Thermal conductivity: An example of structure-property relations in crystals Ram Seshadri Materials Department, and Department of Chemistry and Biochemistry Materials Research Laboratory University of California, Santa Barbara CA 93106 http://www.mrl.ucsb.edu/~seshadri +++ seshadri@mrl.ucsb.edu
Thermal conductivity in 1D: Definitions T A rate of heat flow Q = x surface area applea dt dx temperature gradient thermal conductivity (units of W m 1 K 1 ) In tensor form (2 nd rank): Q i = apple ij A dt dz j
Mechanisms of thermal conductivity in materials From R. E. Newnham, Properties of Materials: Anisotropy, Symmetry, Structure, Oxford University Press, 2005.
Thermal conductivity by electrons in good metals From R. E. Newnham, Properties of Materials: Anisotropy, Symmetry, Structure, Oxford University Press, 2005. apple/ = LT Lorentz number 2.44 10 8 W Ω K 2 This is the (empirical) Wiedemann-Franz law, a consequence of free electrons in metal.
Thermal conductivity across materials Data from wikipedia
mperature-dependence: 4 regimes At low T, κ is determined by the physical size of the material, grain size and dislocation spacing. In region III, κ (corrected for the thermal expansion) decreases as 1/T largely due to anharmonic phonon scattering, the umklapp processes. At very high T κ plateaus out and becomes independent of T. D. R. Clarke, Surface Coatings chnol. 163 164 (2003) 67 74.
An approximate expression for κ min mean atomic mass of ions in unit cell Young s modulus apple min =0.87k B M m N A 2/3 E 1/2 number of atoms in the unit cell density M. Winters and D. R. Clarke, J. Am. Ceram. Soc. 90 (2007) 533 540.
Some interesting materials: La 2 Mo 2 O 9 Material with a very high oxide-ion conductivity at elevated temperatures. The low T structure is extremely complex. Lacorre et al. Nature 40 (2000) 856 858; Radosavljevic Evans, Howard, Evans, Chem. Mater. 17 (2005) 4074 4077.
Some interesting materials: La 2 Mo 2 O 9 has a record low κ for an oxide M. Winters and D. R. Clarke, J. Am. Ceram. Soc. 90 (2007) 533 540.
Some interesting materials: La 2 Mo 2 O 9 has a record low κ for an oxide M. Winters and D. R. Clarke, J. Am. Ceram. Soc. 90 (2007) 533 540.
Some interesting materials: The gold standard Fulmer, Lebedev, Roddatis, Kaseman, Sen, Dolyniuk, Lee, Olenev, Kovnir, J. Am. Chem. Soc. 135 (2013) 12313 12323.
Some interesting materials: The gold standard Fulmer, Lebedev, Roddatis, Kaseman, Sen, Dolyniuk, Lee, Olenev, Kovnir, J. Am. Chem. Soc. 135 (2013) 12313 12323. WHY?
Some interesting materials: The gold standard Fulmer, Lebedev, Roddatis, Kaseman, Sen, Dolyniuk, Lee, Olenev, Kovnir, J. Am. Chem. Soc. 135 (2013) 12313 12323. WHY?
Thermoelectrics Solid State materials are the key Peltier Effect Active Cooling p n Heat Rejection - + Refrigeration Mode I Seebeck Effect Heat Source p n Heat Sink Power Generation Mode I Refrigeration without moving parts and chemical refrigerant Electricity from waste-heat Materials 286 G: Structural Families of Functional Inorganic Materials Ram Seshadri x6129 seshadri@mrl These ppt slides were created by Professor M. A. Subramanian, Oregon State.
Thermoelectrics Automobile Waste Incinerator Nuclear Power Plant Thermal Power Plant Primary Energy 66% 34% Energy Used Energy Loss/Waste Heat Factory Retrieval Natural Gas Electrical Energy Materials 286 G: Structural Families of Functional Inorganic Materials Ram Seshadri x6129 seshadri@mrl These ppt slides were created by Professor M. A. Subramanian, Oregon State.
Thermoelectrics March 2006 March 2006 Thermoelectric Materials, Phenomena, and Applications: A Bird's Eye View: T. M. Tritt, M. A.Subramanian Recent Developments in Bulk Thermoelectric Materials: G. S. Nolas, M. Kanatzidis Properties of Nanostructured One-Dimensional and Composite: Thermoelectric Materials : A. M. Rao, X. Ji, and T. M. Tritt Guest Editors: Tritt and Subramanian Materials 286 G: Structural Families of Functional Inorganic Materials Ram Seshadri x6129 seshadri@mrl These ppt slides were created by Professor M. A. Subramanian, Oregon State.
Thermoelectrics Electrical conductivity Seebeck coefficient or thermopower (ΔV/ΔT) α Contra-indicated Properties σ α 2 σ α ZT = σ 2 α (κ e + κ L ) T Total Κ σ semiconductor κ κ e Total thermal conductivity κ L No upper limit for ZT ZT insulator ZT max metal 10 17 10 18 10 19 10 20 10 21 Carrier Concentration Materials 286 G: Structural Families of Functional Inorganic Materials Ram Seshadri x6129 seshadri@mrl
Thermoelectrics + + Glass (amorphous) Very low thermal conductivity Metal High electrical conductivity Semiconductor High Thermopower Materials 286 G: Structural Families of Functional Inorganic Materials Ram Seshadri x6129 seshadri@mrl These ppt slides were created by Professor M. A. Subramanian, Oregon State.
Thermoelectrics ZT 1.0 Bi 2 3 alloys alloys Si 0.7 Ge 0.3-200 -75 25 450 mperature o C 850 Narrow band gap semiconductors (increasing numerator) Elements of high atomic weight e.g. Bi,, Hg, (decreasing the denominator) Materials 286 G: Structural Families of Functional Inorganic Materials Ram Seshadri x6129 seshadri@mrl These ppt slides were created by Professor M. A. Subramanian, Oregon State.
Thermoelectrics Ag In 0.2 Co 4 S b 12 CsBi 4 6 : Kanatzidis et al., Science, 287, 1024(2000) Ag m Sb 2+m : Kanatzidis et al., Science, 303, 818 (2004) In 0.2 Co 4 Sb 12 : Subramanian et al., Chemistry of Materials, 18, 759 (2006) Yb 0.19 Co 4 Sb 12 : Nolas, Tritt et al., J. Appl. Phys. 97, 113715 (2005). Materials 286 G: Structural Families of Functional Inorganic Materials Ram Seshadri x6129 seshadri@mrl These ppt slides were created by Professor M. A. Subramanian, Oregon State.
Thermoelectrics Co 4 Sb 12 Large numerator Large Denominator ZT ~ 0.4 at 600K R x Co 4 Sb 12 (R = Rare-earth, In) Large numerator Small denominator ZT~ 1.3 at 600K Subramanian et al., Chemistry of Materials, 18, 759 (2006) Nolas, Tritt et al., J. Appl. Phys. 97, 113715 (2005) Singh et al., Phys. Rev. B 53, 6273 (2003) Materials 286 G: Structural Families of Functional Inorganic Materials Ram Seshadri x6129 seshadri@mrl These ppt slides were created by Professor M. A. Subramanian, Oregon State.
Thermoelectrics Intermetallics with rare earths in intermediate valence states Yb 2+,3+ (4f 13-4f 14 ) ; Ce 3+,4+ (4f 1-4f 0 ) Large Density of States at the Fermi Level - interaction between conduction electrons and partially localized 4f electrons leads to large α - very large numerator (power factor) - large denominator (thermal conductivity) low ZT YbAl 3 and CePd 3 Materials 286 G: Structural Families of Functional Inorganic Materials Ram Seshadri x6129 seshadri@mrl
Thermoelectrics Se Se S α = 2 2 π k BT 3e d (ln σ ( E )) de E = E F Bulk Electronic properties may be dramatically modified due to carrier confinement in nanostructures Thermoelectric power enhancement (rippling effect on DOS) Materials 286 G: Structural Families of Functional Inorganic Materials Ram Seshadri x6129 seshadri@mrl
Thermoelectrics nanostructure Sb Ag Ag 18 Sb 20 Power factor still high Lattice Thermal Conductivity (W/mK) 2.5 2 1.5 1 0.5 Lattice thermal conductivity LAST-18 0 300 400 500 600 700 800 mperature (K) Kanatzidis et al Science, 2004, 303, 818 Materials 286 G: Structural Families of Functional Inorganic Materials Ram Seshadri x6129 seshadri@mrl
Thermoelectrics Dissociated state..unstable Ag Sb Ag Sb Sb Ag Ag Associated state..stable Sb Materials 286 G: Structural Families of Functional Inorganic Materials Ram Seshadri x6129 seshadri@mrl These ppt slides were created by Professor M. A. Subramanian, Oregon State.