  Temperature-dependent, in-plane, thermoelectric power data are presented for
single crystals of Ba(Fe1-xCox)2As2, 0\leqx\leq0.05, and Ba(Fe1-xRhx)2As2,
(0\leqx\leq0.171). Given that previous thermoelectric power and angle resolved
photoemission spectroscopy studies of Ba(Fe1-xCox)2As2 delineated a rather
large Co-concentration range for Lifshitz transitions to occur, and the
underdoped side of the phase diagram is poorly explored, new measurements of
thermoelectric power on tightly spaced concentrations of Co, 0\leqx\leq0.05,
were carried out. The data suggest evidence of a Lifshitz transition, but
instead of a discontinuous jump in thermoelectric power between 0\leqx\leq0.05,
a more gradual evolution in the S(T) plots as x is increased was observed. The
thermoelectric power data of Ba(Fe1-xRhx)2As2 show very similar behavior to
that of Co substituted BaFe2As2. The previously outlined T - x phase diagrams
for both systems are further confirmed by these thermoelectric power data.
