar Kelimeler: Ni-tabanlı Heusler Alasımları, Düzen Karakteristikleri, Elektro-

nik Teori, Manyetokalorik Etki, Manyetik Sogutma, Bagıl Sogutma Gücü

viii

To my dear mother and my uncle

ix

ACKNOWLEDGMENTS

First of all, I would like to express my sincerest gratitude to my supervisors Prof. Dr.

Amdulla O. Mekhrabov and Prof. Dr. M. Vedat Akdeniz for their guidance, patience,

support and encouragement during this study. They gave me the opportunity to carry

out independent research work.

Also, I am very thankful to Yüksel Özkan for his endless helps and insightful attitude.

He played an important role in performing the magnetic measurements in this study.

I would also like to express my special thanks to my boss Dr. T. Yasar Katırcıoglu for

his precious helps, patience and friendly attitude.

Moreover, I would like to thank my lab mates in Novel Alloys Design and Devel-

opment Laboratory (NOVALAB) for their friendships. I thank to the Department of

Metallurgical and Materials Engineering for providing facilities for my research. I

sincerely acknowledge the members of GÜNAM facility, especially Deniz Bender

and Mustafa Ünal for their helps.

I would like to express my deepest thanks to my twin-sister Gözdenur Toraman,

Yasemin Özmen, Murat Özdemir for their psychological support, goodwill and friend-

ship. Whenever I have problems related to computer or any software it was always

Ilker Moral who had the right answers for me. I appreciate my friend Sahin Kürekci

who shared his amazing stories with me and provided cheerful environment. I am

indebted to all of them for providing a comfortable and fun filled environment.

I am glad to have friends like Tansu Altunbasak Göynük, Hilal Kılınç Seyhun, Selen

Yüksel, and Alma Gül Uçar who always supported me in my difficult times. They

were very kind and helpful in all aspects.

x

Last but not least, I would like to thank my family. I gratefully thank my mother

Sırma Toraman for her endless support, confidence and for always standing by me. I

wish to thank my uncle Aydın Dursun for his help and support throughout my whole

life. I am also thankful to Suna Dursun for her positive energy and encouragement.

xi

TABLE OF CONTENTS

ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v

ÖZ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii

ACKNOWLEDGMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x

TABLE OF CONTENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xii

LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv

LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvii

LIST OF ABBREVIATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . xxii

CHAPTERS

1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

2 LITERATURE REVIEW . . . . . . . . . . . . . . . . . . . . . . . . 5

2.1 MAGNETIC REFRIGERATION (MR) . . . . . . . . . . . . 5

2.2 MAGNETIC PROPERTIES OF MATERIALS . . . . . . . . 6

2.3 MAGNETOCALORIC EFFECT (MCE) . . . . . . . . . . . 9

2.3.1 Thermodynamics of the Magnetocaloric Effect . . 9

2.3.2 Magnetic Refrigeration Thermodynamic Cycles . . 13

2.4 MAGNETOCALORIC MATERIALS FOR MAGNETIC RE-FRIGERATION . . . . . . . . . . . . . . . . . . . . . . . . 14

3 HEUSLER ALLOYS FOR MAGNETIC REFRIGERATION . . . . . 19

xii

3.1 FULL HEUSLER ALLOYS . . . . . . . . . . . . . . . . . . 20

3.2 MARTENSITIC TRANSFORMATION (MT) . . . . . . . . 22

3.3 SHAPE MEMORY EFFECT (SME) . . . . . . . . . . . . . 23

3.4 FERROMAGNETIC SHAPE MEMORY EFFECT (FSME) . 25

3.5 PROPERTIES OF Ni-Mn BASED HEUSLER ALLOYS . . . 26

4 METHODOLOGY . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

4.1 THEORETICAL STUDIES . . . . . . . . . . . . . . . . . . 29

4.1.1 Atomic Ordering Processes in Full Heusler Alloys 29

4.1.2 Methods of Theoretical Modelling and Simulationof Atomic Ordering Processes in Full Heusler Alloys 31

4.1.3 Calculation of the B2↔ A2 (Tc1) and L21 ↔ B2 (Tc2)Critical Transformation Temperatures in A50B50−xCx

Full Heusler Alloys . . . . . . . . . . . . . . . . . 31

4.1.4 Calculation of Partial Ordering Energies Using theElectronic Theory of Ternary Alloys in Pseudopo-tential Approximation . . . . . . . . . . . . . . . 37

4.2 EXPERIMENTAL STUDIES . . . . . . . . . . . . . . . . . 38

4.2.1 Methods of Experimental Investigation of Struc-tural and Magnetic Properties of Full Heusler Alloys 38

4.2.1.1 Sample Preparation . . . . . . . . . . 38

4.2.2 Sample Characterization . . . . . . . . . . . . . . 39

5 RESULTS AND DISCUSSIONS . . . . . . . . . . . . . . . . . . . . 43

5.1 MODELLING AND SIMULATION OF ATOMIC ORDER-ING PROCESSES IN FULL HEUSLER ALLOYS . . . . . . 43

5.2 STRUCTURAL AND MAGNETIC PROPERTIES OF Ni-Mn-In FULL HEUSLER ALLOYS . . . . . . . . . . . . . . 53

6 SUMMARY AND CONCLUSIONS . . . . . . . . . . . . . . . . . . 81

xiii

6.1 SUMMARY OF FINDINGS . . . . . . . . . . . . . . . . . 81

6.2 CONCLUSION . . . . . . . . . . . . . . . . . . . . . . . . 84

6.3 FUTURE WORKS . . . . . . . . . . . . . . . . . . . . . . 84

REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

APPENDICES

A OPTICAL MICROSCOPY IMAGES . . . . . . . . . . . . . . . . . 95

B SCANNING ELECTRON MICROSCOPY IMAGES . . . . . . . . . 99

xiv

LIST OF TABLES

TABLES

Table 5.1 a, R1 and R2 values of the Ni50Mn50−xCx (C=Ga, In, Sb, Sn) . . . . 44

Table 5.2 Calculated partial ordering energies for B-C atomic pairs at the sec-

ond coordination sphere for the Ni50Mn50−xCx (C=Ga, In, Sb and Sn)

alloys (15 ≤ x ≤ 35). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

Table 5.3 Calculated partial ordering energies for A-B, A-C and B-C atomic

pairs at the first coordination sphere for the Ni50Mn50−xGax (×10−3)

(at.u.). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51


pairs at the first coordination sphere for the Ni50Mn50−xInx (×10−3)

(at.u.). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51


pairs at the first coordination sphere for the Ni50Mn50−xSbx (×10−3)

(at.u.). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51


pairs at the first coordination sphere for the Ni50Mn50−xSnx (×10−3)

(at.u.). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

Table 5.7 Compositions and e/a ratio for the Ni51Mn34In15. . . . . . . . . . . 53

Table 5.8 The composition values from different regions of the alloy. . . . . . 59

Table 5.9 EDS analysis result of the as-cast Ni51Mn34In15 alloy for selected

region. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

xv

Table 5.10 EDS analysis result of the 24 hours-aged Ni51Mn34In15 alloy for

selected region. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

Table 5.11 EDS analysis result of the 48 hours-aged Ni51Mn34In15 alloy for

selected region. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

Table 5.12 Magnetic parameter values of the Ni51Mn34In15 alloy. . . . . . . . . 66

Table 5.13 The structural and magnetic phase transition temperatures, values

of the thermal hysteresis and the martensitic transformation temperatures

of the Ni51Mn34In15 alloy under 500 Oe field. . . . . . . . . . . . . . . . 71

Table 5.14 The structural and magnetic phase transition temperatures, values

of the thermal hysteresis and the martensitic transformation temperatures

of the Ni51Mn34In15 alloy under 1 T field. . . . . . . . . . . . . . . . . . 72

Table 5.15 The structural and magnetic phase transition temperatures the Ni50Mn34In16. 72

Table 5.16 RC and RCP values of the as-cast, 24 hours-aged and 48 hours-aged

of Ni51Mn34In15 alloy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

Table 5.17 RC and RCP values of the as-cast and aged of CoMn0.95V0.05Ge

and CoMn0.90V0.10Ge alloys [90]. . . . . . . . . . . . . . . . . . . . . . . 79

xvi

LIST OF FIGURES

FIGURES

Figure 2.1 Classification of elements in periodic table based on magnetic prop-

erties [14]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

Figure 2.2 The alignment of magnetic moments in diamagnetic materials with-

out and with magnetic field (H) [14]. . . . . . . . . . . . . . . . . . . . . 6

Figure 2.3 The alignment of magnetic moments in paramagnetic materials

without and with magnetic field (H) [14]. . . . . . . . . . . . . . . . . . . 7

Figure 2.4 The alignment of magnetic moments in ferromagnetic materials [14]. 7

Figure 2.5 The hysteresis loop [14]. . . . . . . . . . . . . . . . . . . . . . . . 8

Figure 2.6 Magnetic ordering in ferrimagnetic materials [14]. . . . . . . . . . 8

Figure 2.7 The alignment of magnetic moments in antiferromagnetic materials. 9

Figure 2.8 Entropy (S) - Temperature (T) graph of MCE. . . . . . . . . . . . . 11

Figure 2.9 The comparison between the conventional cycle and MR cycle [37]. 13

Figure 2.10 Variation of the magnetic entropy change according to the transfor-

mation temperature for Gd, RCo2, RAl2, Gd5(Si1−xGex)4, Mn(As1−xSbx),

MnFe(P1−xAsx), La(Fe13−xSix), Heusler alloys (point 46) and other com-

pounds under ∆H = 50 kOe [39]. . . . . . . . . . . . . . . . . . . . . . . 16

Figure 3.1 The crystal structure of half-Heusler alloys. . . . . . . . . . . . . . 20

Figure 3.2 The crystal structure of full Heusler alloys. . . . . . . . . . . . . . 20

xvii

Figure 3.3 Periodic table of elements which form the Heusler structure and

their preferred occupancy [49]. . . . . . . . . . . . . . . . . . . . . . . . 21

Figure 3.4 Schematic representation of structural transformations (L21-type,

B2 and A2 structures) [43]. . . . . . . . . . . . . . . . . . . . . . . . . . 22

Figure 3.5 The austenite – martensite transformations depending on the tem-

perature [8] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

Figure 3.6 Schematic representation of the SME. . . . . . . . . . . . . . . . . 24

Figure 3.7 The transformation temperatures and crystal structures of some Ni-

Mn based Heusler alloys according to the ratio of e/a [71]. . . . . . . . . . 27

Figure 4.1 The unit cell of the L21-type ordered structure [76]. . . . . . . . . . 32

Figure 4.2 Arc melting device used for the production of sample. . . . . . . . 39

Figure 4.3 VSM used for magnetic measurements. . . . . . . . . . . . . . . . 40

Figure 5.1 Variation of partial ordering energies for Ni-Mn (green line), Ni-

Ga (red line) and Mn-Ga (blue line) pairs with interatomic distance for

the stoichiometric Ni2MnGa alloy. (1 at.u.(energy) = 2 Ry = 27.2 eV; 1

at.u.(length) = 0.529177 Å). . . . . . . . . . . . . . . . . . . . . . . . . . 45


In (red line) and Mn-In (blue line) pairs with interatomic distance for

the stoichiometric Ni2MnIn alloy. (1 at.u.(energy) = 2 Ry = 27.2 eV; 1

at.u.(length) = 0.529177 Å). . . . . . . . . . . . . . . . . . . . . . . . . . 45


Sb (red line) and Mn-Sb (blue line) pairs with interatomic distance for

the stoichiometric Ni2MnSb alloy. (1 at.u.(energy) = 2 Ry = 27.2 eV; 1

at.u.(length) = 0.529177 Å). . . . . . . . . . . . . . . . . . . . . . . . . . 46

xviii


Sn (red line) and Mn-Sn (blue line) pairs with interatomic distance for

the stoichiometric Ni2MnSn alloy. (1 at.u.(energy) = 2 Ry = 27.2 eV; 1

at.u.(length) = 0.529177 Å). . . . . . . . . . . . . . . . . . . . . . . . . . 46

Figure 5.5 Order-order transition temperatures calculated by using Equation

(4.27) (blue line) and Equation (4.31) (red line) for the Ni50Mn50−xGax

alloy (15 ≤ x ≤ 35). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48


(4.27) (blue line) and Equation (4.31) (red line) for the Ni50Mn50−xInx

alloy (15 ≤ x ≤ 35). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48


(4.27) (blue line) and Equation (4.31) (red line) for the Ni50Mn50−xSbx

alloy (15 ≤ x ≤ 35). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49


(4.27) (blue line) and Equation (4.31) (red line) for the Ni50Mn50−xSnx

alloy (15 ≤ x ≤ 35). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

Figure 5.9 Order-order transformation temperatures as a function of number

of valence electrons at In, Sn and Sb sites for the stoichiometric Ni2MnIn,

Ni2MnSn and Ni2MnSb alloys. . . . . . . . . . . . . . . . . . . . . . . . 50

Figure 5.10 Order-disorder transition temperature calculated by using Equation

(4.22) for Ni50Mn50−xInx alloy (15 ≤ x ≤ 35). . . . . . . . . . . . . . . 52

Figure 5.11 XRD pattern for the as-cast Ni51Mn34In15 alloy measured at RT. . . 54

Figure 5.12 XRD pattern for the 24 hours-aged Ni51Mn34In15 alloy measured

at RT. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

Figure 5.13 XRD pattern for the 48 hours-aged Ni51Mn34In15 alloy measured

at RT. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

Figure 5.14 Optical microscopy images of various magnifications for the as-

cast Ni51Mn34In15 alloy. . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

xix

Figure 5.15 Optical microscopy images of various magnifications for the 24

hours-aged Ni51Mn34In15 alloy. . . . . . . . . . . . . . . . . . . . . . . . 57

Figure 5.16 Optical microscopy images of various magnifications for the 48


Figure 5.17 SEM images of various magnifications for the as-cast Ni51Mn34In15

alloy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

Figure 5.18 EDS results of the as-cast Ni51Mn34In15 alloy. . . . . . . . . . . . 60

Figure 5.19 SEM images of various magnifications for the 24 hours-aged Ni51Mn34In15

alloy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

Figure 5.20 EDS results of the 24 hours-aged Ni51Mn34In15 alloy. . . . . . . . 61

Figure 5.21 SEM images of various magnifications for the 48 hours-aged Ni51Mn34In15

alloy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

Figure 5.22 EDS results of the 48 hours-aged Ni51Mn34In15 alloy. . . . . . . . 62

Figure 5.23 Hysteresis loop for the as-cast Ni51Mn34In15 alloy measured at RT,

inset shows the hysteresis in more detail. . . . . . . . . . . . . . . . . . . 64

Figure 5.24 Hysteresis loop for the 24 hours-aged Ni51Mn34In15 alloy mea-

sured at RT, inset shows the hysteresis in more detail. . . . . . . . . . . . 64

Figure 5.25 Hysteresis loop for the 48 hours-aged Ni51Mn34In15 alloy mea-

sured at RT, inset shows the hysteresis in more detail. . . . . . . . . . . . 65

Figure 5.26 Temperature dependent magnetizations measured for the as-cast

Ni51Mn34In15 alloy under fields (a) 500 Oe (b) 1 T. . . . . . . . . . . . . 67

Figure 5.27 Temperature dependent magnetizations measured for the 24 hours-

aged Ni51Mn34In15 alloy under fields (a) 500 Oe (b) 1 T. . . . . . . . . . . 68

Figure 5.28 Temperature dependent magnetizations measured for the 48 hours-

aged Ni51Mn34In15 alloy under fields (a) 500 Oe (b) 1 T. . . . . . . . . . . 69

xx

Figure 5.29 Magnetization of the as-cast Ni51Mn34In15 alloy as a function of

magnetic field measured in the temperature interval of 233 K<T<313 K,

∆T=6K for clarity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

Figure 5.30 Magnetization of the 24 hours-aged Ni51Mn34In15 alloy as a func-

tion of magnetic field measured in the temperature interval of 255 K<T<335

K, ∆T=4K for clarity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

Figure 5.31 Magnetization of the 48 hours-aged Ni51Mn34In15 alloy as a func-

tion of magnetic field measured in the temperature interval of 253 K<T<353

K, ∆T=4K for clarity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

Figure 5.32 Magnetic entropy change of the as-cast Ni51Mn34In15 alloy. . . . . 76

Figure 5.33 Magnetic entropy change of the 24 hours-aged Ni51Mn34In15 alloy. 76

Figure 5.34 Magnetic entropy change of the 48 hours-aged Ni51Mn34In15 alloy. 77

Figure 5.35 Schematic representation of temperature-dependent magnetic en-

tropy change. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

Figure A.1 Optical microscopy images of various magnifications for the as-

cast Ni51Mn34In15 alloy. . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

Figure A.2 Optical microscopy images of various magnifications for the 24


Figure A.3 Optical microscopy images of various magnifications for 48 hours-

aged Ni51Mn34In15 alloy. . . . . . . . . . . . . . . . . . . . . . . . . . . 97

Figure B.1 SEM images of various magnifications for the as-cast Ni51Mn34In15

alloy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

Figure B.2 SEM images of various magnifications for the 24 hours-aged Ni51Mn34In15

alloy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

Figure B.3 SEM images of various magnifications for the 48 hours-aged Ni51Mn34In15

alloy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

xxi

LIST OF ABBREVIATIONS

MR Magnetic Refrigeration

MCE Magnetocaloric Effect

MT Magnetic Transformation

SME Shape Memory Effect

FSME Ferromagnetic Shape Memory Effect

XRD X-ray Diffraction

SEM Scanning Electron Microscopy

VSM Vibrating Sample Magnetometer

EDS Energy Dispersive Spectroscopy

RC Refrigerant Capacity

RCP Relative Cooling Power

xxii

CHAPTER 1

INTRODUCTION

Cooling systems are used in houses, cars, hospitals, defence systems and many other

such areas. However, the gases (chlorofluorocarbons and hydrochlorofluorocarbons)

present in today’s refrigerant systems are harmful to the environment and cause global

warming. Moreover, today’s cooling technology is expensive and low-efficiency tech-

nology. Therefore, new and cost-effective with higher energy efficiencies cooling sys-

tems have begun to be developed to eliminate the use of these harmful gases. Lately,

magnetic refrigeration technology has a great potential to enter markets due to its

more efficient and environmentally friendly technology. Magnetic refrigerations have

many advantages such as low maintenance and operating cost, reliability, compact-

ness, higher efficiency, environmental friendly, etc. as compared to the traditional

refrigeration systems based on gas compression/expansion. The magnetic refriger-

ants which were the first technic improved for cooling below about 0.3 K have been

of interest since 1933 [1].

In order to obtain efficient magnetic refrigeration, various materials have been devel-

oped for many years. At present, Heusler alloys, especially full Heusler alloys, are

the most attractive materials among these materials. They are ternary intermetallic

compounds which crystallize in the L21-type crystal structure and undergo a marten-

sitic transition from the high temperature austenite phase to low temperature marten-

site phase, a paramagnetic to ferromagnetic transformation and order↔order and

order↔disorder phase transitions. The full Ni-Mn based Heusler alloys are the most

studied systems in Heusler alloys.

The full Heusler alloys can be used in many technological applications with their

1

unique properties like ferromagnetic shape memory effect and magnetocaloric effect.

The magnetic refrigeration is based on the magnetocaloric effect which is defined as

the change in temperature of a magnetic material under application or removal of a

magnetic field. The giant magnetocaloric effect was first discovered in Ni-Mn-Ga

alloy [2]. Another important feature of Heusler alloys is that they can have a ferro-

magnetic shape memory effect. Ni-Mn based Heusler alloys have become significant

as the ferromagnetic shape memory effect was discovered in the Ni2MnGa Heusler

alloy [3]. The martensitic transformation which is a phase transformation from the

high temperature austenite phase to the low temperature martensite phase has a crucial

role in the ferromagnetic shape memory effect. The changes of martensitic transfor-

mation temperatures of Ni-Mn-Ga Heusler alloy which is the most studied material

are 0.8 to 1.6 K under a magnetic field of 2 T [4]. In addition to Ni-Mn-Ga alloys,

new Heusler alloy systems have been investigated for many years. Ni-Mn-In [5],

Ni-Co-Mn-In [6] and Ni-Co-Mn-Sn [7] alloys are considered as potential candidate

Heusler alloys due to martensitic transformation and ferromagnetic shape memory

effect. According to the authors [8], although the difference between martensite and

austenite magnetizations is narrow in Ni-Mn-Ga alloys, the martensitic transforma-

tion in Ni-Mn-In, Ni-Mn-Sn and Ni-Mn-Sb Heusler alloys is companioned with a

large decrease in magnetization.

It can be seen in the literature that Ni50Mn50−xInx Heusler alloys are mostly studied

on the composition x = 16 [9]. In addition to experimental studies on this alloy, theo-

retical studies have also been carried out a lot. This alloy undergoes a transition from

the high temperature austenite phase to low temperature martensite phase at about

TC=304 K. The largest magnetic entropy change of this alloy (under the magnetic

field of 5 T and, near 240 K) was found as 19 J/kg ·K [10].

The aim of this thesis is to develop new and superior material for magnetic refrig-

eration technology. In accordance with this purpose, theoretical and experimental

studies on Ni-based Heusler alloys were carried out. The theoretical part covers

the modelling and simulation of atomic processing in full Ni-Mn-C (C=Ga, In, Sb,

Sn) Heusler alloys. The composition of the Ni-Mn-In alloy system was determined

according to the results obtained by the theoretical studies. The experimental part

involves experimental investigations on structural and magnetic properties, magne-

2

tocaloric effect and relative cooling power in Ni-Mn-In Heusler alloy system. Chap-

ter 2 gives a literature review of magnetic refrigeration and its thermodynamic cycles,

magnetocaloric effect and magnetic properties of materials. Also, in this chapter, the

theory of magnetocaloric effect is described in detail. In chapter 3, a theoretical

background of Heusler alloys, especially full Heusler alloys, martensitic transforma-

tions, shape memory effect and ferromagnetic shape memory effect and the proper-

ties of Ni-Mn based Heusler alloys are briefly explained. Chapter 4 presents the

theoretical and experimental studies. The calculation of the order-order and order-

disorder critical phase transition temperatures in A50B50−xCx full Heusler alloys and

the calculation of partial ordering energies using the electronic theory of ternary al-

loys in pseudopotential approximation are defined clearly. Moreover, the technical

aspects of methods used for study of theoretical and experimental investigations are

described. The sample preparation technique and sample characterization methods

like X-ray diffraction (XRD), Scanning Electron Microscope (SEM), Optical Micro-

scope and Vibrating Sample Magnetometer (VSM) are briefly described. Chapter

5 gives the theoretical results of order-order and order-disorder critical phase trans-

formation temperatures for the Ni50Mn50−xCx (C=Ga, In, Sb, Sn) alloys. Moreover,

the experimental results of Ni51Mn34In15 Heusler alloy are discussed in this chapter.

Chapter 6 involves the conclusion of the thesis with a summary of the theoretical and

experimental results and brief discussions. Also, possible future works are discussed

in this chapter.

3

4

CHAPTER 2

LITERATURE REVIEW

2.1 MAGNETIC REFRIGERATION (MR)

Recently, magnetic refrigeration (MR) is an emerging technology that has become

competitive with traditional refrigeration systems based on gas compression and ex-

pansion. Magnetic refrigeration has prominent properties and advantages compared

to conventional refrigeration in use today. Primarily, the use of magnetic refrigeration

has the potential to provide higher energy efficiencies because it is capable of reducing

energy consumption by up to 40%. In a MR system, permanent magnets which do not

require an energy source to produce field are used instead of the energy-consuming

compressor of the conventional refrigeration system. MR can remove the high cost of

the compressor and the high cost of electricity to run the compressor which based on

conventional refrigeration system. Thus, it reduces operating and maintenance costs

in terms of low rotational speed, low pressure, no leaks and no hazardous chemicals.

Moreover, solid refrigerant which usually in a form of spheres or thin sheets is used

as a working material; so, MR has much more compact and produces less noise and

vibrations. Furthermore, MR is an environmentally friendly technology because of

not using hazardous chemicals (NH3), ozone depleting gases (CFCs – chlorofluoro-

carbons) and/or greenhouse gases (HCFCs – hydrochlorofluorocarbons and HFCs –

hydrofluorocarbons) [11-13].

5

2.2 MAGNETIC PROPERTIES OF MATERIALS

The magnetic properties of materials are based on the orbital and spin motion of

electrons, and how electrons interact with each other. The magnetic behavior of ma-

terials can be categorized into five groups depending on the existence and alignment

of magnetic moments with or without magnetic field: diamagnetism, paramagnetism,

ferromagnetism, ferrimagnetism and antiferromagnetism (Figure 2.1).

Figure 2.1: Classification of elements in periodic table based on magnetic properties

[14].

Diamagnetism

Even though diamagnetism is a weak form of magnetism, it is basic property of all

matter. Diamagnetic materials have no magnetic moment in the absence of a mag-

netic field. When a diamagnetic material is exposed to a field, the magnetic moment

of atoms is aligned to the opposite direction of the applied field (Figure 2.2) [14].

Therefore, diamagnetic materials possess negative magnetization.

Figure 2.2: The alignment of magnetic moments in diamagnetic materials without

and with magnetic field (H) [14].

6

Paramagnetism

In paramagnetic materials, there is a non-zero magnetic moment without any external

magnetic field because magnetic moments between electron pairs are not cancelled

out completely. The magnetic moments are randomly aligned and when paramag-

netic materials are subjected to an external magnetic field, these magnetic moments

are aligned in the direction of the field (Figure 2.3) [14].

Figure 2.3: The alignment of magnetic moments in paramagnetic materials without

and with magnetic field (H) [14].

Ferromagnetism

Ferromagnetic materials exhibit permanent magnetic moments which originate be-

cause of uncancelled electron spins even in the absence of a magnetic field. Parallel

alignment of moments is observed in ferromagnetic materials due to the coupling of

electron spins of adjacent atoms (Figure 2.4) [14].

Figure 2.4: The alignment of magnetic moments in ferromagnetic materials [14].

The spontaneous magnetization and the critical temperature are unique properties of

ferromagnetic materials. As an external magnetic field is applied to ferromagnetic

materials, the magnetization increases and tends to a constant maximum value called

the saturation magnetization, Msat, or spontaneous magnetization. When the applied

field diminishes, the magnetization decreases gradually; however, it does not become

7

zero. This is called as hysteresis which is irreversibility of magnetization (Figure 2.5).

When the applied magnetic field is zero, the magnetization takes a non-zero value

which is called as remanent magnetization (Mr). In order to reset the magnetization,

a reverse magnetic field is required. This magnetic field is called the coercive field

(HC). Below a certain temperature known as Curie temperature, TC, ferromagnetism

appears. However, above the Curie temperature paramagnetism appears [14-16].

Figure 2.5: The hysteresis loop [14].

Ferrimagnetism

Ferrimagnetic materials exhibit permanent magnetism due to partial cancellation of

spin moments. The opposing moments are not equal and a spontaneous magnetiza-

tion stays (Figure 2.6) [17].

Figure 2.6: Magnetic ordering in ferrimagnetic materials [14].

8

Antiferromagnetism

In antiferromagnetic materials, the magnetic moments are in equal magnitude and

opposite direction due to antiparallel arrangement of spins (Figure 2.7). Thus, the net

moment is zero. Also, antiferromagnetic materials have no spontaneous magnetiza-

tion [15].

Figure 2.7: The alignment of magnetic moments in antiferromagnetic materials.

2.3 MAGNETOCALORIC EFFECT (MCE)

Magnetic refrigeration is a cooling technology based on magnetocaloric effect (MCE).

This effect describes that some metal alloys or magnetocaloric materials heat up when

placed in a magnetic field and cool down when removed from it. In other words, MCE

gives rise to a temperature change in a material because of the application of a mag-

netic field.

MCE can be used to obtain absolute near zero temperature [11]. German physicist

Emil Warburg discovered MCE in iron in the year 1881 [18]. Debye [19] in 1926 and

Giauque [20] in 1927 suggested cooling by means of adiabatic demagnetization using

to reach temperatures below liquid helium. In 1933, Giauque and MacDougall [21]

experimentally reached a temperature value of 0.25 K by adiabatic demagnetization

[22].

2.3.1 Thermodynamics of the Magnetocaloric Effect

The magnetocaloric effect is a reversible change in temperature of a material which

is subjected to a magnetic field. The MCE can be quantified as the adiabatic temper-

9

ature change (∆Tad) and the isothermal magnetic entropy change (∆SM) due to the

application of the magnetic field H at constant pressure [23]. Both ∆Tad and ∆SM

measure the MCE according to the initial temperature and the magnetic field change.

These two quantities can be derived by the entropy state function S(H,T) at constant

pressure, which is combined magnetic entropy of the magnetization of the material

(SM), lattice entropy caused by the vibrations of crystal lattice (SL) and electronic

entropy of the material’s free electrons (SE) [23, 25]. As seen from Equation (2.1),

the magnetic entropy is dependent on the magnetic field and temperature, while the

lattice and electronic entropy are only dependent on temperature.

S(H,T ) = SM(H,T ) + SL(T ) + SE(T ) (2.1)

The relationship between ∆Tad and ∆SM can be shown in an S-T sketch of Figure

2.8 [24]. When an external magnetic field is applied to a material, the ordering of

the magnetic spin increases, and the magnetic entropy is decreased since the material

releases more heat. Also, in this case ∆Tad is positive, while ∆SM is negative. On the

other hand, with the decreasing of the external magnetic field, the magnetic moments

of material get disoriented. Therefore, the material absorbs heat and the magnetic

entropy increases. ∆Tad and ∆SM are correspondingly reversed when the magnetic

field is decreased [11, 22, 26].

10

Figure 2.8: Entropy (S) - Temperature (T) graph of MCE.

The change in internal energy which is used to describe MCE can be written as [22,

27, 28]:

dU = TdS − pdV + µ0HdM (2.2)

where T is the absolute temperature, p is the pressure, µ0 is the magnetic permeability

of the vacuum and H is the magnetic field. The internal energy (U) of a system can be

expressed as a function of the entropy (S), the volume (V) and the magnetic moment

(M). If the system’s volume is not changed, dV=0, Equation (2.2) can be rewritten as

[22]:

dU = TdS + µ0HdM (2.3)

With respect to the H and T, the total entropy change of the system can be expressed

as [22]:

dS =

(∂S

∂T

)H

dT +

(∂S

∂H

)T

dH (2.4)

cx = (δq/dT )x (2.5)

Equation (2.5) shows the specific heat (c) of a substance under a constant parameter

(x). Also, the second law of thermodynamics is given in Equation (2.6) [22].

dS = δq/T (2.6)

When Equation (2.6) is combined with Equation (2.5), the specific heat of a substance

under constant pressure and magnetic field (cp,H) can be defined as Equation (2.7)

[22]:

cp,H = T (∂S/∂T )H (2.7)

11

The dependence of the entropy in the magnetic field can be represented with regard

to magnetization through a Maxwell relation [22]:(∂S

∂H

)T

= µ0

(∂M

∂T

)H

(2.8)

The Equation (2.9) can be obtained by introducing Equations (2.7) and (2.8) into

Equation (2.4) [22]:

dS = (cp,H/T )dT + µ0(∂M/∂T )dH (2.9)

The adiabatic temperature change, ∆Tad, is implemented under the condition of dS=0

in Equation (2.9) [11, 13, 22, 24, 29].

∆Tad(H,S) = T (H1, S)− T (H0, S) (2.10)

∆Tad = −µ0

∫ H1

H0

(T

cp,H

)(∂M

∂T

)H

dH (2.11)

The isothermal magnetic entropy change, ∆SM, can be determined from Equation

(2.9), dT=0, [11, 13, 22, 24, 26, 29].

∆SM(H,T ) = SM(H1, T )− SM(H0, T ) (2.12)

∆SM = µ0

∫ H1

H0

(∂M

∂T

)H

dH (2.13)

As it seen from Equations (2.11) and (2.13) [22];

• Direct MCE: (∂M/∂T)H< 0→ ∆SM < 0 and ∆Tad > 0

• Inverse MCE: (∂M/∂T)H> 0→ ∆SM > 0 and ∆Tad < 0

MCE will be large if [13, 22]:

• the magnetic field change is high,

• |(∂M/∂T)H| is large and cp,H is small at the same temperature.

12

2.3.2 Magnetic Refrigeration Thermodynamic Cycles

A magnetic working material, a magnetizing/demagnetizing system, hot and cold ex-

changers and a heat transfer system with a thermal fluid are parts of the magnetic

refrigeration system. The heat transfer fluid which pumps the heat from the working

magnetic material to the hot and cold heat exchangers can be a gas or a liquid depend-

ing on the operating temperature. The combination of thermodynamic processes of

isothermal magnetization, adiabatic magnetization and processes at a constant field

enable the acquisition of magnetic refrigerators with different thermodynamic cycles

such as Carnot cycle, Brayton cycle, Ericsson cycle, Cascade magnetic cycles, active

magnetic regenerator cycle [22].

The Brayton cycle which works between two adiabatic and two isomagnetic field

lines is the basic of thermodynamic cycle of the magnetic refrigerator. In Figure

2.9, the comparison between the conventional cycle and MR cycle is demonstrated

graphically (Joule – Brayton cycle).

Figure 2.9: The comparison between the conventional cycle and MR cycle [37].

1. Adiabatic Magnetization: The increasing of external magnetic field (+H) un-

der adiabatic conditions causes the alignment of spins and thereby decreasing

SM and increasing SL and SE because of the spin lattice connections and vi-

brations. This results in the increase in the temperature of the magnetocaloric

material (+∆Tad).

13

2. Isomagnetic Cooling: The added heat can be removed by placing the system

in contact with any gas or fluid. After a sufficient cooling, the magnetocaloric

material and the coolant are separated (H=0).

3. Adiabatic Demagnetization: The decreased external magnetic field under adi-

abatic conditions results in the increase in the SM is compensated by the de-

crease in the SL and SE to keep the total entropy constant. The electron spins

return to original alignment and the temperature of the magnetocaloric material

decreases.

4. Isomagnetic Heating: Under constant magnetic field, the material is placed in

thermal contact with the environment being refrigerated. When the refrigerant

and refrigerated environment are in thermal equilibrium, the cycle continuous.

2.4 MAGNETOCALORIC MATERIALS FOR MAGNETIC REFRIGERATION

The magnetocaloric materials can be categorized as regards the order of the phase

transition which they undergo: first and second order phase transitions.

First Order Phase Transition

A first order phase transition which is also called as first order magneto-structural

transition (coupled magnetic and structural transitions) should take place at constant

temperature. Thus, the change in magnetization with temperature, i.e., |(∂M/∂T)H|can be infinitely large, resulting quite large MCE values. This is called as giant mag-

netocaloric effect (GMCE) by Pecharsky and Gschneidner in 1997 [26]. The GMCE

materials are Gd5Si2Ge2 [30], La(FeSi)13 [31], Ni-Mn-Ga [32] and Mn-As-(Fe, Sb,

P) [33-35].

Second Order Phase Transition

The magnetic materials which display conventional MCE order through a second or-

der magnetic phase transition like the ferromagnet, ferrimagnet or antiferromagnet

↔ paramagnet transitions. In the second order magnetic phase transition, the mag-

netization diminishes continuously to zero. The second order phase transition is also

referred as continuous phase transition. Gadolinium (Gd) or transition metal based

amorphous alloys are examples of magnetic refrigerant materials which undergo this

14

kind of transition [36].

Although the magnetic materials with high MCE become high potential for MR, they

must perform following features and characteristics to be used as cooling materials

[22, 38, 39].

• Curie temperature near working temperature - Heusler alloys become promis-

ing candidates among magnetic cooling materials since they have a Curie tem-

perature near RT;

• A low magnetic hysteresis in order to minimise magnetic work losses which

result from the rotation of domains in a magnetic refrigeration cycle, and so

large cooling power;

• Excessively large entropy peak to maximise refrigerant capacity;

• A low heat capacity cp,H – high cp,H gives rise to entropy loss because it en-

hances the thermal load and more energy is required to heat the material itself;

• High electrical and corrosion resistance;

• Low cost and low environmental effect.

MCE materials used in the researches to improve MR technology and MCE proper-

ties can be grouped as follows.

1. Crystal Materials

a. Alloys with Rare Earth Elements

i. La[Fe(Si,Al)]13 systems

ii. Gd5(Si,Ge)4 systems

iii. Ferromagnetic lanthanum manganites

iv. Other intermetallics

b. Alloys without Rare Earth Elements

i. Heusler Alloys

15

ii. Mn-TM-(Si,Ge) compounds

iii. (Mn,TM)5X3 compounds

iv. MnAs allloys

v. MnFe(P,As) alloys

vi. FeRh alloys

2. Amorphous Materials

3. Multiphase Materials and Composites

4. Nanostructured Materials

Figure 2.10: Variation of the magnetic entropy change according to the trans-

formation temperature for Gd, RCo2, RAl2, Gd5(Si1−xGex)4, Mn(As1−xSbx),

MnFe(P1−xAsx), La(Fe13−xSix), Heusler alloys (point 46) and other compounds un-

der ∆H = 50 kOe [39].

16

The change in magnetic entropy of the potential MCE materials used in MR tech-

nology according to the transition temperature (TC) is given in Figure 2.10 [39]. As

can be seen from this figure, among these materials, Heusler alloys are the strongest

candidate MCE materials due to their giant MCE and FSME properties.

17

18

CHAPTER 3

HEUSLER ALLOYS FOR MAGNETIC REFRIGERATION

The Heusler compound, a long-standing research topic more than a century, was first

discovered by German mining engineer and chemist Friedrich Heusler in 1903. He

produced a Heusler-type alloy by adding the third group elements such as Al, Sn, Sb,

Bi or In to the binary Cu-Mn alloy. Moreover, although the component elements are

not magnetic, the Heusler alloy exhibits ferromagnetic properties [40]. In 1929, Pot-

ter performed X-ray studies on the Cu2MnAl Heusler alloy to determine the crystal

structures of Heusler alloys and found that these alloys were arranged in a surface-

centred cubic superstructure [41]. The subsequent work by Bradley and Rodgers

showed that the chemical composition and magnetic properties of Heusler alloys are

interdependent [42]. After the observation of the shape memory effect in Ni2MnGa

[43] and the discovery of the semi-metallic ferromagnetism feature in NiMnSb [44],

Heusler alloys have become attractive alloys. Heusler alloys with more than 1000

members have received considerable attention because of extraordinary properties

like ferromagnetic shape memory effect, magnetocaloric effects, large magnetoresis-

tance, etc [45]. This interest causes improvement of their potential technological ap-

plications such as actuators [46], sensors [47], energy technologies [48] and magnetic

refrigeration applications [49].

Recently, the half-Heusler and full Heusler alloys are classified as Heusler alloys.

The half-Heusler alloys with the composition 1:1:1 have the general formula ABC

and crystallize in a non-centrosymmetric cubic structure (space group no. 216, F43m,

C1b) which is a ternary ordered variant of the CaF2 structure and can be derived from

the tetrahedral ZnS-type structure by filling the octahedral lattice sites [39]. The unit

cell consists of three interpenetrating fcc sublattices with Wyckoff positions which

19

are 4a (0, 0, 0), 4b (1/2, 1/2, 1/2), and 4c (1/4, 1/4, 1/4). The crystal structure of

half-Heusler alloys is given in Figure 3.1 [50].

Figure 3.1: The crystal structure of half-Heusler alloys.

3.1 FULL HEUSLER ALLOYS

The full Heusler alloys are ternary systems with the composition 2:1:1 represented

by the formula A2BC. They crystallize in the L21 structure with space group Fm3m

(space group no. 225) [51]. Figure 3.2 shows the completely ordered L21- type or-

dered crystal structure of full Heusler alloys [50]. In the L21 ordered structure, the

unit cell consist of four interpenetrating fcc sublattices with the positions (0, 0, 0) and

(1/2, 1/2, 1/2) for A, (1/4, 1/4, 1/4) for B and (3/4, 3/4, 3/4) for C atoms.

Figure 3.2: The crystal structure of full Heusler alloys.

A element is typically the most electronegative transition metal like Co, Cu, Ni or Fe;

20

B element is the less electronegative transition metal which is mainly Mn. In some

cases, the B element may also be an alkaline earth metal. C element is a main group

element such as Ge, Si, Ga, Sn, Sb, Al or In (Figure 3.3).

Figure 3.3: Periodic table of elements which form the Heusler structure and their

preferred occupancy [49].

The characteristics of full Heusler alloys depend strongly on the atomic order. Figure

3.4 shows a schematic representation of transformations. If the A atoms are located in

(0, 0, 0) and (1/2, 1/2, 1/2) positions and B and C atoms are randomly sited, this par-

tially disordered structure is known as B2-type structure (CsCl-like structure). When

all positions become equivalent with a bcc lattice, the A, B and C atoms are randomly

distributed. This type disordered structure is known as A2-type structure.

21

Figure 3.4: Schematic representation of structural transformations (L21-type, B2 and

A2 structures) [43].

3.2 MARTENSITIC TRANSFORMATION (MT)

The martensitic transformation (MT) is a solid-state first order phase transition which

also called a shear or displacive or diffusionless transformation [8]. The diffusive

and displacive transformations are groups of the solid-state phase transformations.

The atoms of an alloy structure replace during phase transformation. In the diffusive

transformation, the neighbourhood of the atoms changes; thus, long range diffusion

of atoms occurs during this transformation. On the other hand, there is no long range

motion of the atoms in the displacive or diffusionless transformation. The atoms

move less than their interatomic spacing and keep their relative relationship at the

time of phase transition [52]. Such a formation is defined as a martensite phase tran-

sition. The first studies on this transition were carried out by the German scientist

Adolf Martens on the microstructure of steels [53]. Several Heusler alloys undergo

a martensitic transformation from the high temperature symmetric phase (austenite)

to a low temperature with lower symmetry (martensite) [54]. As it is explained in

[50], if the austenite structure is cooled rapidly from the thermodynamic equilibrium

temperature, after a critical temperature, the martensite structure begins to form. This

critical temperature is called martensite start temperature (Ms). The transformation

22

starting at Ms continues at a certain temperature range and ends at martensite finish

temperature (Mf). When the sample is heated in martensite phase, the austenite phase

starts to form again from the austenite start temperature (As). The temperature at

which the sample is completely transformed to an austenite phase is called austenite

finish temperature (Af). The solidification temperature of each alloy is different from

each other, and the martensite phase transition is completed at a certain temperature

range. Therefore, the hysteresis which is a characteristic property of martensite phase

transition is observed during transformation. The austenite – martensite transforma-

tions depending on the temperature are shown schematically in Figure 3.5.

Figure 3.5: The austenite – martensite transformations depending on the temperature

[8]

3.3 SHAPE MEMORY EFFECT (SME)

Shape memory alloys (SMAs) which exhibit unique property like shape memory ef-

fect (SME) have the ability to remember their original shape that they had before

the deformation. The first studies of SME were widely realised by Russian metal-

lurgist G. Kurdjumov, Chang and Read [55] and then in 1962 Buehler and Wang

[56] determined the SME on the nickel-titanium (Nitinol) alloys. Since then, various

alloys have been researched such as Ag-Cd, Au-Cd, Cu-Zn, Cu-Zn-Al, Cu-Al-Ni, Cu-

Sn, Cu-Au-Zn, Ni-Al, Ti-Ni, Ti-Ni-Cu, Ni-Ti-Cu, Ni-Ti-Nb, Ti-Pd-Ni, In-Ti, In-Cd.

Among these alloys, Ni-Ti, Cu-Zn-Al and Cu-Al-Ni are the most effective and widely

used alloys. SMAs have two phases below and above the critical transition tempera-

23

ture: martensite and austenite. The martensite phase which is easily deformed phase

of SMAs occurs at lower temperatures and has twinned molecular structure. On the

other hand, the austenite phase which is the stronger phase of SMAs exists at higher

temperatures. The transformation of material to austenite phase by heating is called

one-way shape memory effect. When the material passes through the austenite phase

by heating, then the transformation to the martensite phase by cooling, it is defined as

the two-way shape memory effect [57]. The SME is shown schematically in Figure

3.6.

Figure 3.6: Schematic representation of the SME.

The structure of the L21 cubic material which is in the austenite phase is deformed

due to cooling and begins to transform to martensite phase which is in tetragonal,

orthorhombic or monoclinic structures. The structure of the material in the marten-

site phase depends on the concentration of the C (A2BC) atom. If the concentration

of C atom is low, the transition is usually between L21 and L10, whereas if the con-

centration of C atom is high, the modulated structures are formed in relation to the

tetragonal structure. The most common of these modulated structures are the 5M and

7M structures, which are also called 10M and 14M [58].

24

3.4 FERROMAGNETIC SHAPE MEMORY EFFECT (FSME)

Ferromagnetic shape memory alloys (FSMAs) which display ferromagnetic behaviour

are a subgroup of SMAs. They undergo a transformation from the high tempera-

ture with higher symmetry phase to the low temperature with lower symmetry phase.

When an external magnetic field is applied to a material in a twinned structure whose

martensite phase is ferromagnetic, the magnetic moments of the martensite variants

are aligned along the direction of the magnetic field. As a result, the twinned struc-

tures are removed, and a single variant is obtained. If the magnetic field is removed,

the material returns to its original shape with the twinned structure. This phenomenon

is called ferromagnetic shape memory effect (FSME) and materials with this capabil-

ity are termed as ferromagnetic shape memory alloys. If the deformed material is

heated up to the austenitic state, it passes to the martensitic phase through the shape

memory feature and returns to its original shape.

Today, actuator materials that mix large strain and fast dynamic response have re-

ceived attention for application of smart materials and SMAs are conventionally con-

sidered as actuator materials. The FSME was first shown in Ni2MnGa which exhibits

10% field-induced strain [59]. Recently, many FSMAs have been developed, such

as Ni2MnGa [60], Ni2FeGa [61], Ni2MnAl [62], Co–Ni–Ga [63], Ni–Co–Al [64]

and Ni– Mn–Sn (Sb, In) [65]. The FSMAs have some advantages compared to the

conventional SMAs. The SMAs have a relatively slow actuation response time than

FSMAs since conventional SMAs require the flow of heat for actuation. The shape

deformation obtained by the magnetic field is higher and faster than the shape defor-

mation obtained by the temperature.

25

3.5 PROPERTIES OF Ni-Mn BASED HEUSLER ALLOYS

Recently, Ni-Mn based Heusler alloys have received great interest due to the dis-

covery of their unique properties such as ferromagnetic shape memory effect and

giant magnetocaloric effect. Ni2MnC where C can be Ga, Al, In, Sn, Sb etc. is the

general formula of the Ni-Mn based Heusler alloys. Among these series of alloys,

Ni2MnGa alloy is the most studied one for being a magnetic refrigerant material

since it exhibits GMCE and FSME properties. Firstly, in 1996, it was observed a

strain of ∼ 0.2% under an applied magnetic field in Ni2MnGa alloy in martensite

phase [60]. Then, a large magnetic field induced strain of ∼ 10% has been informed

in Ni44.8Mn29.7Ga21.5 alloy [66]. While a B2 or L21 structure is shown in the austenite

phase, the martensite phase exhibits a non-modulated tetragonal structure. Also, the

martensite phase shows 5 M and 7 M with the increase of Mn substitution of Ga [67].

The stoichiometric Ni2MnGa alloy undergoes a martensitic transformation from cu-

bic phase to tetragonal phase at around TM=202 K [60]. Furthermore, in this alloy, the

austenite phase is ferromagnetic at TC = 380 K. This alloy also has order-order and

order-disorder transitions at 1071 K and 1382 K, respectively [68, 69]. Even though

Ni-Mn-Ga alloys are strong candidates for magnetic refrigerants, there are some diffi-

culties with the practical applications of these alloys. For instance, their highly brittle

nature and the high cost of pure element Ga are serious difficulties. Therefore, other

suitable Heusler based ferromagnetic shape memory alloys have been investigated

during the last years in order to overcome these serious concerns. Ni-Mn-Al alloys

are candidate materials among these FSMAs. The austenite phase exhibits a B2 or

L21 structure and the martensite phase shows a change according to the Al and Mn

content. With low Al and Mn content, the non-modulated tetragonal structure is ob-

served while 5 M and 7 M tetragonal martensite structure exist with high Al and Mn

content [70]. The Ni-Mn-Al alloys have relatively low order-order transformation

temperatures which is about 660 K [16].

In addition, the off-stoichiometric Ni50Mn50−xCx (C= In, Sn, Sb) Heusler alloys

which undergo a martensitic transition from the high temperature cubic austenite

phase to low temperature orthorhombic martensite phase have been investigated since

last years. These alloy systems have ferro/anti-ferro magnetic state in the martensitic

26

phase [46].

The e/a ratio, which indicates the valence-electron-per-atom in the alloy, plays an

important role on the structure and properties of Ni-Mn based Heusler alloys since it

controls the order-order transformations in full Heusler alloys. The e/a ratio for the

Ni50Mn50−xInx alloy can be calculated as follows [50].

e/a =10× (Ni at.%) + 7× (Mn at.%) + 3× (In at.%)

100(3.1)

Figure 3.7: The transformation temperatures and crystal structures of some Ni-Mn

based Heusler alloys according to the ratio of e/a [71].

Figure 3.7 shows that the transformation temperatures and the crystal structures of

a Ni-Mn based Heusler alloy according to the ratio of e/a [71]. It can be seen from

Figure 3.7 that the martensite start temperature (Ms) is directly proportional to the e/a

ratio.

27

28

CHAPTER 4

METHODOLOGY

4.1 THEORETICAL STUDIES

4.1.1 Atomic Ordering Processes in Full Heusler Alloys

Ordered structures which occur in solid phases form symmetric patterns that repeat

along the principal directions of three-dimensional space in matter. The investigation

of the factors determining physical properties of solids is an important issue. Re-

cently, theoretical and experimental studies of atomic ordering processes in alloys

have led to a significant increase in the technological and scientific interest in materi-

als science. This is due to interesting properties of ordered structures like mechanical,

electrical and magnetic properties.

An intermetallic phase (also called an intermetallic compound, ordered intermetallic

alloy, and a long range ordered alloy) is a solid-state compound containing of two

or more elements. Also, it exhibits ordered crystal structure of the different atom

types. The quantitative explanations of the changes in the properties of intermetallic

phases are necessary to design and develop them with required properties. Although

a considerable number of theoretical and experimental studies have been devoted to

investigation of the superlattice formations in binary alloys, the theoretical and ex-

perimental works on ternary alloys have not been satisfactory, only a few studies are

known. This can be explained by requirement complicated treatment with too many

parameters for the ternary alloys. As a consequence, explaining the type of ordered

structure and the effect of temperature and composition on atomic ordering processes

are significant importance to improve treatments of ternary alloy systems.

29

The L21 crystal structure is a fully ordered atomic arrangement in full Heusler alloys,

however, B2-type partially disordered and A2-type fully disordered structures also

exist. Characterization of atomic ordering in the order-order (L21 ↔ B2) and order-

disorder (B2↔ A2) transitions in A2BC type Heusler alloys is an important concern.

Thus, atomic ordering processes in Heusler alloys can be qualitatively analysed by

using relatively simple analytical calculations based on the Bragg-Williams-Gorsky

(BWG) approximation. To model the order-disorder transitions in binary alloys, the

Bragg-Williams theory was investigated by W. L. Bragg and E. J. Williams in 1934

[72]. This theory on the binary alloys was developed by T. Hirone and T. Katayama

in order to research the impact of the third alloying element addition on the super-

lattice formation of CsCl-type [73]. S. Matsuda studied the superlattice formation in

ternary b.c.c. alloys by taking into consideration the interactions of the pairs between

first and second nearest neighbour atoms in the stoichiometric Cu2MnAl alloy [74].

Moreover, V. P. Fadin et al. investigated a model which is the formation of CsCl-type

superstructure of arbitrary compositions, however, their calculations were confined

only the interactions between first nearest neighbours [75]. Y. Murakami et al. es-

tablished a model for the ternary b.c.c. alloy of off-stoichiometric compositions in

β phase region by using the Bragg-Williams approximation and by taking into ac-

count the interactions between first and second neighbour atoms [76]. The derived

thermodynamical relations and the calculated L21 ↔ B2 and B2 ↔ A2 transition

temperatures were compared against experimental data from Au-Cu-Zn [77, 78] and

Au-Ag-Zn [79, 80] alloys in the study of Y. Murakami et al. In 1997, R. Kainuma

et al. analysed the L21 ↔ B2 transition temperatures in the Ni-Al-Ti-Fe system on

the basis of the BWG model by considering the interactions between the nearest and

next nearest neighbour atoms. [81]. The authors of [81], firstly, calculated the partial

ordering energies and then obtained the L21 ↔ B2 transition temperatures according

to the values of ordering energies. Furthermore, in this study, for the NiAl - Ni2AlTi

pseudobinary system, the theoretical values of L21 ↔ B2 transition temperatures

were compared with the experimental results obtained by thermal analysis. For Co-

Al-Ti ternary system, the ordering and phase separation were also investigated by R.

Kainuma et al. [82].

30

4.1.2 Methods of Theoretical Modelling and Simulation of Atomic Ordering

Processes in Full Heusler Alloys

In the theoretical part of this thesis, the partial ordering energies for the first two

coordination spheres calculated by means of the electronic theory of alloys in pseu-

dopotential approximation were used as input data in order to model the order-order

and order-disorder phase transformations in full Heusler alloys.

Firstly, the partial ordering energies between A-B, B-C and A-C pairs for the A2BC-

type Heusler alloys were determined by the help of a computer program which was

formulated based on Equations (4.32) and (4.33) by Prof. Dr. Amdulla Mekhrabov.

Secondly, these partial ordering energies were used as input data for models of Y.

Murakami et al. [76] and R. Kainuma et al. [81] which are explained below. By

using this method, the order-order (L21 ↔ B2) and order-disorder (B2↔ A2) critical

phase transformation temperatures were calculated for Ni50Mn50−xCx (C=Ga, In, Sb

and Sn) full Heusler alloys.

4.1.3 Calculation of the B2↔ A2 (Tc1) and L21 ↔ B2 (Tc2) Critical Trans-

formation Temperatures in A50B50−xCx Full Heusler Alloys

As explained in the previous section, Y. Murakami et al. [76] reported the statisco-

thermodynamical model which includes the order-disorder (B2 ↔ A2) and order-

order (L21 ↔ B2) transformations by containing interactions between first and sec-

ond neighbour atoms for b.c.c. structure near the β phase region. In A2BC-type fully

ordered Heusler structure, all A, B and C atoms are located on the α, β and γ sites,

respectively (Figure 4.1).

31

Figure 4.1: The unit cell of the L21-type ordered structure [76].

[α] + [β] + [γ] = N (4.1)

here N is the total number of atoms and the number of the α, β and γ sites can be

shown by [α], [β] and [γ], respectively. Let show the number of A, B and C atoms as

NA, NB and NC and the atomic fractions of A, B and C as χA, χB and χC respectively.

NA +NB +NC = N and χA + χB + χC = 1 (4.2)

If PαA and Aα symbolize respectively the probability and the number of A atom on α

site, then obviously,

PαA = [Aα] / [α] , P β

B = [Bβ] / [β] and P γC = [Cγ] / [γ] (4.3)

[Aα] + [Bα] + [Cα] = [α]

[Aβ] + [Bβ] + [Cβ] = [β] (4.4)

[Aγ] + [Bγ] + [Cγ] = [γ]

PαA + Pα

B + PαC = P β

A + P βB + P β

C = P γA + P γ

B + P γC = 1 (4.5)

2PαA + P β

A + P γA = 4χA

2PαB + P β

B + P γB = 4χB (4.6)

2PαC + P β

C + P γC = 4χC

32

The number of α sites is twice as many as that of β and γ sites. That is why the

factor 2 in terms including PαA, Pα

B and PαC in Equation (4.6) exists. When Pα

A, PβB,

PγC, and Pβ

A are chosen as independent parameters, Murakami et al. [76] proposed

four long range order parameters (LRO) of η1, η2, η3 and η4 which were defined by

the following relations;

η1 = 2(PαA − χA)

η2 =4

3(P β

B − χB)

η3 =4

3(P γ

C − χC) (4.7)

η4 = 2(χA − P βA)

The order parameters in L21, B2, and A2-type lattices can be described as follows.

• A perfectly ordered L21 lattice can be obtained for the stoichiometric A2BC

alloys, so all A, B and C atoms should occupy their original sites, that is,

PαA=Pβ

B=PγC=1 and Pβ

A=0, which lead to

η1 = η2 = η3 = η4 = 1 (4.8)

• Since in a perfectly ordered B2 lattice, the A atoms locate on their original

lattice site of in a perfectly ordered B2 lattice of α (PαA=1) and B and C atoms

occupy β and γ sites with an equal probability (PβB=(Pγ

C=1/2), and also PβA=0

then,

η1 = η4 = 1 and η2 = η3 = 1/3 (4.9)

• The complete disordered A2 lattice can be attained when there is a random

distribution of A, B and C atoms over α, β and γ sites;

η1 = η2 = η3 = η4 = 0 (4.10)

The potential energies of the pairs of the first and second neighbour atoms are denoted

by VAA, VBB etc. and WAA, WBB etc. respectively. Let the number of A-A, A-B etc.

pairs of the first and second neighbours be shown by QAA, QBB and PAA, PBB etc.

respectively. Moreover, the coordination numbers of the first and second neighbour

33

atoms are expressed by z (= 8) and y (= 6), respectively. Then, the numbers of atomic

pairs of the first neighbour atoms are given;

QAA =1

2(zNA −QAB −QAC)

QBB =1

2(zNB −QBA −QBC) (4.11)

QCC =1

2(zNC −QCA −QCB)

QAB = 2N(PαAP

βB + P β

APαB + Pα

APγB + P γ

APαB)

QAC = 2N(PαAP

βC + P β

APαC + Pα

APγC + P γ

APαC ) (4.12)

QBC = 2N(PαBP

βC + P β

BPαC + Pα

BPγC + P γ

BPαC )

and the number of atomic pairs of the second neighbour atoms are shown;

PAA =1

2(yNA − PAB − PAC)

PBB =1

2(yNB − PBA − PBC) (4.13)

PCC =1

2(yNC − PCA − PCB)

PAB =3

2N(2Pα

APαB + P β

APγB + P γ

APβB)

PAC =3

2N(2Pα

APαC + P β

APγC + P γ

APβC) (4.14)

PBC =3

2N(2Pα

BPαC + P β

BPγC + P γ

BPβC)

Therefore, the potential energies of the system considering interactions of atoms at

the first and second coordination spheres (E1 and E2) can be obtained as;

E1 = VAAQAA + VBBQBB + VCCQCC

+VABQAB + VBCQBC + VCAQCA (4.15)

E2 = WAAPAA +WBBPBB +WCCPCC

+WABPAB +WBCPBC +WCAPCA (4.16)

Then, the free energy of A2BC alloy system is given by [76];

F = E1 + E2 − TΦ (4.17)

34

where T is the temperature and Φ is the configurational entropy;

Φ = klnZ (4.18)

In Equation (4.18), Z is the number of ways arranging atoms on the α, β and γ sites

and it can be represented as;

Z =[α]!

[Aα]! [Bα]! [Cα]!· [β]!

[Aβ]! [Bβ]! [Cβ]!· [γ]!

[Aγ]! [Bγ]! [Cγ]!(4.19)

In order to calculate the order-disorder (B2↔ A2 - Tc1) and order-order (L21 ↔ B2 -

Tc2) critical phase transformation temperatures, the free energy should be minimized

with respect to the two LRO parameters η1 and η2 [76].

∂F

∂η1

=∂F

∂η2

= 0

and∂2F

∂η21

> 0,∂2F

∂η22

> 0,

(∂2F

∂η21

)(∂2F

∂η22

)−(

∂2F

∂η1∂η2

)2

> 0. (4.20)

The B2 ↔ A2 critical transformation temperature (Tc1) can be obtained at the tem-

perature where the free energy minimum condition (4.20) changes to the following

conditions [76];

η1 = η2 = 0

and(∂2F

∂η21

)(∂2F

∂η22

)−(

∂2F

∂η1∂η2

)2

= 0 (4.21)

Then solving Equation (4.21), Tc1 can be determined as [76];

Tc1 =8

k

(xA · xB ·WAB(R1) + (xA · xC ·WAC(R1) + (xB · xC ·WBC(R1))2

+[(xA · xB ·WAB(R1) + (xA · xC ·WAC(R1) + (xB · xC ·WBC(R1))2

−xA ·xB ·xC(4 ·WAC(R1) ·WBC)(R1−WAC(R1)−WAB(R1) +WBC(R1))2]1/2(4.22)

Furthermore, Tc2 can be written as [76];

35

Tc2 =3 ·WBC(R2)

k

[64 · χB · χC · (1− χA) · (1− χA + η1) + (5 · χB − χC) · (5 · χC − χB)η21]

8 · (1− χ2A) · (2− 2 · χA + η1)

(4.23)

Here k is the Boltzmann’s constant; WAB(R1), WAC(R1) and WBC(R1) are the par-

tial ordering energies for A-B, A-C, B-C atomic pairs at the first coordination sphere,

respectively and WBC(R2) represents the partial ordering energy at the second coor-

dination sphere for B-C atomic pair in A2BC Heusler alloys.

The partial ordering energies at the first coordination sphere for A-B, A-C and B-C

atomic pairs are expressed by

WAB(R1) = V AA(R1) + V BB(R1)− 2V AB(R1) (4.24)

WAC(R1) = V AA(R1) + V CC(R1)− 2V AC(R1) (4.25)

WBC(R1) = V BB(R1) + V CC(R1)− 2V BC(R1) (4.26)

where VAA(R1), VBB(R1), VCC(R1), VAB(R1), VAC(R1) and VBC(R1) are the pair-

wise interaction energies between the atoms of suffixed letters for the first coordina-

tion sphere.

For perfectly ordered L21-type superlattice, the L21 ↔ B2 critical transformation

temperature (Tc2) by considering Equation (4.8) can be rewritten as;

Tc2 =3 ·WBC(R2)

k

[64 · χB · χC · (1− χA) · (2− χA) + (5 · χB − χC) · (5 · χC − χB)]

8 · (1− χ2A) · (3− 2 · χA)

(4.27)

In addition, R. Kainuma et al. [81] proposed an approximation to analyse the ordering

reaction in the Ni-Al-Ti-Fe system by using BWG theory. In order to calculate the

36

L21 ↔ B2 critical transformation temperature (Tc2), R. Kainuma used the following

equation:

Tc2 =3

k·

Ω + [Ω2 − (4 ·WAC(R2) ·WBC(R2)− (WAC(R2

)

+WBC(R2)−WAB(R2))2) · (χA − η1) · (χB − η2) · (χC − η3)]1/2 (4.28)

where

Ω = (χA − η1) · (χB − η2) ·WAB(R2)

+(χB − η2) · (χC − η3) ·WBC(R2)

+(χA − η1) · (χC − η3) ·WAC(R2) (4.29)

ηi = (Pα1i + Pα2

i − Pβi − P

γi )/4 (4.30)

Here ηi is the value of the LRO parameter of the component i at Tc2 and PLi are the

occupation probabilities in sublattice site L (L=α1, α2, β, γ) [83]. In the β phase re-

gion (χA=1/2), when all A atoms locate on their original α sites (χA = η1, χB = −η2,

and χC = η3), then R. Kainuma et al. [81] obtained the following equation;

Tc2 =24

k·WBC(R2) · χC · (1/2− χC) (4.31)

4.1.4 Calculation of Partial Ordering Energies Using the Electronic Theory of

Ternary Alloys in Pseudopotential Approximation

The sign and magnitude of partial ordering energies between first and second nearest

neighbour atoms are needed in order to calculate order-disorder (Tc1) and order-order

(Tc2) critical phase transformation temperatures. However, the sign and magnitude of

the pair wise interatomic interaction potentials and/or partial ordering energies which

are constant parameters of theory in the statisco-thermodynamical approximations

cannot be determined by means of statistical methods. Thus, electronic theory of

ternary alloys in different approximations can be used to reach that aim [16].

37

The partial ordering energies, Wij(Rl), on the basis of electronic theory of multicom-

ponent alloys in the pseudopotential approximation can be determined by using the

following equations [84-87]

W ij(Rl) =Ω0

π2·∫ ∞

0

F ij(q) · sinqRl

qRl

· q2dq (4.32)

where

F ij(q) = −Ω0

8π·∣∣w0

i (q)− w0j (q)

∣∣2 ·q2 · ε(q)− 1

ε∗(q)+

2π

Ω0q2·∣∣Z∗i − Z∗j ∣∣2 · exp(− q2

4ϕ) (4.33)

In equations (4.32) and (4.33), Ω0 is the average atomic volume of the ternary alloy;

ε(q) is the dielectric constant in the Hartree approximation; ε∗(q) is the modified

dielectric constant which considers the correlation and exchange effects; w0i (q) and

w0j (q) are the form factors of unscreened pseudopotentials of i and j component ions,

respectively; Z∗i (Z∗j ) is the effective valency of the i(j) component atoms; ϕ is the

Ewald parameter.

4.2 EXPERIMENTAL STUDIES

4.2.1 Methods of Experimental Investigation of Structural and Magnetic Prop-

erties of Full Heusler Alloys

In the experimental part of this thesis, the preparation of sample of Ni-Mn-In Heusler

alloy and characterization of this sample are investigated. Furthermore, the experi-

mental investigations cover the magnetization measurements as a function of temper-

ature and external magnetic field to determine the MCE for Ni-rich Ni-Mn-In alloy.

4.2.1.1 Sample Preparation

Polycrystalline sample of Ni51Mn34In15 was prepared from high purity elements Ni

(99.99%), Mn (99.99%) and In (99.99%). In order to obtain the desired proportion,

these elements weighed and were mixed. The Ni51Mn34In15 sample was produced

38

by Edmund Buhler GmbH Arc Melter device using a water-cooled heart and non-

consumable tungsten electrode under argon atmosphere which is shown in Figure

4.2. Firstly, the mixture of constituent elements was placed on a copper-hearth inside

the arc melting chamber. The stainless steel chamber was evacuated up to 5× 10−5

mbar and rinsed with high purity argon gas for four times to remove any undesired

gas. Then, the specimen was turned over and remelted four times to provide homo-

geneity of the sample. After the melting process, the alloy was cut by using wire

erosion machine. For heat treatment, the ingot was vacuum sealed in a quartz tube

and annealed at 900C for 24 hours and 48 hours followed by quenching in ice water.

Figure 4.2: Arc melting device used for the production of sample.

4.2.2 Sample Characterization

In this thesis, to obtain more information about microstructural evolution, crystalliza-

tion phenomena and magnetic properties, various characterization techniques were

used. These techniques are described in brief below.

X-ray Diffraction (XRD)

X-ray diffraction is one of the techniques to get detail information about the crystal

structure of a material. XRD method using Bruker D8 Advance was utilized to carry

39

out the effects of composition and heat treatment on crystal structures in the samples

at RT. Cu-Kα radiation of wavelength 1.540562 Å was used in the diffraction angle

2Θ range of 20-120. By using qualitative analysis software, XRD patterns were

analysed.

Scanning Electron Microscopy (SEM) and Optical Microscopy

Microstructural investigations on the as-cast and heat treated Ni51Mn34In15 samples

were done by using FEI Nova Nano430 Scanning Electron Microscope (SEM). To

verify the general composition of samples, Energy Dispersive Spectroscopy (EDS)

analyses were employed. Moreover, optical microscopy was used to investigate of

the microstructure of the samples.

Vibrating Sample Magnetometer (VSM)

Magnetization measurements of samples were carried out using an ADE Magnetics

Model EV9 Vibrating Sample Magnetometer (VSM) (Figure 4.3) with an optional

temperature controller. Magnetization measurements were applied as a function of

temperature and magnetic field up to 18 kOe.

Figure 4.3: VSM used for magnetic measurements.

40

Measurements for MCE were done by following steps:

1. Magnetization measurements based on temperature (M-T) measurements: M-

T measurements were carried out both cooling and heating to investigate and

characterize the phase transformations.

2. Magnetic field dependent magnetization (M-H) measurements: To calculate

the MCE of the alloys, it is necessary to calculate the magnetic entropy changes

(∆SM). Therefore, isothermal M-H measurements were performed in the vicin-

ity of the phase transformation temperatures. In order to achieve demagnetiza-

tion, samples were heated above TC prior to each M-H measurements.

3. Determination of the magnetocaloric effect (MCE): In Heusler alloys, a large

magnetic entropy change occurs when the external magnetic field is applied

at the temperatures where the martensite transition is observed. This property

specifies whether the produced samples can be used in magnetic coolers or not.

The values of magnetic entropy change (∆SM) were calculated by employing

the M-H data in Equation (4.34).

∆SM(T,H) =∑i

Mi+1(Ti+1, H)−Mi(Ti, H)

Ti+1 − Ti∆H (4.34)

where Mi+1(Ti+1,H) and Mi(Ti,H) represent the values of the magnetization in

a magnetic field H at the temperatures Ti+1 and Ti, respectively.

41

42

CHAPTER 5

RESULTS AND DISCUSSIONS

This thesis contains two main parts as theoretical and experimental studies. First part

involves the modelling and simulation of relatively high temperature atomic ordering

processing in full Ni-Mn-C (C=Ga, In, Sb, Sn) Heusler alloys and second part cov-

ers experimental investigations on structural and magnetic properties, magnetocaloric

effect and relative cooling power of Ni-Mn-In Heusler alloy system.

5.1 MODELLING AND SIMULATION OF ATOMIC ORDERING PROCESSES

IN FULL HEUSLER ALLOYS

Theoretical part covers modelling and simulation studies of atomic ordering processes

in full Heusler alloys of Ni50Mn50−xCx (C=Ga, In, Sb, Sn) system, for which the or-

der–order (L21 ↔ B2) and order-disorder (B2 ↔ A2) phase transformation temper-

atures were calculated for 15 ≤ x ≤ 35 composition range. In addition, a variation

trend of L21 ↔ B2 critical phase transformation temperatures with the number of

valence electrons of C element atoms is presented.

To calculate the L21 ↔ B2 (order-order) and B2 ↔ A2 (order-disorder) transition

temperatures, the partial ordering energies calculated by means of the electronic the-

ory of alloys in pseudopotential approximation were used as input data for the models

of Y. Murakami et al. [76] and R. Kainuma et al. [81].

For the stoichiometric Ni2MnGa, Ni2MnIn, Ni2MnSb and Ni2MnSn alloys, the cal-

culated radii for the first (R1) and second (R2) coordination spheres from experimen-

tal lattice parameters (a) [43] are given in Table 5.1. While the radius of second

43

coordination sphere equals to lattice parameter (a = R2), the radius of first coordina-

tion sphere is determined as R1 = a√

32

.

Table 5.1: a, R1 and R2 values of the Ni50Mn50−xCx (C=Ga, In, Sb, Sn)

Alloy Ni2MnGa Ni2MnIn Ni2MnSb Ni2MnSn

a (at.u.) 5.529 5.734 5.673 6.047

R1 (at.u.) 4.788 4.966 4.913 5.237

R2 (at.u.) 5.529 5.734 5.673 6.047

The calculated partial ordering energies as a function of interatomic distance are

shown in Figures 5.1-5.4 for A-B, A-C and B-C pairs in the Ni2MnGa, Ni2MnIn,

Ni2MnSb and Ni2MnSn alloys. The sign changing and quasi-oscillatory character are

well-recognized property for metallic interactions. It can be seen from Figure 5.1-5.4

that the sign changing and quasi-oscillatory character are observed in the variation of

partial ordering energies for A-B, A-C and B-C pairs with interatomic distance for the

stoichiometric A2BC (A=Ni, B=Mn, C=Ga, In, Sb and Sn). This situation indicates

that the magnitudes of partial ordering energies are differ for A-B, A-C and B-C pairs

in terms of both quantity and sign.

44

Figure 5.1: Variation of partial ordering energies for Ni-Mn (green line), Ni-Ga (red

line) and Mn-Ga (blue line) pairs with interatomic distance for the stoichiometric

Ni2MnGa alloy. (1 at.u.(energy) = 2 Ry = 27.2 eV; 1 at.u.(length) = 0.529177 Å).

Figure 5.2: Variation of partial ordering energies for Ni-Mn (green line), Ni-In (red

line) and Mn-In (blue line) pairs with interatomic distance for the stoichiometric

Ni2MnIn alloy. (1 at.u.(energy) = 2 Ry = 27.2 eV; 1 at.u.(length) = 0.529177 Å).

45

Figure 5.3: Variation of partial ordering energies for Ni-Mn (green line), Ni-Sb (red

line) and Mn-Sb (blue line) pairs with interatomic distance for the stoichiometric

Ni2MnSb alloy. (1 at.u.(energy) = 2 Ry = 27.2 eV; 1 at.u.(length) = 0.529177 Å).

Figure 5.4: Variation of partial ordering energies for Ni-Mn (green line), Ni-Sn (red

line) and Mn-Sn (blue line) pairs with interatomic distance for the stoichiometric

Ni2MnSn alloy. (1 at.u.(energy) = 2 Ry = 27.2 eV; 1 at.u.(length) = 0.529177 Å).

46

Table 5.2: Calculated partial ordering energies for B-C atomic pairs at the second co-

ordination sphere for the Ni50Mn50−xCx (C=Ga, In, Sb and Sn) alloys (15 ≤ x ≤ 35).

Ni50Mn50−xCx

(at. %)

x

Partial Ordering Energies (x10−3)

WBC(R2) (at.u.)

C=Ga C=In C=Sb C=Sn

15 1.9101 2.8681 1.9005 1.0099

20 1.8921 2.7603 1.9539 1.0112

25 1.8649 2.6515 2.0017 1.0173

30 1.7784 2.5449 2.0458 1.0212

35 1.7531 2.4408 2.0867 1.036

According to the superlattice formation models of Y. Murakami et al. [76] and R.

Kainuma et al. [81], L21 ↔ B2 (order-order) phase transformation temperature, Tc2,

can be calculated by using the magnitudes of partial ordering energies for B-C atomic

pairs at the second coordination sphere. The values of calculated of these partial or-

dering energies for Ni50Mn50−xCx (C=Ga, In, Sb and Sn) alloys for x composition

range of 15 ≤ x ≤ 35 are given in Table 5. 2.

As can be seen from Table 5.2, WBC(R2) values increase when Mn is substituted

by Sb and Sn in Ni50Mn50−xSbx and Ni50Mn50−xSnx alloys, respectively. On the

other hand, substituting In and Ga for Mn in Ni50Mn50−xInx and Ni50Mn50−xGax

alloys tends to decrease in WBC(R2) values. It can be easily understood from Equa-

tions (4.27) and (4.31) that the order-order (L21 ↔ B2) critical phase transforma-

tion temperature, Tc2, is directly proportional to the WBC(R2), that is, when the

alloy has a greater WBC(R2) value, it has a higher order-order transition temperature.

Figure 5.5-5.8 display the calculated order-order (L21 ↔ B2) transition tempera-

tures for Ni50Mn50−xCx (C=Ga, In, Sb and Sn) alloys in the composition range of

15 ≤ x ≤ 35. According to these figures, it can be said that the model proposed

by Y. Murakami et al. [76] yields to lower order-order transformation tempera-

tures than that of model proposed by R. Kainuma et al. [81] for Ni50Mn50−xGax,

Ni50Mn50−xInx, Ni50Mn50−xSbx and Ni50Mn50−xSnx alloys.

47

Figure 5.5: Order-order transition temperatures calculated by using Equation (4.27)

(blue line) and Equation (4.31) (red line) for the Ni50Mn50−xGax alloy (15 ≤ x ≤ 35).


(blue line) and Equation (4.31) (red line) for the Ni50Mn50−xInx alloy (15 ≤ x ≤ 35).

48


(blue line) and Equation (4.31) (red line) for the Ni50Mn50−xSbx alloy (15 ≤ x ≤ 35).


(blue line) and Equation (4.31) (red line) for the Ni50Mn50−xSnx alloy (15 ≤ x ≤ 35).

49

In Figure 5.9, the L21 ↔ B2 transformation temperature, Tc2, as a function of num-

ber of valence electrons of C element atoms is given for the stoichiometric Ni2MnC

(C=In, Sn, Sb) Heusler alloys. As can be seen from Figure 5.9, order-order phase

transformation temperature decreases as number of valence electrons of C element

atoms increases. The number of valence electrons for In, Sn and Sb atoms is taken as

3, 4 and 5 respectively.

Figure 5.9: Order-order transformation temperatures as a function of number of va-

lence electrons at In, Sn and Sb sites for the stoichiometric Ni2MnIn, Ni2MnSn and

Ni2MnSb alloys.

To determine the order-disorder (B2↔ A2) phase transformation temperatures, Tc1,

via model proposed by Y. Murakami et al. [76] (Eq. (4.22)), the magnitudes of partial

ordering energies for A-B, A-C and B-C atomic pairs at the first coordination sphere

are required. The calculated values of the partial ordering energies for x composition

range of 15 ≤ x ≤ 35 of Ni50Mn50−xCx (C=Ga, In, Sb and Sn) alloys are given in

Tables 5.3–5.6.

50

Table 5.3: Calculated partial ordering energies for A-B, A-C and B-C atomic pairs at

the first coordination sphere for the Ni50Mn50−xGax (×10−3) (at.u.).

at. %C WAB(R1) WAC(R1) WBC(R1)

15 0.6121 -2.6226 -2.9446

20 0.6111 -2.6385 -2.9729

25 0.6101 -2.6524 -2.9984

30 0.6091 -2.6645 -3.0228

35 0.6081 -2.6754 -3.0452


the first coordination sphere for the Ni50Mn50−xInx (×10−3) (at.u.).


15 0.505 6.1549 3.8764

20 0.5014 5.8264 3.6121

25 0.5187 5.544 3.3784

30 0.498 5.2969 3.1718

35 0.4978 5.0841 2.9884


the first coordination sphere for the Ni50Mn50−xSbx (×10−3) (at.u.).


15 0.5465 15.9905 9.7995

20 0.5456 16.1704 9.9488

25 0.5446 16.3335 10.0843

30 0.5446 16.4828 10.2081

35 0.5436 16.4828 10.3205

51


the first coordination sphere for the Ni50Mn50−xSnx (×10−3) (at.u.).


15 0.5695 9.3027 4.0548

20 0.5675 9.3694 4.1033

25 0.5658 9.4339 4.5033

30 0.5648 9.4952 4.1956

35 0.5638 9.555 4.2389

The calculated order-disorder (B2 ↔ A2) critical phase transformation temperature,

Tc1, of Ni50Mn50−xInx alloy as a function of In alloying element composition in the

composition range of 15 ≤ x ≤ 35 is given in Figure 5.10. It is evident from Figure

5.10 that B2↔ A2 critical phase transformation temperature starts around 1700 K at

15 at.% of In, then linearly increases with increasing In content and reaches to a very

high temperature of 2700 K at 35 at.% In, which is above the alloys melting point.

Figure 5.10: Order-disorder transition temperature calculated by using Equation

(4.22) for Ni50Mn50−xInx alloy (15 ≤ x ≤ 35).

52

Thus, current predictions based on the statisco-thermodynamical theory of ordering

by means of BWG methods combined with the electronic theory of alloys in the pseu-

dopotential approximation, in regard to the modelling of the order-order (L21 ↔ B2)

and order-disorder (B2 ↔ A2) phase transformations in the complex Ni50Mn50−xCx

(C=Ga, In, Sb, Sn) full Heusler alloys are consistent qualitatively at the wide con-

centration range of 15 ≤ x ≤ 35, with experimental observations reported in the lit-

erature. However, there are small discrepancies between present calculations and

experimentally determined values of, Tc2 and Tc1, phase transformation tempera-

tures published in literature, which may be attributed to the assumptions made in the

calculation of partial ordering energies.

5.2 STRUCTURAL AND MAGNETIC PROPERTIES OF Ni-Mn-In FULL

HEUSLER ALLOYS

In this part, the experimental results are discussed by means of experimental methods

described in Chapter 4 for the Ni-Mn-In full Heusler alloys, focusing particularly

on the Ni51Mn34In15 alloy. For this alloy system, the effect of aging on the crystal

structures and the magnetic properties were investigated. Moreover, the MCE and

RCP were calculated for Ni-rich Ni-Mn-In full Heusler alloy.

As explained in Chapter 3, the e/a ratio has a crucial role on the structure and proper-

ties of full Heusler alloys. The Curie temperature, TC, and martensitic transformation

temperature, TM, can be normalized with e/a ratio. For Ni51Mn34In15 Heusler alloy,

the e/a ratio was calculated by using Equation (3.1) and given in Table 5.7.

Table 5.7: Compositions and e/a ratio for the Ni51Mn34In15.

Nom. Comp. Ni (at.%) Mn (at.%) In (at.%) e/a

Ni51Mn34In15 51 34 15 7.93

53

Effects of Aging on Crystal Structure:

To investigate the effect of the heat treatment process at 1173 K for 24 and 48 hours

on crystal structure in Ni51Mn34In15 Heusler alloy, XRD measurements were per-

formed within the scope of this thesis study. After the heat treatment processes, rapid

cooling was applied to prevent the formation of intermediate phases in alloy. Fig-

ures 5.11-5.13 present the room temperature (RT) XRD patterns of the as-cast and

aged Ni51Mn34In15 alloy which was examined with Cu-Kα radiation of wavelength

1.540562 Å.

Figure 5.11: XRD pattern for the as-cast Ni51Mn34In15 alloy measured at RT.

54

Figure 5.12: XRD pattern for the 24 hours-aged Ni51Mn34In15 alloy measured at RT.

Figure 5.13: XRD pattern for the 48 hours-aged Ni51Mn34In15 alloy measured at RT.

55

The Ni-Mn-In alloy belongs to the family of Heusler alloy which crystallize in the

L21- type structure. The three types of reflections are observed in the XRD pattern of

a Heusler alloy [8].

1. h, k, l all odd,

2. h, k, l all even and h+k+l2

= 2n + 1,

3. h, k, l all even and h+k+l2

= 2n.

The reflections with h+k+l=4n are called as the principal reflections. While the group

with h,k,l all odd is designated as type – I superlattice reflections, the other group

with h+k+l=4n+2 is categorised as type – II superlattice reflections [8].

Because of texturing in the Ni51Mn34In15 alloy, there is no correlation between the

intensities of some principal reflections and the type – I and type – II superlattice

reflections indicating of the presence of L21 structure were not observed in some

instances.

As seen in Figures 5.11–5.12, peaks associated with the fully disordered A2 phase,

partially disordered B2 phase and fully ordered L21 phase are present for the as-

cast and 24 hours-aged Ni51Mn34In15 alloy, respectively. Ni, Mn and In atoms are

randomly sited over the body centred lattice sites in the fully disordered A2 phase

and partially disordered B2 phase occur due to random distribution of Mn and In

atoms in the unit cell of Ni51Mn34In15 alloy (Figure 3.4). It is evident from Figure

5.13 that after the second aging (at 900C for 48 h), all the peaks in the XRD pattern

of Ni51Mn34In15 alloy can be indexed according to the L21 – type ordered crystal

structure. The unit cell parameters and space group of Ni51Mn34In15 sample are

found as 6.024 and Fm-3m no. 225, respectively, which agree well with the results

reported by F. X. Hu et al. [88] for the nearby nominal composition.

The microstructure of the Ni51Mn34In15 alloy was examined by optical microscopy

using a solution with 2% Nital. The optical microscope images for as-cast, 24 hours-

aged and 48 hours-aged alloy with and without etching at various magnifications are

shown in Figures 5.14-5.16, respectively. As seen from these figures, along the grain

boundaries, there are some cracks due to brittle structure of this alloy system.

56

Figure 5.14: Optical microscopy images of various magnifications for the as-cast

Ni51Mn34In15 alloy.

Figure 5.15: Optical microscopy images of various magnifications for the 24 hours-

aged Ni51Mn34In15 alloy.

57

Figure 5.16: Optical microscopy images of various magnifications for the 48 hours-


The samples of before and after heat treatment of Ni51Mn34In15 alloy produced in

thesis study were investigated by means of Scanning Electron Microscope (SEM).

Firstly, it was aimed to obtain the alloy with close composition with the composition

of the target material. Energy Dispersive Spectroscopy (EDS) analysis was performed

with SEM in the direction of this target in order to determine the general composi-

tions of the alloy. The compositional analysis was carried out from two different

regions of the alloy (Table 5.8). It can be seen that each region are very close to each

other in terms of composition, showing that the alloy was produced homogeneously.

Furthermore, when the average composition values are considered, it is seen that the

composition of target is close to the desired composition of alloy.

58

Table 5.8: The composition values from different regions of the alloy.

Element 1. Reg. (at. %) 2. Reg. (at. %) Av. (at. %) Av. e/a

Ni 51.1 15.5 51.5

Mn 33.4 32.7 33.1 7.93

In 15.5 15.3 15.4

The SEM images and EDS result of the as-cast Ni51Mn34In15 alloy are given in Figure

5.17 and Figure 5.18, respectively. According to the SEM analysis, the alloy was

found to be in the desired composition, but not homogeneous. As it can be seen in

Figure 5.17, light and dark areas were observed in the alloy. These regions show that

Mn-In amounts are not evenly distributed, which means that partially disordered B2

phase exists in the as-cast Ni51Mn34In15 alloy. According to the EDS analysis (Table

5.9), the as-cast alloy was found to be very close to the desired composition. (Percent

error demonstrates the difference between the EDS results of atomic percent and the

nominal atomic percent when compared to the nominal atomic percent expressed in

percent format.)

Figure 5.17: SEM images of various magnifications for the as-cast Ni51Mn34In15

alloy.

59

Figure 5.18: EDS results of the as-cast Ni51Mn34In15 alloy.

Table 5.9: EDS analysis result of the as-cast Ni51Mn34In15 alloy for selected region.

ElementAtomic per.

(at. %)

Percent

error (%)

Ni 51.4 0.78

Mn 33.3 2.1

In 15.3 2

In order to ensure the homogeneity of the alloy in terms of composition and to obtain

the desired phase, heat treatments were applied. The formation of any intermedi-

ate phases was prevented by applying rapid cooling processes to the alloy after heat

treatments. The SEM images and EDS results of the Ni51Mn34In15 alloy after heat

treatment processes are given in Figures 5.19-5.22. The Ni51Mn34In15 alloy was ob-

tained in homogeneous and desired composition after aging of 900C for 48 hours.

60

Figure 5.19: SEM images of various magnifications for the 24 hours-aged

Ni51Mn34In15 alloy.

Figure 5.20: EDS results of the 24 hours-aged Ni51Mn34In15 alloy.

61

Table 5.10: EDS analysis result of the 24 hours-aged Ni51Mn34In15 alloy for selected

region.

ElementAtomic per.

(at. %)

Percent

error (%)

Ni 51.1 0.19

Mn 33.4 1.76

In 15.5 3.33

Figure 5.21: SEM images of various magnifications for the 48 hours-aged

Ni51Mn34In15 alloy.

Figure 5.22: EDS results of the 48 hours-aged Ni51Mn34In15 alloy.

62

Table 5.11: EDS analysis result of the 48 hours-aged Ni51Mn34In15 alloy for selected

region.

ElementAtomic per.

(at. %)

Percent

error (%)

Ni 51.2 0.39

Mn 33.7 0.88

In 15.1 0.67

After the heat treatments, martensite variants with the lamellar microstructure are

observed in the Ni51Mn34In15 alloy according to the SEM images. These marten-

site variants consist of packets which are either plate- or spear-shaped. During phase

transformation, self-established microstructures are constituted by means of marten-

site variants. In the SEM images, these martensite variants which form with different

orientations are observed without any compositional contrast. The absence of any

contrast difference in the SEM images indicates that the alloy composition is homo-

geneously dispersed. According to the EDS results (Tables 5.9-5.11), it was found

that the actual compositions of the Ni51Mn34In15 alloy are very close to the nominal

ones; but, there are small composition differences in this alloy system.

Effects of Aging on the Magnetic Properties and Phase Transitions:

In this study, how the aging processes affect the magnetic properties of Ni51Mn34In15

Heusler alloy were also investigated. Hysteresis curves (RT M-H curves) of the as-

cast, 24 hours-aged and 48 hours-aged Ni51Mn34In15 alloy are given in Figure 5.23,

Figure 5.24 and Figure 5.25, respectively.

63

Figure 5.23: Hysteresis loop for the as-cast Ni51Mn34In15 alloy measured at RT, inset

shows the hysteresis in more detail.

Figure 5.24: Hysteresis loop for the 24 hours-aged Ni51Mn34In15 alloy measured at

RT, inset shows the hysteresis in more detail.

64

Figure 5.25: Hysteresis loop for the 48 hours-aged Ni51Mn34In15 alloy measured at

RT, inset shows the hysteresis in more detail.

As seen from Figures 5.23-5.25, even if relatively small magnetic fields were ap-

plied, large magnetization was acquired in the Ni51Mn34In15 alloy and saturation

magnetization was achieved above H=16 kOe magnetic field. It is evident that the

Ni51Mn34In15 alloy behaves ferromagnetic characteristics. The ferromagnetic materi-

als are classified in accordance with their hysteresis characteristics and the magnitude

of HC coercive force as soft or hard magnetic materials. Soft ferromagnetic materials

should have a high initial permeability and a low coercivity. The magnetic parameters

obtained from the RT M-H measurements are given in Table 5.12.

65

Table 5.12: Magnetic parameter values of the Ni51Mn34In15 alloy.

HC Mr HS MS

Max.

perm.BHmax

As-cast

alloy1.287 5.27×10−3 1.6304×104 22.22 3.39×10−4 8090

24h-aged

alloy0.833 1.71×10−3 1.6406×104 22.15 6.84×10−5 3500

48h-aged

alloy1.228 2.51×10−3 1.6305×104 19.6 1.41×10−4 6380

HC (Oe)- Coercive force; Mr (emu/g)– Remanent magnetization (M at H=0); HS

(Oe) – Saturation field; MS (emu/g) -Saturation magnetization; Maximum perme-

ability (emu/Oe); BHmax (MGsOe) – Maximum energy loss of hysteresis loop.

It is evident from this table that the Ni51Mn34In15 alloy shows a low hysteresis loss,

a low remanent magnetization, a low coercive force and a high saturation magnetiza-

tion and thus, this alloy exhibits soft ferromagnetic behaviour. In addition, the area

under the hysteresis curves are small leading to low energy losses under alternating

magnetic fields, which are the most efficient and/or desired magnetic characteristics

for magnetocaloric materials. Moreover, it can be seen from Table 5.12 that when

the duration of heat treatment process increases, the saturation magnetization slightly

decreases.

Furthermore, temperature and magnetic field dependent magnetization measurements

were carried out in order to determine the magnetocaloric properties of Ni51Mn34In15

alloy. The magnetic entropy changes (∆SM) of the samples were calculated from the

magnetic field dependent magnetization measurements. Then, the relative cooling

power (RCP) of the magnetocaloric material was calculated according to the magnetic

entropy changes.

Temperature dependent magnetization under 500 Oe and 1 T fields was measured

and Figures 5.26, 5.27 and 5.28 show these measurement results for the as-cast, 24

66

hours-aged and 48 hours-agedNi51Mn34In15 alloy, respectively.

(a)

(b)

Figure 5.26: Temperature dependent magnetizations measured for the as-cast

Ni51Mn34In15 alloy under fields (a) 500 Oe (b) 1 T.

67

(a)

(b)

Figure 5.27: Temperature dependent magnetizations measured for the 24 hours-aged


68

(a)

(b)

Figure 5.28: Temperature dependent magnetizations measured for the 48 hours-aged


69

These temperature dependent magnetization, M-T, measurements were realised be-

tween 200 K and 350 K under the field cooling (FC) and the field heating (FH) con-

ditions. As a result of these measurements, the critical ferromagnetic-paramagnetic

transition temperatures (Curie temperatures, TC) of each sample were determined.

If some alloy undergoes also the structural phase transformation in the ferromag-

netic region, then there should be a thermal hysteresis in between FC and the FH

curves. When the magnetization graphs in the Figures 5.26-5.28 are examined, a

thermal hysteresis is observed between the measurements taken in the direction of

heating and cooling. The thermal hysteresis between the FC and FH curves in the

M versus T graphs indicate that the samples have coupled structural-magnetic phase

transitions around room temperature. The magnitude of thermal hysteresis can be cal-

culated from austenite start and martensite final temperatures (Th = As −Mf). The

Ni51Mn34In15 alloy shows ferromagnetic behaviour under TC, while it shows param-

agnetic property above TC. The austenite-martensite structural phase transition tem-

peratures of the samples were determined from the M-T curves, as shown in Figure

5.26. Also, the martensitic transformation temperature was calculated from marten-

site start and martensite final temperatures, such as TM = Ms+Mf

2. The structural and

magnetic phase transition temperatures, magnitudes of the thermal hysteresis and the

martensitic transformation temperatures of the samples are given in Tables 5.13-5.14.

70

Table 5.13: The structural and magnetic phase transition temperatures, values

of the thermal hysteresis and the martensitic transformation temperatures of the

Ni51Mn34In15 alloy under 500 Oe field.

Ms

(K)

Mf

(K)

As

(K)

Af

(K)

TC

(K)

Th

(K)

TM

(K)

As-cast

alloy280 243 246 282 298 3 261.5

24 h-aged

alloy289 272 288 296 304 16 280.5

48 h-aged

alloy296 293 298 305 312 5 294.5

As it can be seen from these Tables 5.13-5.14, there is a slight increase in the both

structural and magnetic transition temperatures with the increase of the magnetic field

strength from 500 Oe to 1 T. Furthermore, the increase in the magnetic field strength

does not expand the thermal hysteresis too much for all samples under investigation.

The presence of small thermal hysteresis is a preferred property in magnetocaloric

materials which can be used for magnetic refrigeration applications [88]. Therefore,

the Ni51Mn34In15 alloy can be considered as an attractive MCE material for magnetic

refrigerations.

71

Table 5.14: The structural and magnetic phase transition temperatures, values

of the thermal hysteresis and the martensitic transformation temperatures of the

Ni51Mn34In15 alloy under 1 T field.

Ms

(K)

Mf

(K)

As

(K)

Af

(K)

TC

(K)

Th

(K)

TM

(K)

As-cast

alloy281 232 243 284 308 11 256.5

24 h-aged

alloy298 288 288 297 306 9 293

48 h-aged

alloy301 290 298 311 318 8 295.5

Table 5.15: The structural and magnetic phase transition temperatures the

Ni50Mn34In16.

Ms (K) Mf (K) As (K) Mf (K) TC (K) TM (K)

Ni50Mn34In16 210 175 200 230 305 192.5

72

In addition, the structural and magnetic transition temperatures taken from literature

for the Ni50Mn34In16 alloy are given in the Table 5.15 [89]. Comparison of data given

in Tables 5.13-5.14 and 5.15 indicate that MCE properties of Ni-Mn-In full Heusler

alloys are very sensitive to the composition of constituent elements. Little increase

in Ni content in present study (Ni51Mn34In15) tend to improve MCE properties lead-

ing to increase both the structural and magnetic transition temperatures closer to RT,

which is another necessary criteria for application of MCE materials in magnetic re-

frigeration systems.

Furthermore, in this thesis study, the magnetocaloric properties of the Ni51Mn34In15

Heusler alloy which exhibits the magneto-structural phase transition near RT were in-

vestigated. The MCE is a significant parameter because magnetic cooling efficiency

solely depends on the MCE of the magnetic materials. That is why, it is vital to

calculate the magnetic entropy change (∆SM) in order to define the magnetocaloric

property of the magnetic materials. The magnitude of the MCE in magnetic materi-

als can be determined by providing two different experimental methods: direct and

indirect. In direct measurements, the temperature change in the magnetic material is

measured directly by changing magnitude of applied magnetic field. In the indirect

method, on the other hand, the MCE of the material is determined by providing M-

T measurements around magneto-structural phase transition temperatures. The main

advantage of the indirect measurement method is that both the isothermal magnetic

entropy change (∆SM) and the adiabatic temperature change (∆Tad) values can be

calculated. In this thesis study, the MCE was determined by indirect measurement

method and magnitudes of ∆SM was calculated from the magnetization data by using

Equation (4.34) in a magnetic field change of ∆H=18 kOe.

The thermal hysteresis in the samples observed in the vicinity of the TC before and

after the heat treatments indicates a magneto-structural phase transformation in the

Ni51Mn34In15 alloy. The magnetic entropy change (∆SM) is directly proportional

to (∂M/∂T) (Equation (4.34)), so it is expected that this alloy should show a high

magnetic entropy change around the TC. The isothermal M-H measurements were

performed in the vicinity of magneto-structural phase transformation temperatures of

the Ni51Mn34In15 alloy in order to calculate magnitude of ∆SM. Figure 5.29, Figure

5.30 and Figure 5.31 display the isothermal M-H graphs for the as-cast, 24 and 48

73

hours-aged Ni51Mn34In15 alloy, respectively.

Figure 5.29: Magnetization of the as-cast Ni51Mn34In15 alloy as a function of mag-

netic field measured in the temperature interval of 233 K<T<313 K, ∆T=6K for clar-

ity.

Figure 5.30: Magnetization of the 24 hours-aged Ni51Mn34In15 alloy as a function of

magnetic field measured in the temperature interval of 255 K<T<335 K, ∆T=4K for

clarity.

74

Figure 5.31: Magnetization of the 48 hours-aged Ni51Mn34In15 alloy as a function of

magnetic field measured in the temperature interval of 253 K<T<353 K, ∆T=4K for

clarity.

The temperature steps in M-H measurements were taken as 6 K for the as-cast and as

4 K for the 24 and 48 hours-aged Ni51Mn34In15 alloy under magnetic fields up to 18

kOe. It easily can be seen from these figures that magnetization values are relatively

small at high temperatures in comparison with low temperature values and magne-

tization values increases upon cooling for all samples. In addition, upon cooling,

the curvature of the M-H curves increases; however, M-H curves are linear at high

temperatures.

Figures 5.32, 5.33 and 5.34 show variation of calculated ∆SM as a function of tem-

perature for the as-cast, 24 hours-aged and 48 hours-aged Ni51Mn34In15 alloy, respec-

tively.

75

Figure 5.32: Magnetic entropy change of the as-cast Ni51Mn34In15 alloy.

Figure 5.33: Magnetic entropy change of the 24 hours-aged Ni51Mn34In15 alloy.

76

Figure 5.34: Magnetic entropy change of the 48 hours-aged Ni51Mn34In15 alloy.

It is seen from these figures that the maximum magnitudes of ∆SM are 4.8 J/kg ·K,

5.6 J/kg ·K and 12.8 J/kg ·K at 271 K, 294 K and 305 K temperatures for the as-

cast, 24 and 48 hours-aged Ni51Mn34In15 alloy, respectively. As it is expected, the

magnitudes of ∆SM are greater for heat-treated samples in comparison of ∆SM for as-

cast sample. The positive ∆SM values indicate that the Ni51Mn34In15 alloy exhibits

inverse MCE around the TM. The calculated magnitudes of ∆SM for Ni51Mn34In15

Heusler alloy are comparable with data published in literature for similar Heusler

alloys [89].

One of the most important factors for determining the efficiency of magnetocaloric

material is the relative cooling power (RCP) of the material. The material to be used

in magnetic refrigerants is expected to have high relative cooling power. RCP shows

the amount of heat transferred during cooling in an ideal magnetic refrigeration cycle.

The refrigerant capacity (RC) and relative cooling power (RCP) of the magnetocaloric

material can be calculated by using following Equations [90]:

RC =

∫ Thot

Tcold

∆SM(T )∆HdT (5.1)

and

RCP = −∆SM(max) × FWHM (5.2)

77

where FWHM is the full width at half maxima of the ∆SM curve and it is shown in

Figure 5.35 [90].

Figure 5.35: Schematic representation of temperature-dependent magnetic entropy

change.

Calculated based on the magnetic entropy changes, RC and RCP values of the as-

cast, 24 and 48 hours-aged Ni51Mn34In15 alloy are given in Table 5.16. It is evi-

dent from Table 5.16 that magnitudes of both the refrigerant capacity and the relative

cooling power of the Ni51Mn34In15 alloy increases after the heat treatment processes.

For the comparison with literature, RC and RCP values of CoMn0.95V0.05Ge and

CoMn0.90V0.10Ge Heusler alloys [90] are given in the Table 5.17, which show that

the alloy under investigation, Ni51Mn34In15 alloy, have better MCE properties.

78

Table 5.16: RC and RCP values of the as-cast, 24 hours-aged and 48 hours-aged of

Ni51Mn34In15 alloy.

RC (J/kg) RCP (J/kg)

As-cast alloy 151.8 144

24 h-aged alloy 192 190.4

48 h-aged alloy 614.3 510.4

Table 5.17: RC and RCP values of the as-cast and aged of CoMn0.95V0.05Ge and

CoMn0.90V0.10Ge alloys [90].

CoMn0.95V0.05Ge CoMn0.90V0.10Ge

As-cast Aged As-cast Aged

RC (J/kg) 270 295 473 378

RCP (J/kg) 230 257 387 327

79

80

CHAPTER 6

SUMMARY AND CONCLUSIONS

6.1 SUMMARY OF FINDINGS

The aim of this thesis is to develop Ni-based Heusler alloys, by means of theoretical

and experimental studies, for magnetic refrigeration applications which are environ-

mentally friendly cooling technology. Firstly, the most appropriate Ni-based Heusler

alloy and its composition were determined by providing theoretical, modelling and

simulation analysis. Then, the structural and magnetic properties of this alloy, its

magnetocaloric effect (MCE) and relative cooling power (RCP) were investigated by

applying various experimental techniques. These theoretical and experimental stud-

ies are summarized as follows:

A. Theoretical Studies

In the theoretical part, the L21 ↔ B2 (order-order) and B2 ↔ A2 (order-disorder)

critical phase transformation temperatures in Ni50Mn50−xCx (C= Ga, In, Sb and Sn)

full Heusler alloys were calculated based on the statisco-thermodynamical theory of

ordering by means of BWG methods combined with the electronic theory of alloys in

pseudopotential approximation. It was shown that:

• Partial ordering energies with interatomic distance dependences have quasi-

oscillatory and sign changing character, a well-known feature for metallic in-

teractions. This suggests that the magnitudes of partial ordering energies may

differ for different pairs (A-B, A-C and B-C), not only in terms of quantity but

also in terms of sign;

81

• The variation of L21 ↔ B2 transformation temperature as a function of com-

position, x, shows a parabolic behaviour for both theoretical predictions and

experimentally reported data;

• The order-order phase transformation temperatures show that the model pro-

posed by Y. Murakami et al. yields to lower order-order transformation tem-

peratures than that of model proposed by R. Kainuma et al. for Ni50Mn50−xCx

(C=Ga, In, Sb, Sn) full Heusler alloys;

• The order-disorder (B2↔ A2) critical phase transformation temperatures would

occur at very high temperatures even above the melting point of the Ni50Mn50−xCx

(C=Ga, In, Sb, Sn) alloys. This would tend to suggest that B2 ordered super-

structure could prevail in the liquid state which makes the experimental deter-

mination of transformation temperatures impractical.

Current predictions based on the statisco-thermodynamical theory of ordering by

means of BWG methods combined with the electronic theory of alloys in the pseu-

dopotential approximation, in regard to the modelling of the order-order (L21 ↔ B2)

and order-disorder (B2 ↔ A2) phase transformations in the complex Ni50Mn50−xCx

(C=Ga, In, Sb, Sn) full Heusler alloys are consistent qualitatively at the wide concen-

tration range of 15 ≤ x ≤ 35, with experimental observations reported in the litera-

ture.

By using these results, Ni-Mn-In alloy system was chosen and the experimental stud-

ies were carried out for Ni51Mn34In15 alloy.

B. Experimental Studies

In the experimental part of this thesis, the alloy in the desired composition was first

prepared by arc furnace technique. Then, the heat treatment processes were applied

at 1173 K for 24 and 48 hours. To investigate the effect of heat treatment processes on

structural and magnetic properties of Ni51Mn34In15 Heusler alloy, XRD, SEM, EDS

and VSM techniques were used:

• Before and after the first heat treatment processes (at 900C for 24 hours) of

Ni51Mn34In15 alloy, A2, B2 and L21 phases were detected in samples according

82

to the XRD analyses. On the other hand, after the second heat treatment (at

900C for 48 h), all the peaks in the XRD pattern of Ni51Mn34In15 alloy were

indexed according to the L21–type crystal structure;

• It was shown that XRD results are consistent with SEM analyses in terms of

phases present. After the heat treatments, martensite variants with the lamel-

lar microstructure were observed in Ni51Mn34In15 alloy according to the SEM

images. In addition, EDS analyses were performed to determine the general

compositions of the alloy. According to the EDS results, it was found that the

actual compositions of Ni51Mn34In15 alloy are very close to the nominal ones;

but, there is small composition differences in this alloy system;

• Furthermore, room temperature (RT) M-H, magnetization-temperature depen-

dence (M-T) and isothermal M-H measurements were carried out using VSM

technique. Hysteresis curves (RT M-H curves) showed that Ni51Mn34In15 al-

loy behaves strongly a ferromagnetic behaviour and ferromagnetic L21 phase is

presented in this alloy. The M-T graphs showed that the samples have structural

phase transitions around RT because of the presence of thermal hysteresis be-

tween the field cooling (FC) and field heating (FH) curves. It was observed that

when magnetic field is increased, the structural transition and Curie tempera-

ture (TC) slightly increases, but the thermal hysteresis did not change much;

• The magnetic entropy changes (∆SM) of the samples were calculated from the

magnetic field dependent magnetization measurements. It was shown that the

maximum of ∆SM reaches the magnitudes of 4.8 J/kg ·K, 5.6 J/kg ·K and

12.8 J/kg ·K at 271 K, 294 K and 305 K temperatures at magnetic field change

of ∆H=18 kOe for the as-cast, 24 hours-aged and 48 hours-aged Ni51Mn34In15

alloy, respectively. Consequently, large magnetic entropy changes with positive

sign were observed in wide temperature ranges and these positive ∆SM values

indicate that this alloy exhibits inverse MCE around the martensitic transfor-

mation temperature (TM). Moreover, the refrigerant capacity (RC) and relative

cooling capacity (RCP) values of all samples were calculated based on the mag-

netic entropy changes. Results of calculations reveal that application of heat

treatment processes tends to increase magnitude of RC and RCP parameter of

Ni51Mn34In15 Heusler alloy.

83

6.2 CONCLUSION

The theoretical studies covers modelling of atomic ordering processes in Ni50Mn50−xCx

(C=Ga, In, Sb, Sn) full Heusler alloys. To calculate the L21 ↔ B2 (order-order) and

B2 ↔ A2 (order-disorder) transition temperatures of Ni50Mn50−xCx (C=Ga, In, Sb,

Sn) alloys, the partial ordering energies for the first two coordination spheres calcu-

lated by means of the electronic theory of alloys in pseudopotential approximation

of these alloys were used as input data for the models of Y. Murakami et al. and

R. Kainuma et al. Firstly, the partial ordering energies between A-B, B-C and A-C

pairs for the A2BC-type Heusler alloys were determined by the help of a computer

program which was formulated by Prof. Dr. Amdulla Mekhrabov. Then, the order-

order and order-disorder critical phase transformation temperatures were calculated

for Ni50Mn50−xCx (C=Ga, In, Sb, Sn) full Heusler alloys. The theoretical studies

were utilized in order to predict potential alloying type (C element) and its composi-

tion in Ni50Mn50−xCx (C=Ga, In, Sb, Sn) Heusler alloys that undergo magnetically

induced simultaneous coupled structural-magnetic phase transformations near room

temperature, resulting in creation a giant magnetocaloric effects (MCE).

In the experimental part, by using the results obtained from the theoretical predic-

tions, Ni-Mn-In alloy system was chosen and structural and magnetic analyses of

Ni51Mn34In15 alloy were performed. By applying a proper heat treatment processes,

formation of stable L21-type ordered structure in Ni51Mn34In15 alloy was achieved,

which is most desirable structure for magnetocaloric applications. It was shown that

Ni51Mn34In15 alloy undergoes a magneto-structural transition around RT. Also, an

inverse MCE around TM and high RC and RCP were obtained in this alloy. In con-

clusion, a little excess of Ni improved the ∆SM, RC and RCP and these results make

Ni51Mn34In15 alloy attractive for magnetic refrigeration applications.

6.3 FUTURE WORKS

For future work, the structural, magnetic, magnetocaloric, as well as thermal and

magnetoresistance properties of the Ni-Mn-In Heusler alloys would be investigated in

detail. In addition to that, the electrical properties of Heusler alloys can be measured

84

as function of temperature and magnetic field by using Physical Properties Measure-

ment System. Furthermore, the effect of Fe, Co etc. fourth elements on the structural

and magnetic properties of ternary Ni-Mn-C (C=In, Sb, Sn) Heusler alloys should be

investigated in order to increase MCE properties.

85

86

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94

APPENDIX A

OPTICAL MICROSCOPY IMAGES

Appendix A demonstrates the optical microscope images with and without etching at

various magnifications for the as-cast, first and second aged Ni51Mn34In15 alloy. It is

seen that some cracks exist along the grain boundaries because of brittle structure of

this alloy system.

Figure A.1: Optical microscopy images of various magnifications for the as-cast

Ni51Mn34In15 alloy.

95

Figure A.2: Optical microscopy images of various magnifications for the 24 hours-


96

Figure A.3: Optical microscopy images of various magnifications for 48 hours-aged

Ni51Mn34In15 alloy.

97

98

APPENDIX B

SCANNING ELECTRON MICROSCOPY IMAGES

Appendix B shows the SEM images of various magnifications for all samples. The

light and dark areas in the as-cast alloy indicates that Mn-In amounts are not evenly

distributed. This situation shows that the partially disordered B2 phase exists in

Ni51Mn34In15 alloy. However, after heat teratment processes, formation of stable

L21-type ordered structure in this alloy was achieved. Also, the alloy composition is

homogeneously dispersed because of the absence of any contrast difference.

Figure B.1: SEM images of various magnifications for the as-cast Ni51Mn34In15 alloy.

99

Figure B.2: SEM images of various magnifications for the 24 hours-aged

Ni51Mn34In15 alloy.

100

Figure B.3: SEM images of various magnifications for the 48 hours-aged

Ni51Mn34In15 alloy.

101

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DESIGN AND DEVELOPMENT OF NI-BASED HEUSLER ALLOYS …