Titre - Title

Mech 473 Lectures

Professor Rodney Herring

ObjectivesAt the end of this lecture you should be able to:Know the theoretical density of materials and how to calculate it for single element and compound materials.Know the thermal properties of materials.Discuss the role of atomic binding energy on the physical properties of materials

Material Properties for Design of Structures and ComponentsPhysical PropertiesDensity One of the most important properties of a material is its density because it determines the weight of the structure or component.It depends on the mean atomic mass of its atoms, their atomic or ionic sizes, and their crystal structures (the way they are packed).The density of materials primarily arises from their atomic mass (1 for H and 207 for lead)Metals are dense because they consist of heavy atoms, which tend to be closely packed.Polymers are not dense because they primarily consist of carbon and hydrogen.Ceramics tend to have low density because they primarily consist of C, O and N and have a low packing fraction.

Theoretical DensityThe theoretical density can be calculated using the properties of the crystal structure. The general formula is:

If a material is ionic or consists of different types of atoms or ions, this formula has to be modified accordingly. We will see some examples to clarify.Avogadros number, NA, is the number of atoms or molecules in one mole.NA = 6.02 x 1023 atoms/mole

Crystal Properties - DensityThe calculation of the density is an immediate extension of the calculation of the packing fraction of a unit cell.The mass per atom(s) is given by the atomic mass, i.e., mass/mole divided by the number of atoms per mole (Avogradros number).The volume is given by the dimensions of the unit cell.Eg., For Indium, the structure is body centered tetragonal with ao = 0.32517 nm and co = 0.49459 nm. The atomic mass = 114.82 g/mol. Calculate its density.Why would there be a difference between the calculated and measured density?

Crystal Properties - DensityCalculate the density of Magnesium Oxide, MgO, which has the NaCl structure.Eg., The atomic weight of Mg = 24.312 g/mol and O is 16 g/mole. For MgO, the ions touch along the edge of the cube in the FCC NaCl crystal structure so ao = 2r (Mg) + 2r (O) = 2(0.066) + 2(0.132) nm = 0.396 nm. Calculate its density.

Physical PropertiesThe Melting PointThe bonding energy of the atoms is directly proportional to the melting point (Tm) of the material.The bond energy is due to the long-range attractive energy of the atoms between positive and negative charges, which is Coulombic.The melting point can be related to the modulus of elasticity, E, of a material by,Where k is the Boltzman constant and W is the atomic volume in the structure of the material.

Binding Energy & Interatomic SpacingInteratomic spacingThe equilibrium distance between atoms is caused by a balance between repulsive and attractive forces. Equilibrium separation occurs when the total-atomic energy of the pair of atoms is at a minimum, or when no net force is acting to either attract or repel the atoms.The interatomic spacing is approximately equal to the atomic diameter or, for ionic materials, the sum of the two different ionic radii.

A material that has a high binding energy will have a high melting temperature and a high strength.

Binding Energy, Interatomic Spacing & Linear Thermal ExpansionThe coefficient of thermal expansion is influenced by the interatomic bonding.

Thermal PropertiesThe Melting PointThe thermal properties of a material can be studied in space using plasma crystals and the special condition of microgravity.What is microgravity?What is a plasma crystal?

Microgravity is used to study the physical properties and behaviour of materials because Microgravity reduces:1) hydrostatic pressure2) sedimentation/buoyancy3) thermal convection

In this example, diffusion rather than convection-driven process dominates the burning of a candle in microgravity.A quiescent environment is obtained.1 g0 g(microgravity)Where can we find the microgravity condition? Anywhere that has a free-fall condition, i.e., a satellite, space shuttle or space station orbiting the earth in space, in drop shafts , in drop tubes or at times when a plane flies in a parabola (parabolic flight).

~ 104 electrons on a particle of 5m diameter.Plasma crystals, which only exist in microgravity, can be used to show the atomic melting behaviour of materials.Plasma crystals are a collection of charged dust particles surrounded by trapped electrons, which are generated by irradiation of the particles by a Laser, hnExperiments using plasma crystals are being performed on the International Space Station.

Complex PlasmasCoulomb interaction strong coupling, if the attractive work function (Wpp) is greater than the repulsive work function (Wth).

Complex PlasmasCoulomb interaction strong coupling Coulomb crystallization ~ 0.2 mmPlasma Crystalforms if an ordered structure of the ions occurs.

Crystalline SystemPressure: 370barRF-Voltage (Vss): 32VParticle Size: 3,4mGas: ArgonVolume: 2.3 x 1.7 x 2.3 mmRandom orientation showing three dimensional distribution of ions floating in space.

The Melting of a Plasma Crystal

Plasma Crystals Grown in SpaceGive insight into physical phenomena such as thermal properties, which is otherwise unobservable terrestrially.Useful to study the thermally-induced transition between solid liquid gas plasma states of matter.

Later in this course we will use plasma crystal to study the following:The formation of defectsPhase separation (different crystal structures formed by small and large atoms)Convection of fluids at interfacesFlow of heat through a crystal via phonons (lattice vibrations)

Thermal PropertiesThe Melting PointHow does the melting temperature come into play in material design?It is a factor to use a material in a high temperature environment, such as that used in combustion engines and nuclear reactors.A high temperature for one material may be a low temperature with respect to another due to a difference in melting temperatures.To determine the effect of temperature on materials properties, we normalize the temperature using the absolute scale, Kelvin. As a rule of thumb, the ratio of the environmental temperature, T, to the melting point, Tm must be less than ~ 0.3 0.4, ie.,T/Tm < 0.3in order to neglect temperature effects on the mechanical material properties. Special creep resistant alloys can handle higher T ratios.

Thermal Properties - GlassesThe Glass Transition Temperature, TgThis is a property of noncrystalline or amorphous materials.If a noncrystalline structure forms, there is a gradual change in property below the melting point where the material is considered a supercooled liquid, which is a solid.The glass transition temperature applies to glasses, polymers and more recently, amorphous metals.General property behaviour of glass transition temperature, Tg, for amorphous solids relative to the melting point, Tm, for crystalline solids.

When silica crystallizes on cooling there is an abrupt change in density whereas for the solidification of glass there is not a fixed temperature.

GlassesGlass Transition TemperatureThe most important noncrystalline materials today are glasses.A glass is a solid material that has hardened to become rigid without crystallizing. Thermal Properties

The amorphous materials must cool at a fast enough rate to avoid crystallization. This was very difficult to achieve for the amorphous metals..

Material Properties for Design of Structures and ComponentsCoefficient of Linear Thermal ExpansionThis can also be related to the binding energy between atoms.The higher the bonding energy, the lower its thermal expansion for a given increase in temperature.The coefficient of linear thermal expansion, a, is defined macroscopically as,

Where L is the linear dimension of the body.It is also related to some physical properties such as the specific heat at constant volume, Cv, and volumetric specific heat at constant volume, rCv, and the elastic modulus, E,Where gG is the Gruneisens constant, which varies between 0.4 to 4 and is ~1 for metals.

Material Properties for Design of Structures and ComponentsCoefficient of Linear Thermal Expansion, aThus a is proportional to 1/E.Diamond, which has the highest elastic modulus and one of the lowest coefficients of thermal expansion, whereas, elastomers, which have low E, will expand the most.From the previous relationships, we see that a is also inversely proportional to the absolute melting point by,

For all solids, the thermal strain just before they melt is about the same.

ExamplesCoefficient of Linear Thermal Expansion, aIn structural materials such as the steels, engineers take into account a by incorporating expansion joints in structures used for buildings and bridges.In composites such as NiAl/TiB2, the a of the constituent materials need to be matched very closely to reduce the risk of delamination at the interfaces due to thermal stresses induced by thermal cycling.In the semiconducting industry, electronic devices are composed of multiple layers of different materials such as GaAs/AlGaAS, which can generate defects at the interfaces during thermal cycling. These defects can destroy or reduce the working lifetime of the device.

ExamplesOpto-electronic materails used for solar panels, lasers, LEDs, etc.GaAs will expand or contract more than Silicon for a unit change in temperature.The stress in the epi-layers will be different during the crystal growth temperatures (500o 600 oC) than when cooled to room temperature. For device manufacturing, the residual strain adds another variable to consider when manufacturing these material devices.

An inteface between Silicon and GaAs, showing that the lattice mismatch that has resulted in the generation of dislocations at their interface, which penetrate the GaAs and render it useless as an electronic or photonic material.

Defects in GaAs/InGaAs LaserNote that the laser looks to have a perfect crystal structure when using the 200[011] electron diffraction vector but actually has dislocations when viewed using 220[110].Dark lines are InGaAs layers and light lines are GaAs layers plus substrate and capping layers.

Material Properties for Design of Structures and ComponentsThermal Conductivity, k In heat conduction, thermal conductivity is the analogous property to electrical conductivity, s.When a temperature gradient, DT/Dx is imposed on a material, the flux of heat flow per unit area per unit time, Q, is

where k is in watts per meter per Kelvin.The analogous equation for the conduction of current density, J, isWhere E is the electric field, V is volts and s.

Material Properties for Design of Structures and ComponentsThermal ConductivityElectrons are the principle conductors of heat in materials. There is a relationship between k and s in metals given as,

where L is the Lorentz constant.Thermal conductivity is thus dependent on how fast electrons can move through the material and how much they scatter off atoms. The relationship is given byWhere C is the electron specific heat per unit volume, n is the electron velocity (2 x 10exp5 m/s), and l is the electron mean free path, ~10exp-7 m or ~100 nm. What would happen if we decreased the size of an electronic device to less than l?

Material Properties for Design of Structures and ComponentsThermal ConductivityIf the mean free path of the electron increases, its thermal conductivity increases.Thus superconductors, which have an almost infinitely long mean free path are very good heat conductors.Substituting solid solutes and other atomic-scale defects in metals will scatter electrons, reduce the mean free path, and thus reduce thermal conductivity.

Material Properties for Design of Structures and ComponentsThermal Conductivity, kIn ceramics and polymers, heat conduction is carried by phonons, not electrons, since electrons are not mobile. Phonons are atomic lattice vibrations, which are sensitive to impurities, lattice defects and surfaces.For ceramics and polymers, k is now given by

Where n is the elastic wave speed (~10exp(3) m/s, which is 2 orders of magnitude less than the electron velocity) and r is the density and rCp is the volumetric specific heat.

Material Properties for Design of Structures and ComponentsThermal ConductivityIn microgravity experiments involving plasma crystals conducted in space, phonons can be studied to help understand physical phenomena such as heat transfer.

Laser-excited Phonons in a Plasma Crystal A. Melzer et al. 2001

PhononsPhysical properties of phonons are being studied at UVic using electron holography (my research). The phonons physical properties of interest include their degree of coherence, spatial coherence width, and impact parameter (Coulomb interaction length). What are these?

Phonons The degree of coherence is the fraction of phonons that can interact with other phonons to create regions of maximum and minimum intensity regions (hot spots). The spatial coherence width is the physical dimension of a phonon, which is created at the atomic scale and finishes at the millimeter scale. The impact parameter (Coulomb interaction length) is the ability of phonons to interact with other sources of energy such as another phonon, an electron or hole, or a crystal defect. When an electron flows through a material such as in an electronic device, it caries with it a phonon. When a dislocation moves due to plastic deformation, a phonon travels down the dislocations core.

Phonons And Superconducting FluxonsThe two phonons associated with the two electrons require a high degree of coherence in order to establish a Cooper pair and thus superconductivity.Fluxons are small magnets in superconducting materials created by two revolving electrons coupled by phonons. The phonons act as the glue to bind the two electrons, known as a Cooper pair.The electron creates a phonon or lattice distortion in its path.The phonon is associated with a net positive charge.The other electron is attracted to the net positive charge and visa versa. The two electrons become bound or coupled.

Superconducting Fluxons

Example of a Superconducting Material, MgB2Canfield and Budko, Scientific America (April 2005) 81.The 0 0 0 plane of the hexagonal crystal is occupied by Boron atoms and has a high density of electrons, which are most likely supporting the formation of Cooper pair electrons responsible for the observed superconductivity. This hypothesis needs to be proven, which may be possible by measuring the degree of coherence of the phonons existing on this atomic plane.

Material Properties for Design of Structures and ComponentsThermal ConductivityIf the phonon conductivity is high in ceramics and polymers, then the thermal conductivity is high.Ceramic materials such as diamond, SiC and alumina have this property (high thermal conductivity) when they are cooled below a characteristic temperature called the Debye temperature. Diamond, SiC and alumina are being used for electronic devices operating at higher temperatures.Amorphous glass has poor thermal conductivity due to its irregular amorphous structure. It is used as a thermal and electrical insulator.Polymers have poor thermal conductivity because the elastic wave speed (n) is low and the mean free path of the disordered structure is small.

Material Properties for Design of Structures and ComponentsThermal ConductivityThe best thermal insulators are porous materials such as bricks (firebricks), cork and foams.Their conductivity is limited by the gas phase in their cells and by the heat transfer by radiation through the transparent walls. The walls of porous materials that can be coated with a metal such as Al or Au will reflect the heat wave and thus improve their thermal insulation.NASA uses porous Silica as its heat shield on the Space Shuttle, which ablates when it melts exposing fresh porous Silica for insulation. We will discuss this more towards the end of the course in the photonic materials lecture.

The End(Any questions or comments?)