  Many materials have anisotropic thermal conductivity, with diverse
applications such as transistors, thermoelectrics, and laser gain media. Yet
measuring the thermal conductivity tensor of such materials remains a
challenge, particularly for materials lacking in-plane symmetry (i.e.,
transversely anisotropic materials). This paper demonstrates thermal
conductivity tensor measurements for transversely anisotropic materials, by
extending beam-offset frequency-domain thermoreflectance (BO-FDTR) methods
which had previously been limited to transversely isotropic materials.
Extensive sensitivity analysis is used to determine an appropriate range of
heating frequencies and beam offsets to extract various tensor elements. The
new technique is demonstrated on a model transversely anisotropic material,
x-cut quartz (<110> {\alpha}-SiO2), by combining beam offset measurements from
different sample orientations to reconstruct the full in-plane thermal
conductivity tensor. The technique is also validated by measurements on two
transversely isotropic materials, sapphire and highly oriented pyrolytic
graphite (HOPG). The anisotropic measurements demonstrated very good
self-consistency in correctly identifying isotropic directions when present,
with residual anisotropy errors below 4% for sapphire and 2% for HOPG and
quartz. Finally, a computational case study (simulated experiment) shows how
the arbitrary in-plane thermal conductivity tensor of a fictitious material
with high in-plane anisotropy can in principle be obtained from only a single
sample orientation, rather than multiple orientations like the experiments on
x-cut quartz.
