Microstructure dependent thermal conductivity measurement of Zircaloy-4 using an extended Raman thermometry method

Abstract

In this work, microstructural dependence of thermal conductivity of two polycrystalline zircaloy-4 samples was analyzed by using an extended Raman thermometry method. The thermal conductivity values in examined microstructures were found to vary spatially from 11 to 13 W m⁻¹K⁻¹. These values are in the range reported by other bulk measurements that do not consider spatial distribution. The Kapitza thermal resistance model is shown to describe the measured dependence of thermal conductivity as a function of grain size. Thermal resistance from grain boundaries and inhomogeneities are identified as two potential contributors to the thermal conductivity reduction. Nanoindentation tests were performed to obtain the local elastic modulus distribution in the analyzed samples. The thermal conductivity values increase with elastic modulus increasing in each sample. This result indicates a possibility that at room temperature phonon thermal conductivity makes a non-negligible contribution to the total thermal conductivity in zircaloy-4.

Introduction

Zirconium alloys (zircaloys) have been widely used in light water reactors due to their good thermomechanical properties, corrosion resistance, and low thermal neutron absorption rate [1]. Zircaloy cladding encapsulates nuclear fuel to prevent the nuclear fission products from leaking into the coolant [1]. In normal reactor operation, temperature in zircaloy cladding stabilizes around 300 °C. During transient events, the temperature increases rapidly up to 600 °C. In dry cask storage, the temperature remains above 200 °C for decades. In such scenario, there is a significant possibility of local thermally induced cracking and failure in microscopic regions dominated by inhomogeneity [2,3] leading to catastrophe. Therefore, understanding the thermomechanical properties of zircaloy is crucial. Although thermal properties of zircaloy have been studied during the past decade [[4], [5], [6], [7], [8], [9], [10]], aspects such as relationship between the zircaloy microstructure and local thermomechanical properties remain unknown. The current research focuses on measurement of microstructure dependent spatial variation of thermal conductivity in zircaloy-4.

Typically, there are two types of thermal conductivity measurement techniques: steady state methods (e.g. comparative technique, radial heat flow method, parallel conductance method, and electrical heating methods etc.) and transient methods (e.g. transient plane source method, laser flash method, 3ω method, and hot-wire method etc.) [11,12]. Due to the limitations of these experimental techniques, thermal conductivity is usually reported as an average value over the entire measurement domain. In the past three decades, a range of laser-based nonconductive measurement methods have been developed to improve the speed and spatial resolution of thermal property measurement, such as time-domain thermoreflectance (TDTR) [[13], [14], [15]], frequency-domain thermoreflectance (FDTR) [16], transient grating spectroscopy (TGS) [17], and transient thermorefletance (TTR) [18]. Commonly, these techniques will need to use two laser beams during measurements. One is a strong pump laser beam to heat up sample surface, and the other one is a week probe laser beam to detect the sample surface temperature change. This could be achieved either using a mechanical delay stage or two separate laser sources. The spot size for the pump and probe laser beam varies from 5 μm to 500 μm. Raman thermometry, which was established by Perichon et al. [19] in 1999, is another method that can be used to measure spatial variation of thermal conductivity. In comparison to other laser-based thermal conductivity measurement methods, Raman thermometry has multiple advantages. For example, there is only one laser beam needed in Raman thermometry, which significantly simplifies the optical path design and setup. Raman thermometry can be performed with continuous wave (CW) lasers, which is much less expensive comparing with the pulse lasers required in other techniques. In addition, the spot size and spatial resolution is typically a few microns for Raman thermometry, which makes it suitable for measurements of local properties. In a typical Raman thermometry measurement, local temperature rise is induced by laser heating. Based on a relationship between temperature and the peak Raman shift [20,21], local temperature is estimated by analyzing the reflected laser beam. Thereafter, by using a heat transfer model, local value of thermal conductivity can be obtained [22]. Raman thermometry has been used broadly in thermal conductivity measurements, [[23], [24], [25], [26], [27], [28], [29], [30], [31], [32]]. Besides being used on traditional bulk solid samples, Raman thermometry has been extended to suspended nanowires [30], suspended membranes [24,33,34], and thin film samples [25,28,35]. In this work, Raman thermometry method is used to measure spatial variation of thermal conductivity in two different zircaloy-4 microstructures.

In Raman thermometry the line width broadening of spectra peaks is only affected by the surface temperature. It provides a feasible way to separate stress and thermal effects apart in Raman measurements. Such approach was first used by Abel et al. [23], while studying the temperature distribution in a micron-sized polycrystalline silicon beam with external loading. They showed that stress and thermal signals can be separated within a small range of error [23]. Beechem et al. [36] measured stress distribution in polycrystalline silicon by using the Raman Stokes peak shift and the temperature distribution by using Raman Stokes line width. Gan et al. [[37], [38], [39], [40]] have performed thermal conductivity measurements in silicon cantilevers deforming as a function of temperature. Zhang et al. [41] has used Raman thermometry to analyze temperature distribution in deforming superalloys.

In this work, approach of Gan et al. [[37], [38], [39], [40]] is extended to zircaloy-4 samples by introducing a thin silicon coating on the sample surface. A heat transfer model is derived to relate the substrate thermal conductivity to the laser induced temperature rise. Combining the heat transfer model with the Raman thermometry method, experiments are performed to measure localized spatially resolved thermal conductivity and establish a potential linkage of microstructural features with thermal and mechanical properties.