Lecture 6

Size effects

Lecture 6

OUTLINE

-Why does size influence the material’s properties?-How does size influence the material’s performance? -Why are properties of nanoscale objects different than those of the same materials at the bulk scale?-Why nanomaterials are unstable?

MTX9100Nanomaterials

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Size-dependent propertiesAt the nanometer scale, properties become size-dependent.

For example,

(1) Chemical properties – reactivity, catalysis

(2) Thermal properties – melting temperature

(3) Mechanical properties – adhesion, capillary forces

(4) Optical properties – absorption and scattering of light

(5) Electrical properties – tunneling current

(6) Magnetic properties – superparamagnetic effect

New properties enable new applications2

Materials structures

Most materials are made up of ordered crystalsthat meet at disordered boundaries; the crystals innanomaterials are only 100–10,000 atoms across.

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Amorphous or “glassy” materials are totallydisordered; the only characteristic dimension isthat of the atoms or molecules that make them up.They are an extreme from of nanomaterial.

Thermal property - Melting point

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Thermal property - Melting temperature

Melting Point (Microscopic Definition)Temperature at which the atoms, ions, ormolecules in a substance have enough energy to overcome the intermolecular forces that hold the them in a “fixed” position in a solid

At macroscopic length scales, the melting temperature of materials is size-independent.For example, an ice cube and a glacier both melt at the same temperature.

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Thermal properties

Nanocrystal size decreases

surface energy increases

In contact with 3 atoms

In contact with surface energy increases

melting point decreases

In contact with 7 atoms

Surface atoms require lessenergy to move because they are in contact with fewer atoms of the substance

Example: 3 nm CdSe nanocrystal melts at 700 K compared to bulk CdSe at 1678 K

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Melting point as a function of size

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Thermal transport� Heat is transported in materials by two different

mechanisms: � lattice vibration waves (phonons) and � Free electrons. � In metals, the electron mechanism of heat transport is

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� In metals, the electron mechanism of heat transport is significantly more efficient than phonon processes.

� In the case of nonmetals, phonons are the main mechanism of thermal transport.

� In both metals and nonmetals, as the system length scale is reduced to the nanoscale, there are quantum confinement and classical scattering effects.

Quantum confinement� The presence of nearby surfaces in 0-D, 1-D, and 2-D

nanostructures causes a change in the distribution of the phonon frequencies as a function of phonon wavelength as well as the appearance of surface phonon modes.

� These processes lead to changes in the velocity with which

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� These processes lead to changes in the velocity with which the variations in the shape of the wave’s amplitude propagate, the so-called group velocity.

� The phonon lifetime is modified due to phonon-phonon interaction and free surface and grain boundary scattering.

Thermal property - Conductivity

where v is a particle velocity, l is a free path length, С = сn is a heat capacity of unit volume, c is a heat capacity of single particle, n is a number of particles

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Mechanical PropertiesMechanical PropertiesMechanical PropertiesMechanical Properties

At the nanoscale, surface and interface forces become dominant.

For example,

(1) Adhesion forces(2) Capillary forces

These forces can exceed forces that are normally dominant at macroscopic

(2) Capillary forces(3) Strain forces dominant at macroscopic

length scales

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Mechanical propertiesRelative to microstructural (MSM) metals and alloys, the NSM contain a higher fraction of grain boundary volume (for example, for a grain size of 10 nm, between 14 and 27% of all atoms reside in a region within 0.5–1.0 nm of a grain boundary);therefore,

grain boundaries play a significant role in the materials properties. properties.

Changes in the grain size result in a high density of incoherent interfaces or other lattice defects such as dislocations, vacancies, etc. As the grain size d of the solid decreases, the proportion of atoms located at or near grain boundaries relative to those within the interior of a crystalline grain, scales as 1/d. This has important implications for properties in ultra-fine-grained materials which will be principally controlled by interfacial properties rather than those of the bulk.12

Grain boundariesCrystals contain internal interfacial defects, know asgrain boundaries, where the lattice orientation changes

The misfit between adjacent crystallites in the grain boundaries changes the atomic structure (e.g. the average atomic density, the nearest-neighbor coordination, etc.) of materials.At high defect densities the volume fraction of At high defect densities the volume fraction of defects becomes comparable with the volume fraction of the crystalline regions. In fact, this is the case if the crystaldiameter becomes comparable with the thickness of the interfaces.

Non – equilibrium materials

DEFECTS !!!13

Crystals always contain defects

Vacancies are point defects in the crystalline structure of a solid that may control many physical properties in materials such as conductivity and reactivity.

However, nanocrystals are predicted to be essentially vacancy-free; their small size precludes any significant vacancy concentration. This result has important consequences for all thermo mechanical properties and processes (such as creep and precipitation) which are based on the presence and migration of vacancies in the lattice.

Point defects: 0.1 nm (10-10 m)

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Impurity atoms

Material properties can be alteredsignificantly through the additionof impurity atoms15

Glossary

� Point defects - Imperfections, such as vacancies, that are located typically at one (in some cases a few) sites in the crystal.

� Extended defects - Defects that involve several atoms/ions and thus occur over a finite volume of the crystalline material (e.g., dislocations, stacking faults, etc.).

� Vacancy - An atom or an ion missing from its regular � Vacancy - An atom or an ion missing from its regular crystallographic site.

� Interstitial defect - A point defect produced when an atom is placed into the crystal at a site that is normally not a lattice point.

� Substitutional defect - A point defect produced when an atom is removed from a regular lattice point and replaced with a different atom, usually of a different size.

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Summary of point defects

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(a) vacancy, (b) interstitial atom, (c) small substitutional atom, (d) large substitutional atom, (e) Frenkel defect, (f) Schottky defect. 17

Defects for plasticity

Crystals all contain line defects known as dislocations

Dislocations act as as

the main source of plastic

deformation in crystalline materials

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Plastic deformation

(a) When a shear stress is applied to the dislocation in (a), the atoms are displaced, causing the dislocation to move one Burgers vector in the slip direction (b). Continued movement of the dislocation eventually creates a step (c), and the crystal is deformed. (Adapted from A.G. Guy, Essentials of

Materials Science, McGraw-Hill, 1976.) (d) Motion of caterpillar is analogous to the motion of a dislocation.

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DislocationsDislocations are positioned closer together and dislocations movement in the net is hindered by interaction between them. Together with the reduced elastic strain energy, this fact

Dislocations have a less dominant role to play in the description of the properties of

nanocrystals.

The free energy of a dislocation is made up of a number of terms:

(i) the core energy (within a radius of about three lattice planes from the dislocation

core); strain energy, this fact results in dislocations that are relatively immobile andthe imposed stress necessary to deform a material increases with decrease in grain size.

core); (ii) the elastic strain energy outside the core

and extending to the boundaries of the crystal, and

(iii) the free energy arising from the entropy contributions.

In mc the first and second terms increase the free energy

and are by far the most dominant terms. Hence dislocations, unlike vacancies, do not

exist in thermal equilibrium.20

Increase in strengths and

hardnessThe relation between yield stress and grain size is described mathematically by the Hall-Petch equation

where ky is the strengthening coefficient (a constant unique to each material), σo is a materials constant for the starting stress for dislocation movement (or the resistance of the lattice to dislocation motion), d is the grain diameter, and σy is the yield

stress.21

Grain boundary strengtheningGrain boundary strengthening (or Hall-Petch strengthening) is a method of strengthening materials by changing their average grain size. It is based on the observation that grain boundaries impede dislocation movement and that the number of dislocations within a grain have an effect on how easily dislocations can traverse grain boundaries and travel from grain to grain. So, by changing grain size one can influence dislocation movement and yield strength. yield strength.

This is a schematic roughly illustrating the concept of dislocation pile up and how it effects the strength of the material. A material with larger grain size is able to have more dislocation to pile up leading to a bigger driving force for dislocations to move from one grain to another. Thus you will have to apply less force to move a dislocation from a larger than from a smaller grain, leading materials with smaller grains to exhibit higher yield stress.

http://en.wikipedia.org/wiki/Hall-Petch

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Hall-Petch strengthening limit

Hall-Petch Strengthening is limited by the size of dislocations. Once the grain size reaches about 10 nm, grain boundaries start to slide.

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Ductility

Deformation and fracture of ultra-high-fine materials: (a) Plastic flow localization; (b) nanockrack nucleation; (c) final failure

Fracture surface of a 30 nm grain size electrodeposited Ni tensile specimen.

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Deformation of nano-metal

from Kumar et al., Acta Materialia, 2003, v.51, 5743 – 577425

How to improve ductility?

NC materials with high ductility:

(a) a bimodal single-phase structure composedof nanograins and large of nanograins and large grains; and(b) nano-composite consisting of nanoscalegrains and dendrite – like inclusions of the second phase (from I.A. Ovid’ko, Rev. Adv. Mater. Sci., 2005, v.10, 89–104).

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Nanostructured solids

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Why nanostructured polycrystalline

materials are unstable?

GB consists of several types of extrinsic defects, namely, stationary dislocations with Burgers vectors normal to a boundary plane, gliding or tangential dislocations with Burgers vectors tangential to the boundary plane, and disclinations in triple junctions.Disclinations and grain boundary dislocations form elastically distorted layers (zones) near grain boundaries.distorted layers (zones) near grain boundaries.

High density of defects -> High energyNature -> seek to lower energy

Grain growth occurs in materials to reduce the overall energy of the system by reducing the total grain boundary energy. Therefore, grain growth in NC materials is primarily driven by the excess energy stored in the grain or interphaseboundaries.

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Grain boundaries diffusion

relative increasing of GB diffusion coefficient

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Pileups in a grain and a layer of a

nanolayer structure

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Hardness

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Nanoscale optical propertiesNanoscale optical propertiesNanoscale optical propertiesNanoscale optical properties

• Bulk gold appears yellow in color

• Nanosized gold appears red in color– The particles are so small – The particles are so small that electrons are not free to move about as in bulk gold– Because this movement is restricted, the particles react differently with light

Optical properties are connected with electronic structure, a change in zone structure leads to a change in absorption and luminescence spectra.32

Visible electromagnetic spectrum

CdSe Semiconducting Quantum Dots

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Surface plasmon

absorption Surface plasmon absorption of spherical nanoparticles and its size dependence.(a) A schematic illustrating the excitation of the dipole surface plasmon oscillation. The electric field of an incoming light wave induces a polarization of the (free) conduction electrons with respect to the much heavier ionic core of a spherical metal nanoparticle.nanoparticle.A net charge difference is only felt at the nanoparticle surfaces, which in turn acts as a restoring force. In this way a dipolar oscillation of the electrons is created with period T.(b) Optical absorption spectra of 22, 48 and 99nm spherical gold nanoparticles. The broad absorption band corresponds to the surface plasmon resonance (from S. Link,M.A. El-Sayed Int. Rev. Phys. Chem. 2000, v.19, 409)34

optical propertiesAbsorption (fluorescence) spectrum of Na atom relates to the transition 2S – 2P.The spectrum of Na3 cluster expands into the discrete molecular spectrum reflecting electron excitations and atom oscillations. Continuous spectrum of Na8 cluster reflects the processes of dissociations and defragmentation of cluster on atoms. Spectrum of nanoparticle reflects

Tran

sform

ation of absorption spectra of sodium from atom

to solid

Spectrum of nanoparticle reflects resonance absorption of cluster atoms. Spectrum of massive film reflects the interband transitions of electrons in metal.

Optical absorption spectra of sodium: а) for atom, b) for cluster Na3, c) for cluster Na8, d) for nanoparticle of d<10 nm size (~106 atoms) in NaCl crystal, e) for thin film of d=10 nm width.

Tran

sform

ation of absorption spectra of sodium from atom

to solid

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Blue shiftBlue shift refers to a shortening of a transmitted signal's wavelength, and/or an increase in its frequency. The name comes from the fact that the shorter-wavelength end of the optical spectrum is the blue end, hence, when visible light is compacted in wavelength, it is "shifted towards the blue", or "blue-shifted".

Blue shift phenomenonBlue shift phenomenonis a quantum size effect.

Transformation of zone structure of a solid under

reduction of its size from macro-to nano-scale down to a single atom, showing the increase of the band gap g ∆E and the blue shift hω = ∆E for nanoparticlesand nanostructured state of

matter.

W is a work function, EF is a Fermi energy, HOMO is the highest occupied molecular orbital, LUMO is the lowest unoccupied molecular orbital36

The properties of MC and NC

materials of the same chemical

composition

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In the quantum world, the rules are In the quantum world, the rules are

different….different….

The

classical

world

The

quantum

world

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Quantum tunnelingQuantum tunnelingQuantum tunnelingQuantum tunneling

A nanoscopic phenomenon in which a particle violates the principles of classical mechanics by

penetrating a potential barrier or impedance higher than the kinetic energy of the particle.

Electron tunneling is attained when a particle with lower energy is able to exist on the other side of an energy

barrier with higher potential energy.39

Go through the wallGo through the wallGo through the wallGo through the wall

A barrier, in terms of quantum tunneling, may

Tunneling is the penetration of an electron into a

classically forbidden region.

A barrier, in terms of quantum tunneling, may be a form of energy state analogous to a "hill"

or incline in classical mechanics, which classically suggests that passage through or over such a barrier would be impossible without

sufficient energy.

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The principal of quantum tunneling

Electrons exhibit wave behavior and their position is presented by a wave (probability) function.

The wave function represents a finite probability of finding an electron on the other side of the electron on the other side of the potential barrier.

Since the electron does not posses enough kinetic energy to overcome the potential barrier, the only way the electron can appear on the other side is by tunneling through the barrier. 41