Vibrating in synch is often a low energy configuration (preferred).
Generates waves of atomic motion.
Often called phonons , similar to photons but atomic motion instead of optical quanta.
HEAT CAPACITY Capacity at constant volume = C V Capacity at constant pressure = C P C P is typically > C V , but the difference is small for solids. When heated, materials experience an increase in T. This means that heat is absorbed. Heat capacity represents the amount of energy required to produce a unit temperature rise. H 2 O has a higher heat capacity
HEAT CAPACITY 3 N 0 k b D =Temperature at which D (Cu) D (Al) D (Pb)
THERMAL CONDUCTIVITY • General: The ability of a material to transfer heat. • Quantitative: Atomic view: Electronic and/or Atomic vibrations in hotter region carry energy (vibrations) to cooler regions. In a metal, electrons are free and thus dominate thermal conductivity. In a ceramic, phonons are more important. Fick’s First Law temperature gradient k=thermal conductivity (J/m-K-s): Defines material’s ability to transfer heat. heat flux (J/m 2 -s)
THERMAL CONDUCTIVITY Fick’s Second Law • Non-Steady State: dT/dt is not constant.
Selected values from Table 19.1, Callister 6e . K=k l +k e : Again think about band gaps: metals have lots of free electrons (k e is large), while ceramics have few (only k l is active). THERMAL CONDUCTIVITY
Good heat conductors are usually good electrical conductors .
(Wiedemann & Franz, 1853)
Thermal conductivity changes by 4 orders of magnitude (~ 25 for electrical conductivity ).
Metals & Alloys: free e- pick up energy due to thermal vibrations of atoms as T increases and lose it when it decreases .
Insulators (Dielectrics): no free e- . Phonons (lattice vibration quanta) are created as T increases , eliminated as it decreases .
Thermal conductivity is temperature dependent.
Analagous to electron scattering.
Usually first decreases with increasing temperature
Higher Temp=more scattering of electrons AND phonons, thus less transfer of heat.
Then increases at still higher temperatures due to other processes we haven‘t considered in this class (radiative heat transfer—eg. IR lamps).
Thermal conductivity optimization
To maximize thermal conductivity, there are several options:
Provide as many free electrons (in the conduction band) as possible
free electrons conduct heat more efficiently than phonons.
Make crystalline instead of amorphous
irregular atomic positions in amorphous materials scatter phonons and diminish thermal conductivity
Remove grain boundaries
gb’s scatter electrons and phonons that carry heat
Remove pores (air is a terrible conductor of heat)
THERMAL STRESSES • Occurs due to: --uneven heating/cooling --mismatch in thermal expansion. • Example Problem 19.1, p. 666, Callister 6e . --A brass rod is stress-free at room temperature (20C). --It is heated up, but prevented from lengthening. --At what T does the stress reach -172MPa? Answer: 106C -172MPa 100GPa 20 x 10 -6 /C 20C Strain ( ε ) due to ∆ T causes a stress ( σ ) that depends on the modulus of elasticity (E):
THERMAL SHOCK RESISTANCE • Thermal shock is fracture of brittle ceramics due to asymmetric thermal expansion. • Occurs due to: uneven heating/cooling. • The change in T with position leads to built in strain and thus stress. • Ex: Assume top thin layer is rapidly cooled from T 1 to T 2 : Tension develops at surface Critical temperature difference for fracture (set = f ) Temperature difference that can be produced by cooling: • Result: • Large thermal shock resistance when is large. set equal
THERMAL PROTECTION SYSTEM • Application: Space Shuttle Orbiter Fig. 23.0, Callister 5e . (Fig. 23.0 courtesy the National Aeronautics and Space Administration. Fig. 19.2W, Callister 6e . (Fig. 19.2W adapted from L.J. Korb, C.A. Morant, R.M. Calland, and C.S. Thatcher, "The Shuttle Orbiter Thermal Protection System", Ceramic Bulletin , No. 11, Nov. 1981, p. 1189.) • Silica tiles (400-1260C) : --large scale application Fig. 19.3W, Callister 5e . (Fig. 19.3W courtesy the National Aeronautics and Space Administration. --microstructure: ~90% porosity! Si fibers bonded to one another during heat treatment. Fig. 19.4W, Callister 5e . (Fig. 219.4W courtesy Lockheed Aerospace Ceramics Systems, Sunnyvale, CA.)
THERMOELECTRIC COOLING & HEATING Two different materials are connected at the their ends and form a loop. One junction is heated up. There exists a potential difference that is proportional to the temperature difference between the ends.
THERMOELECTRIC COOLING & HEATING Reversion of the Seebeck effect is the Peltier Effect. A direct current flowing through heterojunctions causes one junction to be cooled and one junction to be heated up. Lead telluride and or bismuth telluride are typical materials in thermoelectric devices that are used for heating and refrigeration .
THERMOELECTRIC COOLING & HEATING Why does this happen? When two different electrical conductors are brought together, e- are transferred from the material with higher E F to the one with the lower E F until E F (material 1)= E F (material 2). Material with smaller E F will be (-) charged. This results in a contact potential which depends on T. e- at higher E F are caused by the current to transfer their energy to the material with lower E F , which in turn heats up . Material with higher E F loses energy and cools down .
THERMOELECTRIC COOLING & HEATING Peltier–Seebeck effect, or the thermoelectric effect , is the direct conversion of thermal differentials to electric voltage and vice versa. The effect for metals and alloys is small , microvolts/K . For Bi 2 Te 3 or PbTe ( semiconductors ), it can reach up to millivolts/K . Applications: Temperature measurement via thermocouples (copper/constantan, Cu-45%Ni, chromel, 90%Ni-10%Cr,…); thermoelectric power generators (used in Siberia and Alaska); thermoelectric refrigerators ; thermal diode in microprocessors to monitor T in the microprocessors die or in other thermal sensor or actuators.
19.18 (a) Is thermal conductivity better for a single crystal or a polycrystal?
The thermal conductivity of a single crystal is greater than a polycrystalline specimen of the same material because both phonons and free electrons are scattered at grain boundaries, thus decreasing the efficiency of thermal transport.
19.19 Is thermal conductivity better for crystalline or amorphous?
Thermal conductivities are higher for crystalline than for noncrystalline ceramics because, for noncrystalline, phonon scattering, and thus the resistance to heat transport, is much more effective due to the highly disordered and irregular atomic structure.
19.20 Is thermal conductivity better for ceramics or metals?
Metals are typically better thermal conductors than ceramic materials because, for metals, most of the heat is transported by free electrons (of which there are relatively large numbers). In ceramic materials, the primary mode of thermal conduction is via phonons, and phonons are more easily scattered than are free electrons.
19.21 Is thermal conductivity better for porous or dense materials?
(a) Porosity decreases the thermal conductivity of ceramic and polymeric materials because the thermal conductivity of a gas phase that occupies pore space is extremely small relative to that of the solid material. Furthermore, contributions from gaseous convection are generally insignificant.
How do atoms in crystals respond to temperature?
What is the atomic mechanism that leads to the coefficient of thermal expansion?
How do we define and measure:
coefficient of thermal expansion?
Thermoelectric heating and cooling
thermal shock resistance?
Be able to calculate the thermal expansion for materials if provided the details.