  A drastic variation 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 and
~47% reduction in \k{appa} is reported for TiCoSb1.02 sample. In depth
structural analysis is performed, employing mixed-phase Rietveld refinement
technique. Embedded phases and vacancy are analyzed from X-ray diffraction
(XRD) and Scanning electron microscopy data. Local structures of the
synthesized samples are explored for the first time by X-ray absorption
spectroscopy measurements for TiCoSb system and corroborated with Rietveld
refinement data. Lattice dynamics are revealed using Raman Spectroscopy (RS)
measurements in unprecedented attempts for TiCoSb system. XRD and 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. Polar nature of TiCoSb HH sample is revealed. LO-TO splitting
(related to polar optical phonon scattering) in phonon vibration is observed
due to polar nature of TiCoSb synthesized samples. Tailoring in LO-TO splitting
due to screening effect, correlated with Co vacancies is reported for TiCoSb1+x
synthesized samples. Lattice softening and LO-TO splitting lead to decreases in
\k{appa}~47% for TiCoSb1.02 synthesized sample.
