Material Properties Lecture (3) PDF

Material Properties Lecture (3) Dr. Marwa Mostafa  Characteristics of a Good Conductor - high electrical and thermal conductivity, - high melting point, - good oxidation resistance, - low cost, - good wear and abrasion resistance, and - better mechanical properties Conductors  The resi...

Material Properties Lecture (3) Dr. Marwa Mostafa  Characteristics of a Good Conductor - high electrical and thermal conductivity, - high melting point, - good oxidation resistance, - low cost, - good wear and abrasion resistance, and - better mechanical properties Conductors  The resistivity of metals essentially increases linearly with increasing temperature: ρ2=ρ1(1+α (T2-T1))  where α is the linear temperature coefficient of resistivity, and Tl and T2 are two different temperatures. Resistivity of Metals  the free electrons are accelerated in a metal under the influence of an electric field maintained.  The drifting electrons can be considered, in a preliminary, classical description, to occasionally collide (that is, electrostatically interact) with certain lattice atoms, thus losing some of their energy.  the drifting electrons are then said to migrate in a zigzag path through the conductor from the cathode to the anode.  Now, at higher temperatures, the lattice atoms increasingly oscillate about their equilibrium positions due to the supply of thermal energy, thus enhancing the probability for collisions by the drifting electrons.  As a consequence, the resistance rises with higher temperatures.  At near-zero temperatures, the electrical resistance does not completely vanish.  There always remains a residual resistivity, ρres, which is thought to be caused by "collisions" of electrons (i.e., by electrostatic interactions) with imperfections in the crystal (such as impurities, vacancies, grain boundaries, or dislocation).  On the other hand, one may describe the electrons to have a wave nature.  The matter waves may be thought to be scattered by lattice atoms. Scattering is the dissipation of radiation on small particles in all directions.  The atoms absorb the energy of an incoming wave and thus become oscillators. These oscillators in turn re-emit energy in the form of spherical waves.  As a result, a wave which propagates through an ideal crystal (having periodically arranged atoms) does not suffer any change in intensity or direction (only its velocity is modified).  This mechanism is called coherent scattering.  If, however, the scattering centers are not periodically arranged (impurity atoms, vacancies, grain boundaries, thermal vibration of atoms, etc.), the wave is said to be incoherently scattered.  This energy loss qualitatively explains the resistance.  the total resistivity arises from independent mechanisms: ρ= ρth + ρimp + ρdef = ρth + ρres  ρth is called the ideal resistivity,  whereas the resistivity that has its origin in impurities (ρimp) and defects (ρdef) is summed up in the residual resistivity (ρres).  The Newtonian-type equation (force equals mass times acceleration) of this free electron model: m.dv/dt + γ.v = e.ζ  Where v is the drift velocity of the electrons, m is the electron mass, γ is a constant which takes the electron/atom collisions into consideration (called damping strength),  𝑁𝑓.𝑒 2.𝜏  the conductivity: 𝜎 = 𝑚 𝜏 is the average time between two consecutive collisions (called the relaxation time), and Nf is the number of free electrons per cubic meter in the material Characteristic band structures for the main classes of materials according to quantum theory  Insulators and semiconductors, have completely filled electron bands. Metals, on the other hand, are characterized by partially filled electron bands. The amount of filling depends on the material, that is, on the electron concentration and the amount of band overlapping Simplified representation for energy bands  the individual energy states (the possibilities for electron occupation) are often denser in the center of a band.  To account for this, one defines a density of energy states, shortly called the density of states, Z(E). Schematic representation of the density of electron states within an electron energy band 1- only those materials that possess partially filled electron bands are capable of conducting an electric current. Electrons can then be lifted slightly above the Fermi energy into an allowed and unfilled energy state. This permits them to be accelerated by an electric field, thus producing a current. according to quantum theory 2- only those electrons that are dose to the Fermi energy participate in the electric conduction. (The classical electron theory taught us instead that all free electrons would contribute to the current.) 3- the number of electrons near the Fermi energy depends on the density of available electron states.  1  𝜎= 𝑒 2 𝑣𝑓2 𝜏𝑁 𝐸𝐹 3  where vF is the velocity of the electrons at the Fermi energy (called the Fermi velocity) and N(EF) is the density of filled electron states (called the population density) at the Fermi energy.  The population density is proportional to Z(E) The conductivity in quantum mechanical terms Report2 :Ceramics and Organic Polymers Report 3 :Alloys and Composites