A possible reason for the dramatic reduction in lattice thermal conductivity is due to the decrease in grain size upon increasing plastic deformation. Our previous TEM investigations reported that the grain size of HPT samples reduces to as low as 10 nm during the HPT processing [14, 15]. Hao et al.  theoretically calculated the thermal conductivity of nanograined silicon and showed that the thermal conductivity AR-13324 can be reduced to as low as 3 Wm−1 K−1 for a grain size of 10 nm which is comparable to the present experimental results. Phonon scattering at the nanograin boundaries increases
as the grain size decreases which leads to the large reduction in the thermal CBL0137 mw conductivity. In addition, the presence
of metastable Si-III/XII phases [14, 15] creates lattice mismatch which further scatters the acoustic phonons. Based on the literature, it is anticipated that the thermal conductivity decreases with decreasing grain size. The present experimental results show that the mean thermal conductivity of 10 torsion cycle case (lower grain size) is marginally find more higher than the 0 torsion cycle case (higher grain size). The reason behind this deviation is still unclear. Nevertheless, the experimental results clearly show an order of magnitude reduction in thermal conductivity upon HPT processing. Annealing of the HPT-processed samples results in an increase of thermal conductivity especially for the 0 torsion cycle case. The effect of annealing becomes less pronounced for the 10 torsion cycles (33 Wm−1 K−1 after annealing) and 20 torsion cycles sample (16 Wm−1 K−1 PLEKHM2 after annealing) resulting in a smaller increase in thermal conductivity. The increase in thermal conductivity is due to the reverse transformation of the metastable phases to Si-I diamond phase and also due
to reduction in the density of lattice defects such as vacancies, dislocations, and grain boundaries. Since our previous study reveals that no appreciable grain coarsening occurs during the annealing process [14, 15], the increase in thermal conductivity can be largely attributed to the reduction of the number of lattice defects; a contribution may also be present from the reverse transformation of metastable phases during annealing. The present experimental results are comparable with the previous investigations in heavily doped p-type and n-type silicon. Existing literature results report a thermal conductivity reduction from approximately 100 W m−1 K−1 to 5 to 10 W m−1 K−1 at room temperature by varying the nature of alloy and the alloy concentration [7–10, 20]. The alloy typically used is germanium and the samples are prepared by ball milling for several hours to achieve small nanograin structures followed by hot pressing at a temperature of 1,473 K to form a bulk sample [7–10].