Alloying (mass difference scattering) and nano-structuring (boundary roughness scattering) are most effective in reducing thermal conductivity, unless you are looking at very high temperatures above the Debye temperature of a material where phonon-phonon scattering could be prominent. In experiments, it is challenging to distinguish between different sources of scattering, but the dependence of thermal conductivity on temperature can help--a positive slope (increasing with temperature) usually implies some type of disorder such as boundary roughness scattering. A constant thermal conductivity is often linked to the presence of impurities, isotopes, alloying, and dislocations. Finally, a negative temperature slope (thermal conductivity decreasing with temperature) implies that phonon-phonon interactions are dominant. All of these mechanisms are usually present simultaneously but in varying amounts; temperature acts as a sort of "selector" between them. The location (and sharpness) of the peak in the thermal conductivity vs temperature curve (relative to the Debye temperature) is usually taken as an indicator of the relative contributions of these mechanisms--if the peak is at low T, then phonon-phonon scattering is prominent, while if the peak is at high T or absent, then disorder in the form of roughness or structural variations (impurities, isotopes, alloying, and dislocations) is the dominant force.

https://balandingroup.ucr.edu/publications/1998/1/prb-conf.pdf

You may find this publication useful to answer your question. It is well described here.

M. Rafsan Nahian thank you very useful discussion

Shamudra Dey thank you very much for your help

Attia, let me send you these useful resources which can help to answer to your questions:

First, a very nice and extended review on thermoelectrics, in the first section the Landauer Theory for bulk materials is described, so, if you follow the derivations of the equations, you can realice what terms and what functions the lattice thermal conductivity is dependen on.

Second, I am attaching here two power point presentations from a summer sourse in Purdue university about the charge and heat transport in 1D, 2D and bulk materials, it is introduced too by the Landauer approach but slightly modified by a Purdue's university professor.

I will leave you here the link of the video series (10) of these summer school

https://www.youtube.com/watch?v=SddB0DWrc7g&list=PL3ADDFF412968CB0E

I think that a big part of the answer is on the mean free path of the phonons and the disperssion relations (or curves) in the material

Hope i'll be helpful !

Best Regards !

Franklin Uriel Parás Hernández thanks..

I am too much confuse to work on thermoelectric I even not know anything but its my superviser demand to work on it.

thanks for your help

I see Attia , It happens,

Give a look at the review I sent you , it has a good description of almost all the important topics when working with thermoelectrics and the phenomena in thermoelectricity.

I'm working myself in thermoelectric devices (TEGs) based on Bi2Te3 compounds. This is a conventional alternative in thermoelectrics but we are trying to modify the nanostructure of our materials with different techniques seeking to enhance the FOM (Figure of Merit) and Power Factor,

Kind Regards ! :)

Franklin Uriel Parás Hernández thank you Sir

Since, the value of lattice parameter increased with reducing size of nano materials, then the lattice thermal conductivity decreased.

Qader, I. N., & Omar, M. S. (2017). Carrier concentration effect and other structure-related parameters on lattice thermal conductivity of Si nanowires. Bulletin of Materials Science, 40(3), 599-607.

Dr. Begun De of CU is expert in this field