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PHAS3447: Materials & NanomaterialsA. Al-Musalhi, M. Motwani, Y. Houston[2018]Collated from the course notes provided by Dr. Mark Buitelaar and Prof. Thanh Nguyen, aswell as Callister and Rethwisch’sMaterial Science and Engineering.Contents 1 Basic Principles 1 Introduction 1 Crystal Structu...

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PHAS3447: Materials & Nanomaterials A. Al-Musalhi, M. Motwani, Y. Houston [2018]

Collated from the course notes provided by Dr. Mark Buitelaar and Prof. Thanh Nguyen, as well as Callister and Rethwisch’s Material Science and Engineering.

Contents 1 Basic Principles 4 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2 Crystal Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2.1 Crystal systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2.2 Stacking sequences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.2.3 Crystallographic directions and planes . . . . . . . . . . . . . . . . . . . . . . . 8 1.2.4 Bragg’s law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.2.5 Additional terms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.3 Bonding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.3.1 Covalent bonding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.3.2 Ionic bonding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.3.3 Metallic bonding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.3.4 Van der Waals forces (secondary) . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.3.5 Interatomic potentials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.4 Defects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.4.1 Point defects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.4.2 Dislocations (line defects) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 1.4.3 Grain boundaries (area defects) . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 1.5 Diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 1.5.1 Fick’s laws . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 1.5.2 Temperature dependence of diffusion coefficient . . . . . . . . . . . . . . . . . . 20 1.5.3 Grain boundary diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2 Mechanical Properties of Materials 22 2.1 Elastic and Plastic Deformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 2.1.1 Stress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 2.1.2 Strain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2.1.3 Elastic deformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2.1.4 Plastic deformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 2.1.5 Deformation mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 2.2 Strengthening Metals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 2.2.1 Solid solution strengthening . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 2.2.2 Precipitation strengthening . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 2.2.3 Strain hardening (cold working) . . . . . . . . . . . . . . . . . . . . . . . . . . 32 2.2.4 Reducing the grain size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 2.3 Failure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 2.3.1 Fracture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 2.3.2 Fatigue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 2.3.3 Creep . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

1

CONTENTS

2

3 Phase Diagrams and Alloys 3.1 Basic Terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Binary Phase Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.1 Binary isomorphous systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.2 Interpretation of phase diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.3 Microstructure development in isomorphous alloys . . . . . . . . . . . . . . . . 3.2.4 Binary eutectic systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.5 Microstructure development in eutectic alloys . . . . . . . . . . . . . . . . . . . 3.2.6 Additional terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 The Iron-Carbon System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.1 The iron-iron carbide (Fe-Fe3 C) phase diagram . . . . . . . . . . . . . . . . . . 3.3.2 Microstructure development in iron-carbon alloys . . . . . . . . . . . . . . . . . 3.4 Phase Transformations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.1 Kinetics of phase transformations . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5 Microstructural and Property Changes in Iron-Carbon Alloys . . . . . . . . . . . . . . 3.5.1 Isothermal transformation diagrams . . . . . . . . . . . . . . . . . . . . . . . . 3.6 Mechanical Behaviour of Iron-Carbon Alloys . . . . . . . . . . . . . . . . . . . . . . . 3.6.1 Pearlite . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6.2 Spheroidite . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6.3 Bainite . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6.4 Martensite . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

44 44 44 45 45 47 50 51 55 56 56 57 62 62 67 67 72 72 73 73 74

4 Non-metallic Materials 4.1 Graphene and Carbon Nanotubes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.1 Graphene . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.2 Carbon nanotubes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Polymers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.1 Basic properties of polymers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.2 Polymer crystallinity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.3 Mechanical properties of polymers . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.4 Types of polymer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.5 Vulcanisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.6 Plastic deformation and fracture of polymers . . . . . . . . . . . . . . . . . . . 4.2.7 Glassy to rubbery transition . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Ceramics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.1 Crystal structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.2 Properties of ceramics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.3 Production and shaping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.4 Strengthening ceramics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.5 Glass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4 Composite Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.1 Particle-reinforced composites . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.2 Fibre-reinforced composites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.3 Nanocomposites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5 Colloids and Optical Nanoparticles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5.1 Electrostatic stabilisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5.2 Steric stabilisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5.3 Surface plasmon resonance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5.4 Quantum dots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5.5 F¨orster resonance energy transfer . . . . . . . . . . . . . . . . . . . . . . . . . .

77 77 77 78 80 81 83 84 84 85 85 86 88 88 89 89 90 90 92 93 93 96 96 97 97 98 98 99

CONTENTS

3

5 Functional Properties 100 5.1 Electrical Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 5.1.1 Conductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 5.1.2 Semiconductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 5.1.3 Dielectric materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 5.1.4 Ferroelectric materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 5.1.5 Piezoelectric materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 5.2 Optical Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 5.2.1 Optical properties of metals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 5.2.2 Optical properties of semiconductors and insulators . . . . . . . . . . . . . . . 107 5.2.3 Luminescence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 5.3 Magnetic Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 5.3.1 Types of magnetic materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 5.3.2 Magnetic hysteresis loop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 5.3.3 Soft magnetic materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 5.3.4 Hard magnetic materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 5.3.5 Magnetic storage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 5.4 Properties of Magnetic Nanoparticles . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 5.4.1 Anisotropy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 5.4.2 Superparamagnetism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 5.4.3 Field cooling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 5.4.4 Zero-field cooling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 5.4.5 Size-dependent magnetic properties . . . . . . . . . . . . . . . . . . . . . . . . . 114 5.4.6 Stoner-Wohlfarth particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 5.4.7 Clinical applicability of magnetic nanoparticles . . . . . . . . . . . . . . . . . . 117

Chapter 1

Basic Principles 1.1

Introduction

Material science is the study of how the structures and manufacture processes of materials influence their properties. As such, a plethora of applications stem from the underlying concepts and techniques with which materials are formed. In contrast to solid-state physics, which aims to explain how and why matter behaves as it does, material science is concerned with exploiting and improving the known behaviours to suit a particular purpose. Material properties depend on the arrangement of atoms (crystal structure), the interaction between the atoms (bonding) and the defects (microstructure).

1.2 1.2.1

Crystal Structures Crystal systems

A unit cell is the smallest repetitive volume which contains the complete lattice pattern of a crystal. The arrangement of atoms in a unit cell is known as a basis. On the other hand, crystal lattice structures are classified according to the symmetry of the unit cell. In 3D, there are 14 different Bravais lattices - grouped into 7 classes (Figure 1.1). The lattice describes the underlying periodicity of the structure, whereas the basis is the group of atoms that is being repeated. Hence, the crystal structure consists of the combination of a lattice structure and basis. Four commonly-encountered crystal structures are the simple cubic (sc), body-centred cubic (bcc), face-centred cubic (fcc) and hexagonal close-packed (hcp) unit cells (Figure 1.2). Note that ’honeycomb’ hcp lattices are not the same as the hexagonal Bravais lattices. The coordination number of a unit cell is defined as the number of nearest-neighbours immediately surrounding an atom in the cell. In addition, a measure of a unit cell’s close-packing efficiency is given by the atomic packing factor (APF): AP F =

N Vatom Vcell

(1.1)

where N is the number of atoms in the unit cell, Vatom is the spherical volume of one atom and Vcell is the volume of the unit cell. This calculation models atoms as hard spheres (Figure 1.2). 4

CHAPTER 1. BASIC PRINCIPLES

5

Figure 1.1: Diagrams of all the 3D Bravais lattices, including sc (primitive), bcc and fcc structures.

Figure 1.2: Illustrations of (a) hcp, (b) fcc and (c) bcc lattice structures. The sc structure was omitted as it simply consists of a cube with an atomic at each vertex.

6

CHAPTER 1. BASIC PRINCIPLES

For example, the calculation of the APF of an bcc lattice is shown below:

Continuing to model atoms as hard spheres, a crystal’s theoretical density can be calculated similarly: ρth =

mass of atoms in unit cell NA = V total volume of unit cell cell N A

(1.2)

where A is the atomic weight and NA is Avogadro’s constant (6.022 × 1023 atoms mol−1 ). The coordination numbers and atomic packing factors for each common structure are summarised below - along with examples of elements that exhibit these properties.

sc bcc fcc hcp

Coordination number 6 8 12 12

APF 0.52 0.68 0.74 0.74

Examples Po Cr, Mo, α-Fe Al, Cu, γ-Fe Co, Zn, Ti

CHAPTER 1. BASIC PRINCIPLES

1.2.2

7

Stacking sequences

Solids with non-directional bonding (e.g. van der Waals solids, elemental metals) favour structures with the closest packing of atoms. In 2D, the closest packing is achieved by a hexagonal arrangements of atoms. In 3D, however, there are two different ways in which these hexagonal layers can be stacked to achieve close packed structures (Figure 1.3). If spheres in the second layer go on top of the B sites, then spheres in the third layer can go on either the A or the C sites. The ABAB arrangement leads to a hcp structure, whereas the ABCABC stacking gives rise to an fcc structure (Figure 1.4).

Figure 1.3: Illustration of potential stacking arrangements for close-packing.

Figure 1.4: Formation of hcp and fcc lattice structures resulting from ABA and ABC sequences.

8

CHAPTER 1. BASIC PRINCIPLES

1.2.3

Crystallographic directions and planes

Point coordinates can be used to refer to positions within a unit cell - with a defined origin typically at one vertex or the centre of the cell. Translating a point by an integer multiple of lattice constants results in an identical position within another  unit cell. The coordinates are typically written in multiples of the lattice parameters, i.e. a 12 , 21 , 21 indicates the centre of a sc unit cell, taking a corner as the origin. Crystallographic directions are labelled in terms of the lattice basis vectors as [uvw] where u, v and w are the smallest integers such that the vector ua1 + va2 + wa3 points in the desired direction. A set of directions equivalent by symmetry is denoted by huvwi, such that e.g. h100i includes the directions [100], [010] and [001]. An overbar on a number indicates a negative, e.g. [¯100]. From this, the atomic linear density (LD) can be defined as: LD =

N |[uvw]|

(1.3)

where |[uvw]| is the unit length of the direction vector and N is the number of atoms along the vector. More importantly, identifying families of lattice planes is crucial to interpret diffraction data. Each family of lattice planes contains all lattice points, has the same lattice point density per plane and a characteristic inter-plane spacing d. These are labelled using Miller indices, denoted as (hkl). The Miller indices of a particular plane are obtained by taking the reciprocals of the points at which the plane intersects the crystallographic axes. The reciprocals are then scaled by a common factor to obtain integer values to represent h, k and l. As with the direction vectors, a set of planes equivalent by symmetry is denoted by {hkl}. Examples of obtaining Miller indices are shown below:

9

CHAPTER 1. BASIC PRINCIPLES

1.2.4

Bragg’s law

Crystal structures are generally determined using diffraction techniques e.g. x-ray diffraction. Assuming that lattice planes reflect electromagnetic radiation with specular geometry (θi = θf ), rays reflect off lattice planes with separation d as depicted in Figure 1.5.

Figure 1.5: Schematic of rays reflecting from lattice planes with spacing d .

For constructive interference to occur, the path difference AO + OB must be equal to an integer n number of wavelengths λ, resulting in Bragg’s law: 2d sin θ = nλ

1.2.5

(1.4)

Additional terms

Single crystals exhibit anisotropic properties, i.e. they vary with dependence on direction. Alternatively, polycrystals have isotropic properties (no variation with direction) if the different grains are randomly oriented. However, textured grains result in anisotropic properties. Allotropy or polymorphism describes instances in which certain materials are able to form different crystal structures, e.g. carbon can form graphite or diamond.

1.3

Bonding

The strength of the bonds in a material is the most important factor in determining its mechanical properties – materials are categorised depending on the type of bonding used.

1.3.1

Covalent bonding

Covalent bonds involve sharing electrons between atoms, and are hence directional. Materials consisting of these bonds exhibit high melting temperatures due to bonds requiring energies on the order of ∼ 5 − 7eV to break. In addition, such materials are strong, low-density as well as stiff and brittle (e.g. ceramics).

1.3.2

Ionic bonding

Electrons are transferred between atoms - This produces oppositely charged ions (positive cation and negative anion) that are electrically attracted via the Coulomb force. As such, unlike covalent bonds, ionic bonds are non-directional. These bonds are also strong, with an energy of ∼ 3 − 5eV . Similarly

10

CHAPTER 1. BASIC PRINCIPLES

to covalent bonds, materials with ionic bonding are stiff, low-density and brittle, with high melting points. Ionic bonds also contain some covalent character depending on the electronegativites of the ions: 2

Ionic character fraction = 1 − e0.25(XA −XB )

(1.5)

where XA and XB are the electronegativities of the two ions.

1.3.3

Metallic bonding

Metallic substances consist of positive ions embedded in a sea of delocalised electrons - which is all held together by the Coulomb force. They are are non-directional and favour close-packed structures (fcc and hcp), though some transition metals exhibit some directional bonding and therefore tend to non-close-packed structures (bcc). With bond energies of ∼ 0.7 − 3eV , metallic bonding results in relatively high melting temperatures. In addition, the free electrons make metallic structures excellent electrical and thermal conductors, as well as high density, strength and ductility.

1.3.4

Van der Waals forces (secondary)

Van der Waals forces occur as a result of weak dipole-dipole interactions between either induced or permanent dipoles. These are mostly present between c...