  Interest in high entropy alloy thermoelectric materials is predicated on
achieving ultralow lattice thermal conductivity $\kappa\sub{L}$ through large
compositional disorder. However, here we show that for a given mechanism, such
as mass contrast phonon scattering, $\kappa\sub{L}$ will be minimized along the
binary alloy with the highest mass contrast, such that adding an
intermediate-mass atom to increase atomic disorder can increase thermal
conductivity. Only when each component adds an independent scattering mechanism
(such as adding strain fluctuation to an existing mass fluctuation) is there a
benefit. In addition, both charge carriers and heat-carrying phonons are known
to experience scattering due to alloying effects, leading to a trade-off in
thermoelectric performance. We apply analytic transport models, based on
perturbation and effective medium theories, to predict how alloy scattering
will affect the thermal and electronic transport across the full compositional
range of several pseudo-ternary and pseudo-quaternary alloy systems. To do so,
we demonstrate a multicomponent extension to both thermal and electronic binary
alloy scattering models based on the virtual crystal approximation. Finally, we
show that common functional forms used in computational thermodynamics can be
applied to this problem to further generalize the scattering behavior that is
modeled.
