Low-temperature thermal conductivity of the substrate material <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi mathvariant="normal">YAlO</mml:mi> <mml:mn>3</mml:mn> </mml:msub> </mml:math> and its unconventional sister co

We present thermal conductivity data on single crystals of ${\mathrm{YAlO}}_{3}$ and ${\mathrm{YbAlO}}_{3}$ for temperatures between 2 K and 300 K and the heat current along $b$ and $c$. Both materials are very good thermal conductors in the investigated temperature range. The thermal conductivity in these electrical insulators is caused by phonons. The effect of Y-Yb exchange is found to be rather small despite the considerable difference in density and average atomic mass. For ${\mathrm{YAlO}}_{3}$, we find a moderate thermal conductivity anisotropy with weak temperature dependence and a ratio of $c$ to $b$ direction between at most 1 and 2.2. It is discussed in terms of the velocities of sound and relevant scattering processes. For ${\mathrm{YbAlO}}_{3}$ the small crystal size limits the precision of absolute thermal conductivity values and does not allow drawing conclusions on the anisotropy. Our results on ${\mathrm{YAlO}}_{3}$ confirm that the material is suitable for applications requiring a good thermal conductivity at temperatures down to liquid helium, such as lasers, substrates, and detectors.