A drastic variation (~47%) in thermal conductivity (\k{appa}) for synthesized samples (TiCoSb1+x, x=0.0, 0.01, 0.02, 0.03, 0.04, and 0.06) is observed. The lowest \k{appa} is reported for the TiCoSb1.02 sample. Thermal variation of \k{appa} is estimated from the temperature and power-dependent Raman spectroscopy data. Embedded phases and Co vacancy are analysed, employing scanning electron microscopy and transmission electron microscopy data. X-ray absorption fine structure (XAFS) spectroscopy reveals the Co vacancy in synthesized samples, and the most ordered phase is TiCoSb1.02 amid the synthesized samples. X-ray photoelectron spectroscopy measurement of the synthesized samples provides direct evidence of Co vacancies and their increase with Sb concentration (x). Lattice dynamics are revealed using Raman Spectroscopy (RS) measurements. RS data accomplishes that variation in \k{appa} as a function of Sb concentration is observed owing to an alteration in phonon group velocity, related to lattice softening. The polar nature of the TiCoSb half-Heusler (HH) sample is revealed. Longitudinal Optical and Transvers Optical phonon (LO-TO) splitting in RS is observed due to the polar nature of TiCoSb1+x synthesized samples. Tailoring in LO-TO splitting due to the screening effect, correlated with Co vacancies, is reported for TiCoSb1+x synthesized samples. Lattice softening and LO-TO splitting lead to a minimum \k{appa} for the TiCoSb1.02 synthesized sample.

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