Accurate knowledge of the thermal conductivity (k) of biological tissues is important for cryopreservation, thermal ablation, and cryosurgery. Here, we adapt the 3ω method-widely used for rigid, inorganic solids-as a reusable sensor to measure k of soft biological samples two orders of magnitude thinner than conventional tissue characterization methods. Analytical and numerical studies quantify the error of the commonly used "boundary mismatch approximation" of the bi-directional 3ω geometry, confirm that the generalized slope method is exact in the low-frequency limit, and bound its error for finite frequencies. The bi-directional 3ω measurement device is validated using control experiments to within ±2% (liquid water, standard deviation) and ±5% (ice). Measurements of mouse liver cover a temperature ranging from -69 °C to +33 °C. The liver results are independent of sample thicknesses from 3 mm down to 100 μm and agree with available literature for non-mouse liver to within the measurement scatter.
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.
The thermal conductivity of crystalline materials is typically one or two orders of magnitude higher than that of their amorphous structures. The phase transition in barium titanate is generally considered to exhibit order–disorder character, suggesting the potential for thermal conductivity switching if this order–disorder transition can be controlled. To investigate this possibility computationally, following the method of Fu and Bellaiche, here electric fields are applied to align the polarizations and transform disordered paraelectric structures to ordered ferroelectric structures. Solving the Boltzmann transport equation, the theoretical limit of a perfectly disordered structure is found to have thermal conductivity of a factor of 3.9 lower than the perfectly ordered structure. The thermal conductivity of the ordered structure can be further enhanced by up to another 2.4 times under electric fields due to the reduction in phonon scattering rates, implying a theoretical maximum thermal conductivity switching ratio of 9.4. This study yields two guidelines in searching for high thermal conductivity switch ratio in ferroelectric materials: the structure should be single domain under electric field and the phase transition should be fully order–disorder rather than displacive.
Maximum operating power densities in ceramic laser media scale with thermal conductivity k. This requires larger grain sizes in polycrystalline ceramics to reduce phonon scattering at grain boundaries. However, smaller grain sizes are preferred to minimize light scattering in the Rayleigh regime in polycrystals made from birefringent materials such as AlN and Al2O3, which are otherwise appealing for their high k. An optimization challenge arises from the opposite scaling laws governing the effects of grain sizes on k and light transmission. Here, this is tackled by introducing anisotropically microstructured materials (columnar/disk‐shaped grains) as the lasing media, and allowing orthogonal heat transfer and lasing directions. For columnar grains, larger grain sizes along the c‐axis help maintain high k for good heat dissipation, while preserving light transmission properties in the orthogonal lasing and pumping directions. Analytical models for the thermal conductivity in such structures are presented and verified using Monte‐Carlo ray‐tracing simulations. Similarly, an approximate Rayleigh–Gans–Debye model is used to predict light transmission and verified with exact simulations using FEM software. Finally, the tradeoff between thermal and optical phenomena is captured in a new anisotropic figure‐of‐merit tensor, which is optimized for the microstructure that maximizes lasing media performance in AlN and Al2O3 model systems.
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