Heat transfer in quartz, orthoclase, and sanidine at elevated temperature

Abstract

 The thermal diffusivity of quartz, orthoclase, and sanidine was measured in different directions by a transient method, to determine the second-rank tensor of thermal transport properties as a function of temperature up to 800 °C. Thermal diffusivity of phonons is described as D=1/3 v l, where v is the phonon velocity and l the mean free path length of phonons. In quartz the thermal diffusivity at room temperature is 3.60 mm² s⁻¹ in [1 0 0] and 7.00 mm² s⁻¹ in [0 0 1] direction. A 1/T dependency of thermal diffusivity is observed for both directions up to 550 °C with a pronounced anisotropy (A=62%; A=(D _max − D _min)/D _average), which decreases with increasing temperature. Close to the α–β-phase transition, we observed a minimum in thermal diffusivity and a negligible anisotropy. Up to 573 °C the maximam of thermal diffusivity, average phonon velocity, and mean free path length are observed in [0 0 1] direction. However, above the temperature of phase transition the maximum values of the properties are observed in [1 0 0] direction. The observed behavior is explained by a model which interrelates velocity and mean free path length of phonons. A further contribution to the thermal diffusivity behavior is related to the higher symmetry of β-quartz, resulting in a reduced phonon–phonon-scattering probability. At ambient temperature, orthoclase and sanidine show similar values of thermal diffusivities (≈1 mm² s⁻¹) and a temperature-independent anisotropy behavior between 22 and 350 °C of ≈30%. For both feldspars a small 1/T temperature dependence of thermal diffusivity up to 350 °C is observed. The transparent sanidine in gemstone quality shows a strong increase in thermal diffusivity above 350 °C proportional to T ³. The contribution of the radiative heat-transfer mechanism leads to values more than two times higher in sanidine than in a milky-cloudy orthoclase at 800 °C. For the feldspars the mean free path length of phonons shows a small temperature dependence on reaching ≈0.4–0.5 nm at 800 °C and thus already in the range of the interatomic distances of ≈0.27–0.34 nm. The pronounced difference in thermal diffusivity behavior between quartz and orthoclase, which have a related tectosilicate structure, is connected to additional cations of K, Na, and Al within the feldspar structure.