Theory of Nanoscale Charge and Phonon Transport
Coherent Potential Approximation (CPA)
There is currently no quantum
mechanical transport model for charge (or phonon) transport in multiphase
nanocrystalline structures. Due to absence of periodicity, one cannot apply any
of the elegant theorems, such as Bloch's theorem, which are implicit in the
basic theory of crystalline solids. Atomistic models such as Kubo and NEGF may
assume an accurate knowledge of the interatomic potentials; however,
calculations for real 3D random multi-phase systems require so large
computational times that makes them practically impossible. Many approximate
approaches have been proposed to calculate the electronic properties of
disordered alloys.
The Coherent Potential Approximation (CPA) has been shown to be one of the most
effective out of a class of theories known as "single-cell" theories. It can
successfully predict the major trends in the band structures of alloys as a
function of their composition. Nevertheless, it remains relatively simple from
computational point of view unlike the first principles calculations which treat
only the system geometries with long range periodicity.
The physical processes in each individual grain no longer follow the well
described classical continuum linear transport theory. Therefore, a proper model
for coupled transport of charge carriers and phonons that takes into account the
effect of their non-equilibrium energy distribution is highly desirable. In a
multi-phase nanocrystalline material, grains and interfacial microstructures may
have three distinct types as depicted in Figure 1.
Achievements
We developed two new theories and associated codes based on Coherent Potential
Approximation (CPA) one for electron transport and one for phonon transport. The
codes calculate the charge and phonon transport parameters in nanocomposite
structures. These can be nano-crystalline (symmetric case) or the material with
embedded nano-particles (asymmetric case). CPA specifically considers
muli-scattering effect that cannot be explained with other semi-classical
methods such as Partial Wave or Fermi’s golden rule. To our knowledge this is
the first CPA code developed to study both electron and phonon transport in
nanocomposite structures.
We also developed a multiband electron transport simulator based on BTE coupled
with phonon transport based on Callaway model of thermal conductivity. We added
the effect of magnetic field to our multiband electron transport simulator. The
code is unique as the derived equations are valid for an arbitrary strength of
the magnetic field (weak to strong). To our knowledge this is the first
calculation with no approximation based on the strength of the magnetic field.
The code will be extremely useful for designing/optimizing thermomagnetic
materials. This project was funded by NSF the thermal transport processes
program. The code can be extend to different types of nanocrystalline materials
taking into account the average grain size, as well as the grain size
distribution, and volume fraction of the different constituents in the
materials. This is a strong tool that can describe more complex systems such as
nanocrystals with randomly oriented
grains with predictive power for the properties of electrical and thermal
properties of disordered nanocomposites.
Integrated First principles-CPA-BTE solver
Due to the complexity of the thermoelectric material systems, full first
principles calculations are not practical; therefore, we have combined the three
different frameworks based on first principle calculations, Coherent Potential
Approximation (CPA), and multiband Boltzmann transport equation (BTE) to design
and sturdy the thermoelectric materials. Figure 2 depicts the overall block
diagram of the calculations.
Based on theoretical computations, we have recently predicted an extraordinarily
large thermoelectric power factor for type-VIII clathrate Si46 due the existence
of a large density of closely packed carier pockets near the band edges of this
so far hypothetical material structure (Figure 3). Our first principles
calculations have predicted a high crystallographic symmetry near both the band
edges for Si46-VIII clathrate. We calculated the predicted thermoelectric
transport properties both for the bulk crystalline and nanostructured Si46-VIII
clathrates. The calculations were based on multiband Boltzamann transport
equation and the data from density functional theory and molecular dynamics
simulations. The predicted figure-of-merit of bulk nanostructured p-type
Si46-VIII clathrate is in the order of 2 at 1000 C, which is higher than that of
the best high temperature thermoelectric materials known today.
Figure 3: (a) Crystal structure of the type-VIII clathrate Si46 in
real space. (b) Brillouin zone of the Si46 type VIII clathrate
showing
the
hole pockets at Γ= (0, 0, 0) point (orange), on the ΓH line (violet),
on the NH line (green), at P= (1/4, 1/4,
1/4) point (blue), and at N= (1/2, 0, 0) points (red). The valley degeneracies
for Γ, N, P, ΓH and NH are 1, 6, 2, 6, and 12, respectively. (c) The predicted
conduction and valance band structures and
the
densities of states.
Representative Publications
1.
Electronic, elastic, vibrational, and thermodynamic properties of type-VIII
clathrates Ba8Ga16Sn30 and Ba8Al16Sn30
by first principles, P. Norouzzadeh, C. W. Myles, and D.
Vashaee, J. Appl. Phys. 114, 163509
(2013).
2.
Prediction of a large number of electron pockets near the band edges in
type-VIII clathrate Si46 and its physical properties from first
principles, P. Norouzzadeh, C. W. Myles, and D.
Vashaee, J. Phys.: Condens. Matter 25, 475502 (2013).
3.
Structural, electronic, phonon and thermodynamic properties of hypothetical
type-VIII clathrates Ba8Si46 and Ba8Al16Si30
from first principles,
P. Norouzzadeh, C. W. Myles, and D. Vashaee, Journal of Alloys and Compounds,
http://www.sciencedirect.com/science/article/pii/ S0925838813026169 (2013).
4.
The effect of crystallite size on
thermoelectric properties of bulk nanostructured Magnesium Silicide (Mg2Si)
compounds, Nikhil Satyala, Daryoosh Vashaee,
Appl. Phys. Lett. 100, 073107 (2012)
5.
The effect of nanostructuring on thermoelectric transport properties of p-type
higher manganese silicide MnSi1.73,
Payam Norouzzadeh, Zahra Zamanipour, Jerzy Krasinski, Daryoosh Vashaee, J. of
Applied Physics, 112, 124308 (2012); doi: 10.1063/1.4769884
6.
Detrimental influence of nanostructuring on the thermoelectric properties of
magnesium silicide, Nikhil Satyala and Daryoosh Vashaee,
J. of Applied Physics, DOI: 10.1063/1.4764872 (2012)
7.
Modeling of Thermoelectric Properties
of Magnesium Silicide (Mg2Si) , Nikhil Satyala, Daryoosh Vashaee,
Journal of Electronic Materials, vol. 499, no. 1, pp. 68-1791 (2012)
8.
Modeling study of thermoelectric SiGe
nanocomposites, A. J. Minnich, H. Lee, X. W. Wang,
G. Joshi, M. S. Dresselhaus, Z. F. Ren, G. Chen, and D. Vashaee, , Physical
Review B 80, 155327 (2009)
9.
Modeling Grain Boundary Scattering in
Nanocomposites,
Austin Minnich, Daryoosh Vashaee, Gang
Chen, Proceedings of IMECE 2008 ASME International Engineering Conference and
Exhibition October 31- November 6, 2008, Boston, Massachusetts.
10.
Thermoelectric transport in Silicon
Germanium nanocomposite,
Hohyun Lee, Daryoosh Vashaee, Xiaowei Wang, Giri Joshi, Gaohua Zhu, Dezhi Wang,
Zhifeng Ren, Sabah Bux, Richard Blair, Pawan Gogna, Jean-Pierre Fleurial, Ming
Y. Tang, Mildred S. Dresselhaus, Gang Chen, ASME International Mechanical
Engineering Congress and Exposition IMECE October 31 – November 6, 2008, Boston,
Massachusetts, USA
11.
The Effect of Grain Size and Volume
Fraction on Charge Transport in Thermoelectric Nanocomposite of Bi2Te3-Sb2Te3, Payam Norouzzadeh, Daryoosh Vashaee,
IEEE Green Technologies Conference 2012 - Energy Generation & Storage
Technologies, Tulsa, Oklahoma, April 19-20, 2012