A 3 omega method to measure an arbitrary anisotropic thermal conductivity tensor

Previous use of the 3 omega method has been limited to materials with thermal conductivity tensors that are either isotropic or have their principal axes aligned with the natural cartesian coordinate system defined by the heater line and sample surface. Here, we consider the more general case of an anisotropic thermal conductivity tensor with finite off-diagonal terms in this coordinate system. An exact closed form solution for surface temperature has been found for the case of an ideal 3 omega heater line of finite width and infinite length, and verified numerically. We find that the common slope method of data processing yields the determinant of the thermal conductivity tensor, which is invariant upon rotation about the heater line's axis. Following this analytic result, an experimental scheme is proposed to isolate the thermal conductivity tensor elements. Using two heater lines and a known volumetric heat capacity, the arbitrary 2-dimensional anisotropic thermal conductivity tensor can be measured with a low frequency sweep. Four heater lines would be required to extend this method to measure all 6 unknown tensor elements in 3 dimensions. Experiments with anisotropic layered mica are carried out to demonstrate the analytical results.