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European Master in Material Science EMMS

Project Work Report

Magnetocaloric effect of Pr(Ni,Co)5 hard magnets and

Ni2Mn(Ga,Bi) shape memory alloys

Rodrigo Pacher Fernandes

Universidade de Aveiro

Aveiro, February 2007

Preface

The present report has been submitted in partial fulfilment of the requirements for the

degree of Master of Science in the European Master in Materials Science (EMMS) pro-

gram.

This project work has been carried out during the course of the winter semester

2006/2007, from September 2006 to February 2007, at the Physics department in the

University of Aveiro. The project was supervised by Professor Dr.Vitor Bras Sequeira

Amaral, and Dr. Mario de Souza Reis Junior.

The author would like to acknowledge the important role of the collaboration network

in the development of this work, specially to MSc. Joao Cunha de Sequeira Amaral, from

Aveiro University, MSc. Andre M. T. Pereira, Prof. Dr. Joao Pedro Esteves de Araujo,

from Porto University, Prof. Dr. Pedro Bandeira Tavares, Eng. Nuno Martins, from

Tras-os-Montes and Alto Douro University.

i

Abstract

The conventional vapor-cycle refrigeration technology has achieved its limits. Even the

most efficient units operate well below the maximum theoretical efficiency (Carnot cycle)

and few improvements may be possible. In the search for more efficient and environmental

friendly alternatives the magnetic refrigeration, based on the magnetocaloric effect(MCE),

has been one of the most promising technologies.

The MCE is detected as the heating or cooling of magnetic materials due to a change of

magnetic field, with a maximum effect close to the magnetic ordering temperature (Curie

temperature, TC) in ferromagnets. Nowadays, most of the effort in magnetic refrigeration

to work at room temperature (RT) is made in searching the best magnetic material; with

large MCE in a wide temperature range around RT, with a competitive price, non-toxic

and with a high thermal conductivity.

This work focuses on the pseudobinary alloy Pr(Ni5−xCox). On one side the com-

pound PrNi5 does not show a magnetic order down to very low temperatures (0,40 mK).

On the other side, PrCo5 is a well know hard magnet, with a high magnetic ordering

temperature(880 K). The aim of this work is to search a composition that has its TC near

room temperature (RT) and therefore study its magnetocaloric properties. Following this

approach, we prepared 6 samples (x=0,1,2,3,4 and 5), and observed that the sample with

TC∼300 K lies in between x=2 (TC=115 K) and x=3 (TC=538 K). For those samples

we found a broad magnetic entropy change curve (∼100 K) and ∆S ∼ −0, 30J/kgK)

, quite useful for applications. Based on these facts, these series are competitive com-

pared with the most promising magnetocaloric materials. Stepping forward, we prepared

intermediate compositions (2 6 x 6 3), to achieve a TC closer to the room temperature.

Another interesting alloy was produced and characterized: Ni2Mn(Ga1−xBix) This

series allows the study of the influence of the bismuth on the martensitic transformation

temperature and the magnetic ordering temperature. Bismuth is suggested in order to

drive those temperatures towards each other, until they are concomitant.

ii

Contents

Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i

Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii

Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv

List of figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi

List of tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii

1 Introduction 1

1.1 The magnetocaloric effect . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2 Thermodynamic relationships . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.2.1 Magnetic entropy change due to isothermal process . . . . . . . . . 3

1.2.2 Adiabatic temperature change due to adiabatic process . . . . . . . 4

1.2.3 Conventional behavior . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.3 Thermodynamic refrigeration cycles . . . . . . . . . . . . . . . . . . . . . . 7

1.4 The Pr(Ni,Co)5 alloy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

1.5 The Ni2Mn(Ga,Bi) alloy . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2 Experimental methods 11

2.1 Sample preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.2 Sample characterization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.2.1 X-ray diffraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.2.2 Energy dispersive x-ray spectroscopy EDS . . . . . . . . . . . . . . 13

2.2.3 Magnetic measurements . . . . . . . . . . . . . . . . . . . . . . . . 13

3 Results and discussions 14

3.1 X-ray diffraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

3.1.1 Pr(Ni5−xCox) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

3.1.2 Ni2Mn(Ga1−xBix) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

3.2 Energy dispersive x-ray spectroscopy EDS . . . . . . . . . . . . . . . . . . 17

3.2.1 Pr(Ni5−xCox) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3.2.2 Ni2Mn(Ga1−xBix) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3.3 Magnetic measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

3.3.1 Pr(Ni5−xCox) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

iii

4 Conclusions and future works 24

4.1 Pr(Ni5−xCox) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

4.2 Ni2Mn(Ga1−xBix) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

Appendices 27

A X-ray diffraction for Pr(Ni5−xCox) 27

B Summary of refinement results for Pr(Ni5−xCox) 33

C Fluxogram to study the MCE in the PrNi5−xCox 45

Bibliography 49

iv

List of Figures

1.1 Adiabatic and isothermal processes . . . . . . . . . . . . . . . . . . . . . . 5

1.2 Conventional behavior of MCE curve . . . . . . . . . . . . . . . . . . . . . 6

1.3 Comparison of RCP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.4 Analogy between AMR and conventional refrigeration cycles . . . . . . . . 8

1.5 Pr(Ni,Co)5 unit cell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

1.6 Ni2MnGa unit cell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

3.1 Phase diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

3.2 X-ray diffraction plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

3.3 Lattice parameters comparison . . . . . . . . . . . . . . . . . . . . . . . . . 16

3.4 SEM images of sample Ni2Mn(Ga1−xBix) . . . . . . . . . . . . . . . . . . . 19

3.5 Curie temperature for Pr(Ni5−xCox) . . . . . . . . . . . . . . . . . . . . . . 20

3.6 Results for PrNi3Co2 sample . . . . . . . . . . . . . . . . . . . . . . . . . . 21

3.7 Results for PrNi2Co3 sample . . . . . . . . . . . . . . . . . . . . . . . . . . 21

3.8 Results for PrNi2,5Co2,5 sample . . . . . . . . . . . . . . . . . . . . . . . . 22

3.9 Comparison of ∆S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.10 RCP comparison with PrNiCo . . . . . . . . . . . . . . . . . . . . . . . . . 23

A.1 X-ray diffraction refinement for PrNi4Co1 . . . . . . . . . . . . . . . . . . . 27


A.3 X-ray diffraction refinement for PrNi2,7Co2,3 . . . . . . . . . . . . . . . . . 28

A.4 X-ray diffraction refinement for PrNi2,65Co2,35 . . . . . . . . . . . . . . . . 29







A.11 X-ray diffraction refinement for PrCo5 . . . . . . . . . . . . . . . . . . . . 32

B.1 Summary of results for PrNi4Co1 . . . . . . . . . . . . . . . . . . . . . . . 34


v

B.3 Summary of results for PrNi2,7Co2,3 . . . . . . . . . . . . . . . . . . . . . . 36

B.4 Summary of results for PrNi2,65Co2,35 . . . . . . . . . . . . . . . . . . . . . 37







B.11 Summary of results for PrCo5 . . . . . . . . . . . . . . . . . . . . . . . . . 44

C.1 Fluxogram of the approach to study the MCE in the PrNi5−xCox system . 45

vi

List of Tables

2.1 Pr(Ni5−xCox) List of materials . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.2 Pr(Ni5−xCox) 0 6 x 6 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.3 Pr(Ni5−xCox) 2, 3 6 x 6 2, 55 . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.4 Ni2Mn(Ga1−xBix) List of materials . . . . . . . . . . . . . . . . . . . . . . 13

2.5 Ni2Mn(Ga1−xBix) compositions . . . . . . . . . . . . . . . . . . . . . . . . 13

3.1 Pr(Ni5−xCox) lattice parameters . . . . . . . . . . . . . . . . . . . . . . . . 16

3.2 Ni2Mn(Ga1−xBix)) XRD identified phases . . . . . . . . . . . . . . . . . . 17

3.3 Comparison between nominal and experimental composition . . . . . . . . 17

3.4 EDS results for Ni2MnGa . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

3.5 EDS results for Ni2MnGa0,9Bi0,1 . . . . . . . . . . . . . . . . . . . . . . . . 18



4.1 Summary of MCE for Pr(Ni5−xCox) . . . . . . . . . . . . . . . . . . . . . . 24

vii

Chapter 1

Introduction

There has always been a need or desire to cool some environments below ambient

temperature. Since a long time ago people knew about the preserving effects of colder

temperatures on food. It is unthinkable to imagine modern life without refrigerators.

The first refrigerators available, in the beginning of the 20th century, were mainly of

the vapor-compression type, operated as start-stop machines using steam engines with

open drive compressors subject to leaking noxious or dangerous refrigerants. They were

too big, unreliable, unresponsive to changing system loads, dangerous, and expensive

for the average home.[1] The development of these systems was fast, and it was in 1930

that Frigidaire announced they new refrigerant, Freon (Chlorofluorocarbon,CFC). It has

rapidly overcome the use of any other refrigerant and dominated the nonindustrial market.

In 1974 Molina and Rowland published an article in the journal Nature (and later

shared the Nobel Prize for Chemistry, in 1995), warning about the damage caused by CFCs

to the stratospheric ozone layer. On January 1, 1989 the Montreal protocol on substances

that deplete the ozone layer entered into force. The treaty provides a timetable on which

the production of those substances must be phased out and eventually eliminated. On

CFC (R-12, Dichlorodifluoromethane) the last step limit was in 1996: “from 1996 its

calculated level of consumption and production of the controlled substances in Group I

of Annex A does not exceed zero”. The CFCs were substituted by the HFCs, that have

no potential to deplete the ozone layer, but may cause the earth’s average temperature

to rise, which is called global warming, or greenhouse effect. Therefore, HFCs are thus

considered as one of six target GHGs under the Kyoto Protocol of the United Nations

Framework Convention on Climate Change (UNFCCC). According to the Kyoto Protocol,

governments around the world are voluntarily committed to reduce target GHGs emissions

to atmosphere.[2]

The Kyoto Protocol also addresses another important topic, the energy efficiency. The

use of electricity represents one fifth of the total energy used in Europe. From 1995 to

2005, European manufacturers have invested e10 billion to improve the energy-efficiency

and the performance of appliances, with impressive results: 34 TWh. It means that about

1

17 Mtons of CO2 were no longer discharged into the atmosphere[3].

Thus the use of Greenhouse gases is not the only point that deserves attention in

the modern refrigeration systems. With more than one century of developments, it is a

mature technology, and even the most efficient units operates well below the maximum

theoretical efficiency (Carnot cycle) with few improvements possible[4].

In the search for more efficient and environmental friendly alternatives, the magnetic

refrigeration, based on the magnetocaloric effect(MCE), has proven to be a promising

technology. The magnetic material is used in solid form, thus there is no need for haz-

ardous gases. The energy efficiency can be very high, 60% of the maximum efficiency

(Carnot). The engineering of magnetic refrigeration systems are already advanced and

the development of improved solid magnetic refrigerant materials with large MCE is the

most important step to advance before magnetic refrigeration becomes a viable technol-

ogy. The following section gives a better idea about the magnetic refrigeration.

1.1 The magnetocaloric effect

The Magnetocaloric Effect (MCE), discovered in 1881 by E. Warburg[5], is an

exciting and promising propriety of magnetic materials. This effect can be seen from

either an adiabatic or an isothermal process; both due to a change of the applied magnetic

field. Considering an adiabatic process, the magnetic material changes its temperature,

whereas from an isothermal process, the magnetic material exchanges heat with a thermal

reservoir. From the quantitative point of view, the MCE is measured trough the isothermal

magnetic entropy change (∆SM(T )∆H) or adiabatic temperature change (∆Tad(T )∆H),

both quantities derived from thermodynamic relationships and, to obtain those, we need

to measure magnetization and specific heat as a function of temperature and magnetic

field.

It is straightforward the idea to produce a thermo-magnetic cycle based on the isother-

mal and/or adiabatic processes (like Brayton and Ericsson cycles); and indeed this idea

begun in the late 1920s, when cooling via adiabatic demagnetization was proposed by

Debye[6] and Giauque[7]. The process was after demonstrated by Giauque and Mac-

Dougall, in 1933, where they reached 250 mK[8] and is used in many laboratories to reach

temperatures below 1 K. Since then, the adiabatic demagnetization was used within some

contexts; for instance, to cool NASA-XRS detectors (∼1.5 K)∗. On the other hand, room

temperature magnetic cooling device technology is still in an early phase of development,

with no commercially available products and only few prototypes. In August 2001, As-

tronautics Corporation of America, USA, announced a prototype of room temperature

magnetic cooler. This machine has a cooling power of 95W, and uses as the active mag-

∗http://www.universe.nasa.gov/xrays/programs/astroe/eng/adr.html

2

http://www.universe.nasa.gov/xrays/programs/astroe/eng/adr.html

netic material Gd spheres[9]. Later, in March 2003, Chubu Electric and Toshiba, Japan,

also announced a room temperature magnetic cooler prototype. This machine has a

cooling power of 60W, and uses a layered bed of a Gd-Dy alloy as the active magnetic

material[9].

On the other hand, prototypes of magnetic cooling devices have not been developed to

cool small loads from above room temperature (RT) down to RT; being therefore a really

open field of research, with promising economic, social and scientific returns. We can

cite, for instance, the multi-million euro market of coolers of high speed clock processors.

Actually, general coolers designed for this specific task, for instance, those using closed

circuit of water and Peltier effect, have a non-sufficient efficiency to make cooling a non-

issue. Using a magnetic cooling system, we can have several advantages, with higher

efficiency, smaller size, lower noise (since there would be no compressor), and also the

ability to control the low temperature to be reached.

However, nowadays, the magnetic materials available and studied by the scientific

community do not have yet the needed characteristics to be used in large scale, due

to technological and/or economic restrictions. For a successful application, we need a

material of low cost, non-toxic, good thermal conductivity and with a huge and broad

∆SM(T )∆H variation vs. temperature (maximum around the magnetic phase transition).

In this sense, most of the research developed world wide is devoted to explore and optimize

the magnetocaloric properties of known materials, as well to seek for new magnetocaloric

features in new materials.

1.2 Thermodynamic relationships

1.2.1 Magnetic entropy change due to isothermal process

The magnetic entropy SM is an important characteristic of a magnetic material.

When the material is subjected to a magnetic field change, at constant pressure, two

processes can occur depending on the conditions imposed.

If the material is allowed to exchange heat with the surroundings, and remains at

constant temperature in a isothermal process, its entropy change is:

∆SM(T )∆H = (S(T )HF− S(T )HI

)T (1.1)

Where HF and HI indicates respectively the final and initial field strength. The ∆SM(T )∆H

is the magnetic entropy change and directly characterizes the cooling capacity q of the

magnetic material:

q = −∫ T2

T1

∆SM(T )∆HdT (1.2)

It indicates how much heat can be transferred from the cold end (at T1) to the hot end

3

(at T2) of the refrigerator in one ideal thermodynamic cycle.

If both the magnetization and entropy are continuous functions of the temperature

and magnetic field, then the magnetic entropy can be related to the magnetization M ,

the magnetic field strength H, and the absolute temperature T using one of the Maxwell

relations [4]: (∂SM(T, H)

∂H

)

T

=

(∂M(T,H)

∂T

)

H

(1.3)

Integration of the above equation yields:

∆SM(T )∆H =

∫ HF

HI

dSM(T, H)T =

∫ HF

HI

(∂M(T, H)

∂T

)

H

dH (1.4)

1.2.2 Adiabatic temperature change due to adiabatic process

The second process occurs when the material is isolated from its surroundings

and the magnetic field is changed, in this way its total entropy remains constant. The

temperature of the material is then changed by

∆Tad(T )∆H = (T (S)HF− T (S)HI

)S (1.5)

and ∆Tad(T )∆H is called adiabatic temperature change, which indirectly characterizes

both the cooling capacity and the temperature difference between the cold and the hot

ends of the system.

Considering S=S(T,H), it is possible to write:

dS =

(∂S(T,H)

∂T

)

H

dT +

(∂S(T, H)

∂H

)

T

dH (1.6)

For an adiabatic process (dS=0) one obtain:

(∂S(T,H)

∂T

)

H

dT = −(

∂S(T,H)

∂H

)

T

dH (1.7)

From the definition of specific heat:

C(T, H) = T∂S(T, H)

∂T

∣∣∣∣∣H

(1.8)

Using equation (1.3) one may find:

dT (T,H) = −(

T

C(T, H)

)

H

(∂M(T, H)

∂T

)

H

dH (1.9)

4

Figure 1.1: Adiabatic and isothermal processes

The integration of (1.9) leads to the adiabatic temperature change ∆Tad(T )∆H

∆Tad(T )∆H =

∫ HF

HI

dT (T, H) = −∫ HF

HI

(T

C(T,H)

)

H

(∂M(T, H)

∂T

)

H

dH (1.10)

Figure 1.1 summarizes the adiabatic and isothermal processes.

1.2.3 Conventional behavior

Both ∆SM(T )∆H and ∆Tad(T )∆H depend on temperature and ∆H, equations (1.4)

and (1.10) respectively, and are usually reported as functions of temperature for a given

∆H, or as functions of ∆H for a given temperature. The behavior of both characteristics

of the magnetocaloric effect, i.e., ∆SM(T )∆H and ∆Tad(T )∆H , is material dependent

and cannot be easily predicted from first principles, therefore must be experimentally

measured. The lanthanide metals and their compounds are considered the best potential

magnetocaloric materials due to their large magnetic moments and magnetic entropy

change.

It is easy to see that both ∆SM(T )∆H and ∆Tad(T )∆H are proportional to the deriva-

tive of the magnetization with respect to temperature at constant magnetic field – equa-

tions (1.4) and (1.10). ∆Tad(T )∆H is also proportional to the absolute temperature and

inversely proportional to the heat capacity at constant magnetic field. Thus, it is ex-

pected that any material should have the largest ∆SM(T )∆Hand ∆Tad(T )∆H when its

5

Figure 1.2: An example of the conventional caret-like behavior of ∆SM(T )∆H and thedata used to characterize the relative cooling power RCP [4]

magnetization is changing rapidly with temperature, i.e., in the vicinity of a spontaneous

magnetic-ordering temperature. The MCE gradually decreases both below and above the

magnetic ordering temperature (Tc), since in those regimes the magnetization is weakly

dependent on the temperature [4].

Therefore, conventional ferromagnets typically display a ‘caret-like’ ∆SM(T )∆H and

∆Tad(T )∆H . This is shown in figure 1.2. The numerical characterization of the MCE

behavior is possible by specifying its temperature at the MCE peak (maximum of ∆SM

or ∆Tad) and its full width at half maximum (δTFWHM=T2-T1). For the case of magnetic

entropy change, the product between ∆SM and δTFWHM yields close to 4/3 times the

cooling capacity (equation (1.2)) in the temperature range T1 to T2 as shown in the

figure 1.2. In the figure is easy to see that the caret-like shape of the MCE peak can be

approximated by a triangle. As Gschneidner has shown [4], the integration of the data

on figure (1.2) for a magnetic field change from 0 up to 2 T using equation (1.2) yields

the cooling capacity, q ∼ 1, 37J/cm3 for Gd between T1 = 276 and T2 = 315K, while

the value calculated as −∆SM(max) × δTFWHM is ∼ 1, 39J/cm3. Thus one defines the

product

RCP (S) = −∆SM(max)× δTFWHM (1.11)

the relative cooling power (RCP ) based on the magnetic entropy change. Using the same

idea, the MCE measured as ∆Tad can be characterized as the product

RCP (T ) = −∆Tad(max)× δTFWHM (1.12)

and it is regarded as the relative cooling power based on the adiabatic temperature change.

It is important to note that the single information about the ∆SM(max) is not enough

6

Gd-Tb Gd

La-Fe-Co-Si

Gd-Si-Ge

La-Fe-Si-H

Mn-As-Sb

Ni-M

n-Ga

Mn-As

La-Gd-Sr-Mn-O

La-Ca-Mn-O

La-Ca-Pb

-Mn-O

La-Sr-M

n-Cr-O

0

50

100

150

200

250

RC

P [J

/kg]

Figure 1.3: Comparison among various materials concerning their relative cooling power(RCP) for a magnetic field change of 20 kOe [11]

to characterize the MCE of the material, since, from the application point of view, the

MCE curve should has a temperature span as large as possible (large δTFWHM , because

that will keep the system working with more efficiency in a wider temperature range).

Figure 1.3 shows a comparison among various materials regarding they RCP, note that i.e.

Ni-Mn-Ga alloys can achieve a very high ∆SM and it is regarded as a class of materials that

present giant magnetocaloric effect (GMCE)[10]. However, due to its narrow temperature

span (around 5 K), the relative cooling power has a low value.

1.3 Thermodynamic refrigeration cycles

In the thermomechanical cycle, the gas is successively compressed and decom-

pressed, absorbing heat from inside the refrigerator to later release to the outside. The

thermomagnetic cycles† work in an analogous way by means of a regenerator, a thermal

device that can receive and release heat during the process (see fig 1.4).

1. Adiabatic magnetization: The regenerator (magnetic material) is placed in an

insulated environment. By increasing the external magnetic field (+H) the overall

entropy keeps unchanged and the net result is that the regenerator heats up (T +

∆Tad).

2. Isofield transfer: This added heat can then be removed by a fluid like water

(-Q). The magnetic field is held constant to prevent the magnetic moments from

reabsorbing the heat. Once sufficiently cooled, the magnetocaloric material and the

coolant are separated.

†http://en.wikipedia.org/wiki/Magnetocaloric

7

http://en.wikipedia.org/wiki/Magnetocaloric

3. Adiabatic demagnetization: The substance is returned to another adiabatic

condition so the total entropy remains constant. However, this time the magnetic

field is decreased and the sample cools (i.e. an adiabatic temperature change).

4. Isofield transfer: The magnetic field is held constant to prevent the working

material from heating back up. The material is placed in thermal contact with

the environment to be refrigerated. Because the working material is cooler than

the refrigerated environment (by design), heat migrates into the working material

(+Q).

Once the refrigerant and refrigerated environment are in thermal equilibrium, the cycle

begins again.

(a) Analogy between magnetic refrigeration andvapor cycle or conventional refrigeration

(b) Active magnetic regenerator (AMR) S-T di-agram

Figure 1.4: Analogy between AMR refrigeration cycle and conventional refrigeration cycle

1.4 The Pr(Ni,Co)5 alloy

It is well known that rare earth-cobalt compounds RCo5 are excellent permanent mag-

nets. As a permanent magnetic material PrCo5 is specially interesting due to it theoretical

higher energy product (BHmax) compared with SmCo5 and also to its high ordering tem-

perature (TC) higher than Nd-Fe-B magnets[12].

On the other hand, the parent compound PrNi5 is non-magnetic due to the high crystal

field of this compound‡ [13]. PrNi5 it has been successfully used for cooling at very low

temperatures through the adiabatic demagnetization process[14].

‡The high crystalline field quench the Pr moment

8

Figure 1.5: Pr(Ni,Co)5 unit cell

Both compounds have the hexagonal CaCu5 (P6/mmm (191)) structure, that can be

visualized in figure 1.5. Studies in Pr(Ni,Co)5 pseudobinary alloys have been carried by

some authors [15, 16, 17, 18, 19] although not focusing in the magnetocaloric effect.

The main focus of this work is to search the composition of the pseudobinary alloy

Pr(Ni5−xCox) that has the Curie temperature TC around room temperature and study

its magnetic properties and specially its magnetocaloric effect. The first approach was

the preparation of a series with 0 6 x 6 5 to analyze the composition dependence of the

TC . After finding the region of interest, a new series with 2, 3 6 x 6 2, 55 was prepared

for a more detailed study. A fluxogram illustrating the process is shown in figure C.1.

1.5 The Ni2Mn(Ga,Bi) alloy

The Ni2MnGa has a cubic structure, shown in figure 1.6 , the same type as Cu2MnAl

(group Fm-3m, 225) and this system is widely studied as a shape memory alloy. It un-

dergoes a transition from the martensitic to austenitic structure on heating and a reverse

process on cooling, accompanying a magnetization jump. The martensitic transition tem-

perature is very sensitive to composition and upon a partial substitution of Mn for Ni

the martensitic transition temperature Tm increases and Curie temperature TC decreases

until they merge in one first order magnetostructural phase transition [20]. Thus, the

properties around the composition Ni2MnGa are interesting for the MCE application

since a large ∆S is expected.

Hu et al [21] and [22] have studied the magnetic behavior of Ni-Mn-Ga alloys around

the martensitic transition, while Albertini et al [23] have shown a giant magnetic entropy

change for Ni2+xMn1−xGa samples displaying a concomitant magnetic and martensitic

transition, that is found to occur in a composition range 0, 18 6 x 6 0, 2. Other authors

have also shown the interesting MCE at the composition where the giant magnetic entropy

9

Figure 1.6: Ni2MnGa unit cell

change occurs [24, 20, 25].

An interesting paper from Soderberg et al [26] shows the effects of a fourth element

addition to the ternary alloy Ni2MnGa, in the martensitic transition temperature. Al-

though the paper is focused only in the transformation temperatures, it suggests that the

addition of 2 % of bismuth in the alloy as a substitute for gallium can shift the martensitic

temperature upwards and the Curie temperature downward. This fact is interesting due

to the higher values of the MCE in Ni-Mn-Ga alloys have a narrow temperature span

δTFWHM of approximately 3K, resulting in a low RCP value. Even though, its high

∆SM and the achievement of the concomitant transition through a forth element (Bi)

(and not the change of Ni and Mn ratio) can lead to a broader temperature span of the

∆SM . One of the objectives of this work is to produce a series of Ni2Mn(Ga1−xBix) with

0 6 x 6 0, 5 quaternary alloy. The time constraints precludes the complete analysis for

this system. However, it would be interesting to confirm that the bismuth addition can

affect the martensitic transition temperature and the Curie temperature.

10

Chapter 2

Experimental methods

2.1 Sample preparation

Intermetallic compounds are generally prepared by melting. The intermetallic

compounds Pr(Ni5−xCox) and Ni2Mn(Ga1−xBix) were prepared in an Buhler arc melt-

ing furnace at University of Porto, CEMUP, starting from the appropriate amounts of

the constituent elements. That furnace has a water-cooled copper crucible pre-evacuated

better than 2 × 10−6 mbar and refilled with high-purity argon gas. In order to obtain

homogeneous samples, arc melting was repeated three times. A titanium piece is melted

inside the furnace as a oxygen trap, and after the melting of each sample, the titanium is

remelted.

For the Pr(Ni5−xCox) alloys, the list of materials used is on table 2.1.

Table 2.1: Pr(Ni5−xCox) List of materials

Material Alpha Aesar Code Purity Form

Praseodymium 40296 99,9% rodNickel 42332 99,995% slugCobalt 10867 99,995% rod

For the preparations of all samples, there was no excess of elements and the nominal

quantities were used. Table 2.2 shows the concentrations used to Pr(Ni5−xCox) in the

series 0 6 x 6 5.

For the series where 2, 3 6 x 6 2, 55 the compositions are shown in table 2.3.

For the Ni2Mn(Ga1−xBix) alloys the list of materials is listed in table 2.4, and the

compositions are listed in table 2.5.

Since the studied alloys are produced by arc melting, the resulting buttons are not

homogeneous. In order to provide a homogeneous structure to the samples, a heat treat-

ment is necessary. Samples from both alloys were sealed in evacuated quartz tubes and

submitted to the desired heat treatment.

11

Table 2.2: Pr(Ni5−xCox) 0 6 x 6 5

Composition Praseodymium %wt Nickel %wt Cobalt%wt

PrNi4Co1 0,3243 0,5402 0,1356PrNi3Co2 0,3240 0,4049 0,2710PrNi2Co3 0,3239 0,2698 0,4063PrNi1Co4 0,3237 0,1348 0,5415

PrCo5 0,3235 0 0,6765

Table 2.3: Pr(Ni5−xCox) 2, 3 6 x 6 2, 55

Composition Praseodymium %wt Nickel %wt Cobalt%wt

PrNi2,7Co2,3 0,3240 0,3644 0,3117PrNi2,65Co2,35 0,3240 0,3576 0,3184PrNi2,6Co2,4 0,3240 0,3508 0,3252

PrNi2,55Co2,45 0,3240 0,3441 0,3319PrNi2,5Co2,5 0,3239 0,3373 0,3387

PrNi2,45Co2,55 0,3239 0,3306 0,3455

The heat treatment temperatures were defined following the literature. For the Pr(Ni5−xCox)

alloy [27] [28], the heat treatment can provide good homogeneities in the alloys when x is

not close to 5 (see the phase diagram 3.1(a)). In this case a proper heat treatment should

use a higher temperature as can be seen in the phase diagram from the Pr-Co system

3.1(b). The partial phase diagram for the Pr-Ni-Co system was studied by Chuang et

al [29]. The samples were thus annealed at 993 K during 7 days, and then quenched in

liquid nitrogen.

For the Ni2Mn(Ga1−xBix) alloy the literature direction were followed [24] [30]. Samples

were annealed at 1073 K for eleven days and then quenched in liquid nitrogen.

2.2 Sample characterization

2.2.1 X-ray diffraction

The x-ray diffraction analysis were done at Universidade de Tras-os-Montes e Alto Douro

(UTAD) in a multichannel x-ray diffractometer from Phillips with a Cu Kα radiation. In

this way, the main phase as well as the impurity phases can be detected, when the latter

are present in amounts of at least 5 vol.%. The crystal structure and the lattice parameters

were analyzed by means of a refinement procedure using the software PowderCell ∗ that

uses the Rietveld method.

The following x-ray structure data† were used: Co[31], PrCo5[32], Pr2Co17[33], PrNi5[34],

∗see http://users.omskreg.ru/~kolosov/bam/a_v/v_1/powder/e_cell.htm†A database is available at http://icsd.ill.fr/icsd/index.html

12

http://users.omskreg.ru/~kolosov/bam/a_v/v_1/powder/e_cell.htm

http://icsd.ill.fr/icsd/index.html

Table 2.4: Ni2Mn(Ga1−xBix) List of materials

Material Alpha Aesar Code Purity Form

Nickel 42332 99,995% slugManganese 36221 99,98% irregular piecesGallium 10185 99,9999% ingotBismuth 14442 99,999% polycrystalline lump

Table 2.5: Ni2Mn(Ga1−xBix) compositions

Composition Nickel %wt Manganese %wt Gallium%wt Bismuth%wt

Ni2MnGa 0,4850 0,2270 0,2881 0Ni2MnGa0,9Bi0,1 0,4586 0,2146 0,2451 0,0816Ni2MnGa0,8Bi0,2 0,4349 0,2036 0,2067 0,1549Ni2MnGa0,7Bi0,3 0,4136 0,1936 0,1720 0,2209Ni2MnGa0,6Bi0,4 0,3942 0,1845 0,1405 0,2807Ni2MnGa0,5Bi0,5 0,3766 0,1763 0,1119 0,3353

Ni[35], Pr(Ni,Co)[19] and [36] and Ni-Co[37].

2.2.2 Energy dispersive x-ray spectroscopy EDS

The EDS was used to check the homogeneity and stoichiometry of the samples. The

measurements were performed in Phillips-FEI/Quanta 400 equipment at Universidade de

Tras-os-Montes e Alto Douro (UTAD). Up to six measurements were done in each sample

to avoid misleading results. Due to the high quality of the calibration, operation of the

equipment and the conditions of the samples, quantitative results can be obtained within

5% of certainty.

2.2.3 Magnetic measurements

The magnetic measurements were carried out in a vibrating sample magnetometer (VSM)

at Porto University with a field strength of 1 T and high temperature capabilities (800

K) and at University of Aveiro (maximum field strength 10 T and temperature from 3

to 300 K). The field strength of 1 Tesla was chosen because that is an feasible field to be

created by a permanent magnet in the magnetic refrigerator.

Many information can be taken from the VSM measurements. For the focus of this

work, the TC‡ and the isothermal curves of magnetization§.

The Pr(Ni5−xCox) system is suggested to have a second-order magnetic phase transi-

tions. Thus, equation 1.4 was applied to calculate the ∆SM(T )∆H .

‡as the derivative of the magnetization versus temperature curves§curves of magnetization versus field strength at different temperatures

13

Chapter 3

Results and discussions

3.1 X-ray diffraction

3.1.1 Pr(Ni5−xCox)

The results (see appendix A and B) indicates some undesirable second phase in the

limits of the series (x=1 and x=5) and the refinement analysis indicates approximately

10% of the Pr2(Co,Ni)17 phase (see appendix A). In addition, in the x=4 composition

there is approximately 2,5% of either Ni or Co as a second phase.

Following Chuang et al [29] in their study of the partial phase diagram for Pr-Ni-

Co system (see an schematic redraw of the room temperature isothermal section in figure

3.1(c)) , it is indicated that when x > 3 for the Pr(Ni5−xCox) a peritectic reaction (L+(2 :

17) → (1 : 5)) takes place and when x < 3 the compound melts congruently.

The presence of the Pr2(Ni,Co)17 phase in the composition x = 5 is probably due

the heat treatment used, since PrCo5 is unstable at low temperatures and decomposes

into Pr2Co17 and Pr5Co19 [38]. The presence of the Pr2(Ni,Co)17 phase for composition

x = 1 may be due to inhomogeneities in the sample, considering that this phase is not

predicted or present in the above mentioned studies for this low Co concentration. The

phase diagrams for the binary systems Pr-Ni and Pr-Co are presented in figure 3.1[38].

The samples in the composition range 2 6 x 6 3 did not present secondary phase.

A summary of the x-ray diffraction plots are presented in figure 3.2(a), and the lattice

parameters for each sample in table 3.1 and figure 3.3.

3.1.2 Ni2Mn(Ga1−xBix)

The sample with Ni2MnGa (x=0) is the only that presented a single phase. All the other

composition (x=0,1;0,2;0,3;0,4 and 0,5) were not single phase materials. The x-ray plots

are presented in figure 3.2(b). The list of phases is given in table 3.2.

14

(a) Pr-Ni

(b) Pr-Co

(c) Partial phase diagram for Pr-Ni-Co

Figure 3.1: Phase diagrams

15

20 40 60 80 1000

2

4

6

8

10 x=5

x=4

x=3

x=2.55

x=2.5

x=2.45

x=2.4

x=2.35

x=2.3

x=2

Inte

nsity

(u.a

.)

2

x=1

(a) X-ray diffraction plots for Pr(Ni5−xCox)

20 40 60 80 1000

1

2

3

4

5

6

x=0,5

x=0,4

x=0,3

x=0,2

x=0,1

Inte

nsity

(a.u

.)

2

x=0

(b) X-ray diffraction plots for Ni2Mn(Ga1−xBix)

Figure 3.2: X-ray diffraction plots

Table 3.1: Pr(Ni5−xCox) lattice parameters

Nominal composition (x) a (A) c (A) cell volume (A3)

2 4,9911 3,9782 99,10122,30 4,9963 3,9804 99,36272,35 4,9977 3,9831 99,48592,40 4,9992 3,9847 99,58562,45 4,9993 3,9840 99,57212,50 4,9964 3,9819 99,40422,55 4,9964 3,9828 99,42663 4,9999 3,9850 99,6210

1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 3.1

3.980

3.984

4.992

4.996

5.000

99.1

99.2

99.3

99.4

99.5

99.6

99.7

a c

latti

ce p

aram

eter

a a

nd c

[Å]

Composition (x)

Cel

l vol

ume

[Å3 ]

Cellvolume

Figure 3.3: Lattice parameters comparison for Pr(Ni5−xCox) 2 6 x 6 3

16

Table 3.2: Ni2Mn(Ga1−xBix)) XRD identified phases

Phases x=0 x=0,1 x=0,2 x=0,3 x=0,4 x=0,5

Ni2MnGa present present present not present not present not presentBi not present present present present present presentMn not present present present ? ? ?

Ga3Ni5 not present not present not present present present presentBi3Ni not present not present not present present present present

3.2 Energy dispersive x-ray spectroscopy EDS


The EDS analysis quantification in atomic % of the elements indicates errors that are

less than 5% when compared with the nominal atomic % for each sample. However it is

important to note that the composition variation are sometimes within this value.

The composition x of the Pr(Ni5−xCox) with 0 6 x 6 5 are within a 5% deviation

and for the composition 2, 3 6 x 6 2, 55 are within a 6% deviation from the nominal

composition. The empirical formula ratios of nickel and cobalt are presented in table 3.3,

Pr is normalized to 1.

Table 3.3: Pr(Ni5−xCox) nominal vs experimental compositions Ni and Co

Nominal composition x Ni Co Pr Co + Ni

2 3,09 1,94 1 5,032,30 2,59 2,21 1 4,802,35 2,57 2,25 1 4,822,40 2,50 2,30 1 4,802,45 2,47 2,34 1 4,812,50 2,46 2,38 1 4,842,55 2,38 2,40 1 4,783 1,98 3,10 1 5,08

3.2.2 Ni2Mn(Ga1−xBix)

In the Ni2Mn(Ga1−xBix) samples the results indicates that a more carefully approach

should be taken for the preparation of this alloy. The presence of a second phase is

clearly seen in the scanning electron microscope (SEM) images 3.4(a) and 3.4(b). The

composition measured also suggest a strong formation of a undesirable phase.

The data from EDS is shown in the following tables. In table 3.4 the average of six

measurements is presented, indicating the good agreement with the nominal composition

for the sample Ni2MnGa.

17

Table 3.4: EDS results for Ni2MnGa

Ni at% Mn at% Ga at%

Nominal 50 25 25EDS 50,4 24,8 24,8

For the sample Ni2MnGa0,9Bi0,1 in table 3.5 the average of six measurements is shown,

indicating a deviation from the nominal composition, the x-ray data confirms the presence

of metallic bismuth and manganese in the sample.

Table 3.5: EDS results for Ni2MnGa0,9Bi0,1

Ni at% Mn at% Ga at% Bi at%

Nominal 50 25 22,5 2,5EDS 51 25,4 22,7 0,8

For sample Ni2MnGa0,8Bi0,2 measurements were made in two different regions, pre-

sented in table 3.6, it is interesting to note that there is the presence of the Ni2MnGa

structure in the x-ray diffraction pattern. Table 3.7 presents the results for two regions

Table 3.6: EDS results for Ni2MnGa0,8Bi0,2 in two different regions


Region 1 15,36 10,49 4,84 69,32Region 2 24,01 48,16 27,49 0,34

that can be seen in figure 3.4(c), although the suggestion of a Ni2MnGa stoichiometry,

that phase is not present in the x-ray diffraction.

It is interesting to note that the images suggest the occurrence of a liquid phase. It

can be due the presence of unalloyed bismuth, that has melting temperature of 545 K.

Soderberg [26] did not mentioned difficulties in the preparation of the alloy, this can

be due to the fact that he used a pre-alloyed Ni2MnGa to include the fourth element and

also because the amount of alloying element (Bi) was 2 %. More indications of liquid

phase can be seen in figures 3.4(c), 3.4(d), 3.4(e) and 3.4(f).

3.3 Magnetic measurements


The magnetic measurements carried out in the Pr(Ni5−xCox) alloy with 0 6 x 6 5

indicate that the composition of interest for room temperature applications, lies between

the composition 2 6 x 6 3, and, for coincidence is exactly the range without spurious

18

(a) Second phase Ni2MnGa0,9Bi0,1 (b) Ni2MnGa0,9Bi0,1

(c) Ni2MnGa0,7Bi0,3 (d) Different region Ni2MnGa0,7Bi0,3

(e) Ni2MnGa0,6Bi0,4 (f) Ni2MnGa0,5Bi0,5

Figure 3.4: SEM images of sample Ni2Mn(Ga1−xBix)

19

Table 3.7: EDS results for Ni2MnGa0,7Bi0,3 in different regions of figure 3.4(c)


Light 10,39 4,06 1,98 83,57Dark 46,49 22,38 28,41 2,71

2.0 2.5 3.0

100

150

200

250

300

350

400

450

500

550

600T C

[K]

Cobalt composition x

Figure 3.5: Curie temperature as function of x for Pr(Ni5−xCox)

phase. Due to this fact the characterization was concentrated in those two compositions.

Figure 3.5 presents the measured Curie temperature as function of the cobalt composition.

The Curie temperature from the minima of the derivatives of the magnetization as function

of temperature measurements.

Figure 3.6(a) is the magnetization versus temperature of the sample PrNi3Co2 and

the derivative in figure 3.6(b) indicate that the Curie temperature of sample is at 120

K. Figure 3.6(c) shows the isothermal magnetization curves for sample PrNi3Co2. Figure

3.6(d) shows the hysteresis cycle of sample PrNi3Co2 below (4 K) and above (300 K)

the magnetic ordering temperature (TC). It is important to note the remanence∗ in the

magnetic material will lead to a less efficient magnetic cycle. However, since applications

of the MCE are around the Curie temperature, this effect is small [39].

Figure 3.7(a) indicates the isothermal magnetization curves for the sample PrNi2Co3

and 3.7(b) the magnetization as function of temperature for several values of magnetic

field, obtained from figure 3.7(a).

The results on the samples with concentration x = 2 and x = 3 indicate that the

interesting† region is between these values of x. Thus, new samples were produced. Based

∗Remaining magnetization when the external field is zero†The composition where the TC is near the room temperature

20

0 50 100 150 200 250 3000

2

4

6

8

10

12

14

16

18

Heating Cooling

Mom

ent [

emu/

g]

Temperature [K]

PrNi3Co

2

H=10 [Oe]

(a) Magnetization vs Temperature with low field

50 60 70 80 90 100 110 120 130 140 150 160 170-0.10

-0.08

-0.06

-0.04

-0.02

0.00PrNi

3Co

2

dM/dT

Temperature [K]

Derivative of the heating curve Derivative of the cooling curve

(b) Derivative of (a)

0 2 4 6 8 100

5

10

15

20

25

30

35

Mom

ent [

emu/

g]

Field [kOe]

PrNi3Co

2

120 K

10 K

300 K

(c) Isothermal magnetization vs field strength

-10 -8 -6 -4 -2 0 2 4 6 8 10-50

-40

-30

-20

-10

0

10

20

30

40

50

4K 300K

Mom

ent [

emu/

g]

Field [kOe]

PrNi3Co

2

(d) Magnetization vs field strength at 4 K and300 K

Figure 3.6: Results for PrNi3Co2 sample

0 2 4 6 8 100

10

20

30

40

50

60

700 K

520 K

M(emu/g)

Field (kOe)

PrNi2Co

3

340 K

(a) Isothermal magnetization vs field strength

250 300 350 400 450 500 550 600 650 700 7500

10

20

30

40

50

60

0.1 kOe

Mom

ent [

emu/

g]

Temperature [K]

PrNi2Co310 kOe

(b) Magnetization vs temperature

Figure 3.7: Results for PrNi2Co3 sample

21

on previous works [16] and [19] and in these results, the composition range 2, 3 6 x 6 2, 55

was defined, see figure C.1.

Figure 3.8 shows the result for sample PrNi2,5Co2,5. With a TC∼420 K it is a step

closer to the objective of this work.

From the isothermal magnetization data and applying the equation (1.4) one can

calculate the ∆SM of the samples. The result is shown in figure 3.9. The calculated ∆SM

values are not high, however due to the large δTFWHM the RCPs are comparable with

other magnetocaloric materials.

As can be seen in the comparison among the results, the change of the Ni-Co ratio can

change the TC of the Pr(Ni,Co)5 system, providing a easy way of tuning the system for

the application. These compositional variation does not seem to affect the large δTFWHM

of the system.

200 300 400 500 600 700 800 900 1000 1100

0

2

4

6

8

10

PrNi2,5Co2,5

M [e

mu/

g]

Temperature [K]

H=50 Oe

(a) Magnetization vs temperature at low field

0 1 2 3 4 5 6 7 8 9 100

10

20

30 300 K

800 K

PrNi2,5Co2,5

M [e

mu/

g]

Field [kOe]

414 K

(b) Isothermal magnetization vs field strength

200 300 400 500 600 700 800 900 1000 1100

-0.14

-0.12

-0.10

-0.08

-0.06

-0.04

-0.02

0.00

0.02

PrNi2,5Co2,5

dM/dT

Temperature [K]

Derivative of the cooling curve Derivative of the heating curve

(c) Derivative of (a)

Figure 3.8: Results for PrNi2,5Co2,5 sample

For a comparison with the before mentioned magnetocaloric materials in figure 1.3,

22

100 200 300 400 500 600 700-0.40

-0.35

-0.30

-0.25

-0.20

-0.15

-0.10

-0.05

0.00

PrNi3Co

2

PrNi2,5

Co2,5

PrNi2Co

3

S (J

/kg*

K)

Temperature (K)

= 10 kOe

Figure 3.9: Magnetic entropy change Pr(Ni5−xCox)

the Pr-Ni-Co system is plotted in figure 3.10.

Gd-Tb Gd

La-Fe-Co-Si

Gd-Si-G

e

La-Fe-Si-H

Mn-As-Sb

Pr-Ni-C

o

Ni-M

n-Ga

Mn-As

La-Gd-Sr-Mn-O

La-Ca-Mn-O

La-Ca-Pb-Mn-O

La-Sr-Mn-Cr-O

0

50

100

150

200

250

RC

P [J

/kg]

Figure 3.10: Comparison among the RCP of different magnetocaloric materials for amagnetic field change of 20 kOe

23

Chapter 4

Conclusions and future works

4.1 Pr(Ni5−xCox)

For the Pr-Ni-Co system table 4.1 summarizes the calculated magnetocaloric properties

of some samples.

Table 4.1: Summary of the magnetocaloric properties for the system Pr(Ni5−xCox)

Nominal composition x ∆S(max) (J/kgK) RCP (J/kg) TC (K) δTFWHM (K)

2 -0,28 29,86 120 1082,50 -0,15 14,70 420 953 -0,31 27,64 550 89

The Pr-Ni-Co system was never before studied with respect to its magnetocaloric

effect. The Curie temperature can be easily changed with the modification in the Ni-Co

ratio without expressive changes in the ∆SM(T )∆H . Even though the ∆SM(max) is not

high, the δTFWHM is large, and that leads to a relatively high RCP for this material. Once

the composition that provides TC around room temperature is found, further studies can

be done to enhance the ∆SM(max) while maintaining the large δTFWHM .

For the completeness of this work, the measurement of the magnetocaloric effect of

the other samples (x=2,30; 2,35; 2,40; 2,45 and 2,55) need to be included and discussed.

As suggestions for future works a study of the influence of other rare-earth elements in

the ∆S(max). For instance, change Pr→Gd, Ho and Sm. Another interesting point is to

better understand the dependence of the lattice parameters with the cobalt composition

and its effect in the ∆S curve, as can be seen in the curve for the sample PrNi2,5Co2,5

where the ∆S(max) is around half of that from samples PrNi3Co2 and PrNi2Co3.

24

4.2 Ni2Mn(Ga1−xBix)

The Ni-Mn-Ga-Bi alloy was produced and the results were not as expected, that means a

single phase with the Ni2MnGa structure. Only the Ni2MnGa sample (x = 0) was correct.

It was only the early beginning of this work and for further studies, the preparation

methods should be reviewed. The presence of pure bismuth in the samples is a problem,

since its melting temperature (545 K) is quite lower than the heat treatment temperature

suggested for the alloy.

For further studies in this series, it is important to obtain single phase samples and

study the magnetocaloric properties. As suggestions: the addition of the forth element

may be done in a pre-alloyed Ni2MnGa, it is also interesting to search for a solubility

limit of bismuth in the alloy.

25

Appendices

26

Appendix A

X-ray diffraction for Pr(Ni5−xCox)

2 theta / deg20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115

3266

1633

0

PowderCell 2.2

PrCo5 89.3%

001

101

110

200

002

201

102

210

112211

202

300

301

003

103

220

310

113

311

203

400

222

401

312 004

303

104

402

410

114

411

223

PR2CO17 10.7%

021

202

113

211

122

024

220

131

027

018

051

208

241

119

407

342

161

247

526 618

PNCo1 4hr.UDF

Rp= 3.02 Rwp= 3.87 Rexp= 4.31

DIFF

Figure A.1: X-ray diffraction refinement for PrNi4Co1

27

2 theta / deg20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115

28124

14062

0

PowderCell 2.2

PrCo5 99.1%

001

101

110

200

002

201

102

210

112

211

202

300

301

003 103220

310

113

311

400

222

401

004

303

104 402

114

223

Co 0.1%

100

002

101

102

004

NICKEL 0.8%

PNCo2 4hr.UDF

Rp= 3.01 Rwp= 3.85 Rexp= 1.39

DIFF


2 theta / deg20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95

28242

14121

0

PowderCell 2.2

PrCo5

001

101

110

200

002

201

102

210

112

211

202

300

301

003 103

220

310

113

311

203

400

222

PrNiCo_1.UDF

Rp= 5.44 Rwp= 6.98 Rexp= 0.79

DIFF

Figure A.3: X-ray diffraction refinement for PrNi2,7Co2,3

28

2 theta / deg25 30 35 40 45 50 55 60 65 70 75 80 85 90 95

28578

14289

0

PowderCell 2.2

PrCo5

001

101

110

200

002

201

102

210

112

211

202

300

301

003 103

220

310

113

302 311

203

400

222

401

213

PrNiCo_2.UDF

Rp= 6.11 Rwp= 7.85 Rexp= 0.79

DIFF


2 theta / deg25 30 35 40 45 50 55 60 65 70 75 80 85 90 95

30397

15198

0

PowderCell 2.2

PrCo5

001

101

110

200

002

201

102

210

112

211

202

300

301

003 103

220

310

113

311

203

400 222

401 213

PrNiCo_3.UDF

Rp= 6.76 Rwp= 8.78 Rexp= 0.52

DIFF


29

2 theta / deg25 30 35 40 45 50 55 60 65 70 75 80 85 90 95

29011

14505

0

PowderCell 2.2

PrCo5

001

101

110

200

002

201

102

210

112

211 202

300

301

003 103

220

310

113

302

311

203

400

222

401 213

PrNiCo_4.UDF

Rp= 6.24 Rwp= 7.96 Rexp= 0.68

DIFF


2 theta / deg20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95

29536

14768

0

PowderCell 2.2

PrCo5

001

101

110

200

002

201

102

210

112 211

202

300

301

003 103

220

310

113

311

203

400

222

401213

PrNiCo_5.UDF

Rp= 5.29 Rwp= 6.79 Rexp= 0.97

DIFF


30

2 theta / deg20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95

29447

14724

0

PowderCell 2.2

PrCo5

001

101

110

200

002

201

102

210

112

211

202

300

301

003 103

220

310

113

311

203

400

222

401

213

PrNiCo_6.UDF

Rp= 5.52 Rwp= 7.08 Rexp= 0.86

DIFF


2 theta / deg20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115

29754

14877

0

PowderCell 2.2

PrCo5 99.3%

001

101

110 200

002

201

102

210

112

202

300

301

003 103

310

113

203 400

222

401312

004

303

104 402

114

411

223

Co 0.7%

100

002

101

PNCo3 4hr.UDF

Rp= 2.91 Rwp= 3.74 Rexp= 0.85

DIFF


31

2 theta / deg20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115

29944

14972

0

PowderCell 2.2

PrCo5 97.1%

001

101

110

200

002

201

102

210

112

211

202

300

301

003 103

220

310

113

302

203 400

222

401

004

303

104 402

114411

223

NICKEL 2.3%

111

222

Co 0.6%

100

101

102

PNCo4 4hr.UDF

Rp= 3.06 Rwp= 4.00 Rexp= 1.22

DIFF


2 theta / deg20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115

29910

14955

0

PowderCell 2.2

PrCo5 91.4%

001

101

110

200

002

201

102

210

112

202

300

301

003 103

220

310

113

311

203 400

222

401 213

320

303

402

114

223

313

PR2CO17 8.6%

021

202

113

211

122

024

220

131

410

018

051

330

009

624

348

541

PNCo5 4hr.UDF

Rp= 2.88 Rwp= 3.66 Rexp= 0.51

DIFF

Figure A.11: X-ray diffraction refinement for PrCo5

32

Appendix B

Summary of refinement results for

Pr(Ni5−xCox)

33

Neu Textdokument

Refinement of PNCo1 4hr.UDF 27.10.2006 17:12:4 ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

PrCo5 89.26 vol.% (scf: 0.1193) PR2CO17 10.74 vol.% (scf: 0.0143)

R-values Rp=3.02 Rwp=3.87 Rexp=4.31 1 iterations of 100

parameter old new

PrCo5 ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ lattice a : 5.0192 5.0192 c : 3.9892 3.9892

profile U : 0.0000 0.0000 PsVoigt1 V : 0.0279 0.0291 W : 0.0149 0.0143

mixing na : 0.9320 0.9327 nb : 0.0000 -

overall B : 0.0000 -

PR2CO17 ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ lattice a : 8.4428 8.4429 c : 12.2465 12.2462


mixing na : 0.8950 0.9118 nb : 0.0000 -


global parameters ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ zero shift : -0.1718 -0.1718

displacement : 0.0000 -

backgr. polynom : 8 8

coeff. a0 : 11150.5170 11131.9600 a1 : -1204 -1201 a2 : 61.25 61.13 a3 : -1.813 -1.81 a4 : 0.03343 0.03339 a5 : -0.0003875 -0.0003873 a6 : 2.738E-6 2.74E-6 a7 : -1.076E-8 -1.078E-8 a8 : 1.8E-11 1.805E-11

Seite 1

Figure B.1: Summary of results for PrNi4Co1

34

Neu Textdokument


PrCo5 99.07 vol.% (scf: 0.7975) Co 0.14 vol.% (scf: 0.0011) NICKEL 0.79 vol.% (scf: 0.0064)


parameter old new

PrCo5 ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ lattice a : 4.9911 4.9911 c : 3.9782 3.9782


mixing na : 1.0000 1.0000 nb : 0.0000 -


Co ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ lattice a : 2.5239 2.5239 c : 4.0866 4.0857

profile U : 0.0300 - PsVoigt1 V : 0.0000 - W : 0.0120 -

mixing na : 0.8200 - nb : 0.0000 -


NICKEL ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ lattice a : 3.5108 3.5160


mixing na : 0.0000 0.0000 nb : 0.0000 -




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Refinement of PrNiCo_1.UDF 30.01.2007 14:45:37 ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯


parameter old new

PrCo5 ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ scaling : 0.9525 0.9380 lattice a : 4.9963 4.9963 c : 3.9804 3.9804


mixing na : 0.9308 0.9328 nb : 0.0000 -





coeff. a0 : 17291.5840 17292.7500 a1 : -2414 -2414 a2 : 138.8 138.8 a3 : -3.954 -3.954 a4 : 0.05599 0.05599 a5 : -0.0002389 -0.0002389 a6 : -3.318E-6 -3.318E-6 a7 : 4.444E-8 4.444E-8 a8 : -1.547E-10 -1.547E-10

Seite 1

Figure B.3: Summary of results for PrNi2,7Co2,3

36




parameter old new



mixing na : 0.8651 0.8650 nb : 0.0000 -





coeff. a0 : 18587.3890 18586.7500 a1 : -2560 -2560 a2 : 149.5 149.5 a3 : -4.592 -4.592 a4 : 0.08088 0.08088 a5 : -0.0008143 -0.0008143 a6 : 4.24E-6 4.24E-6 a7 : -7.466E-9 -7.466E-9 a8 : -1.036E-11 -1.036E-11

Seite 1


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parameter old new



mixing na : 0.6844 0.6848 nb : 0.0000 -






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parameter old new



mixing na : 0.7815 0.7836 nb : 0.0000 -






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parameter old new



mixing na : 0.8905 0.8904 nb : 0.0000 -


global parameters ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ zero shift : 0.0748 0.0748




Seite 1


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parameter old new

PrCo5 ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ scaling : 0.9313 - lattice a : 4.9964 - c : 3.9828 -


mixing na : 0.8291 0.8311 nb : 0.0000 -


global parameters ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ zero shift : 0.0614 -


backgr. polynom : 8 -

coeff. a0 : 18356.8200 - a1 : -2554 - a2 : 156.9 - a3 : -5.248 - a4 : 0.1049 - a5 : -0.001278 - a6 : 9.225E-6 - a7 : -3.568E-8 - a8 : 5.549E-11 -

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PrCo5 99.35 vol.% (scf: 0.9012) Co 0.65 vol.% (scf: 0.0059)


parameter old new

PrCo5 ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ lattice a : 4.9999 - c : 3.9850 -


mixing na : 0.9520 0.9525 nb : 0.0000 -


Co ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ lattice a : 2.5024 2.5024 c : 4.0828 4.0828


mixing na : 1.0000 1.0000 nb : 0.0000 -






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PrCo5 97.06 vol.% (scf: 1.3351) NICKEL 2.32 vol.% (scf: 0.0319) Co 0.61 vol.% (scf: 0.0084)


parameter old new

PrCo5 ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ lattice a : 4.9748 4.9748 c : 3.9755 3.9755


mixing na : 0.8508 0.8499 nb : 0.0000 -


NICKEL ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ lattice a : 3.5327 3.5327


mixing na : 1.0000 1.0000 nb : 0.0000 -


Co ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ lattice a : 2.5311 2.5311 c : 3.9706 3.9706


mixing na : 1.0000 1.0000 nb : 0.0000 -




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PrCo5 91.36 vol.% (scf: 1.1583) PR2CO17 8.64 vol.% (scf: 0.1095)


parameter old new

PrCo5 ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ lattice a : 5.0321 5.0321 c : 3.9843 3.9843


mixing na : 1.0000 1.0000 nb : 0.0000 -


PR2CO17 ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ lattice a : 8.4407 8.4407 c : 12.2782 12.2783


mixing na : 1.0000 1.0000 nb : 0.0000 -






Seite 1

Figure B.11: Summary of results for PrCo5

44

Appendix C

Fluxogram to study the MCE in the

PrNi5−xCox

Figure C.1: Fluxogram of the approach to study the MCE in the PrNi5−xCox system

45

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