A “2-omega” technique for measuring anisotropy of thermal conductivity

Abstract

A popular method of measuring the thermal conductivity of thin films and substrates, the "3-omega" method, is modified to yield a new technique for measuring the anisotropy in thermal transport in bulk materials. The validity of the proposed technique is established by measuring the thermal conductivity of strontium titanate, which is expected to be isotropic because of its cubic unit cell. The technique is then applied to rutile TiO(2). The analysis of experimental results on (100) and (001) TiO(2) reveals that the anisotropy is a function of the crystalline quality, as quantified by the effective thermal conductivity obtained through conventional "3-omega" measurements. The advantages of the proposed technique are similar to those of the standard "3-omega" method, namely the simplicity of sample preparation and measurement, and negligible errors due to radiation because of the small volume of material being heated. For anisotropy determination, the proposed technique has the additional advantage that a single sample is sufficient to determine both components of the thermal conductivity, namely the values in and perpendicular to the plane of cleavage. This is significant for materials in which there is a large variation in the crystalline quality from sample to sample. For such materials, it is unreliable to use two different samples, one for measuring the thermal conductivity in each direction. Experimental data are analyzed using a 3D Fourier-series based method developed in this work. The proposed method determines each component of the thermal conductivity with an estimated accuracy of about 10%.

A new elliptical-beam method based on time-domain thermoreflectance (TDTR) to measure the in-plane anisotropic thermal conductivity and its comparison with the beam-offset method

“…Since these two sources of uncertainty are independent of each other, the total uncertainty for the Kx is determined as 2 2 18.5 9 % 21% is slightly lower than a first-principles calculation in literature (62 W m -1 K -1 ) 35 but is consistent with another TDTR measurement of Kz of ZnO [0001] (55 W m -1 K -1 ) 29 , which has its c-axis along the through-plane direction. [11][12][13][14][15][16][17][18][19][20] with the short radius of the elliptical beam oriented to be (a) parallel to and (b) perpendicular to the c-axis of ZnO, respectively. The curves of 30% bounds on the best-fitted thermal conductivity values are also included as a guide of reading to the sensitivity of the signals.…”

“…The curves of 30% bounds on the best-fitted thermal conductivity values are also included as a guide of reading to the sensitivity of the signals. Figure 10 shows a summary of the in-plane thermal conductivity tensor of ZnO [11][12][13][14][15][16][17][18][19][20] measured by the beam-offset method and the elliptical-beam method under their optimal experimental conditions, respectively. Overall, these two methods compare relatively well with each other, with the measured in-plane thermal conductivities within the error bars.…”

“…We then compare the two techniques under their optimal experimental conditions by measuring the in-plane thermal a) Electronic mail: Ronggui.Yang@Colorado.Edu of both methods in measuring the in-plane anisotropic thermal conductivity. In the end, the two methods are compared by measuring the in-plane thermal conductivity tensor of a ZnO [11][12][13][14][15][16][17][18][19][20] sample.…”

“…Kx of the substrate along the offset direction can thus be found by matching the measured FWHM to the simulated FWHM. We thus extract Ka = 38.5 W m -1 K -1 along the direction perpendicular to the c-axis of ZnO[11][12][13][14][15][16][17][18][19][20].FIG. 8.…”

Theoretical Principles of Determining the Longitudinal Thermal Conductivity of Thin-Walled Structural Elements from Composite Materials

“…The new modifi cations of this method (the 2ω-method) [6] permit determining the thermal conductivity of anisotropic materials, including that in the reinforcement plane, but they have the same limitations as the laser fl ash method.…”