Image-based multi-scale simulation and experimental validation of thermal conductivity of lanthanum zirconate
Introduction
Thermal barrier coatings (TBCs) are multi-layered ceramic coating systems deposited on turbine and combustor parts, which provide thermal insulation to the metallic substrate and improve the durability and energy efficiency of gas turbines [1], [2]. Typically, TBCs are deposited by using air plasma spray (APS) or by electron beam physical vapor deposition (EB-PVD) process. The primary requirements of TBCs for the turbine designer are low thermal conductivity and low density to minimize centrifugal loads [3], [4]. Other basic requirements include high-temperature phase stability, high thermal expansion coefficient, and low sintering activity [5], [6]. Recently, lanthanum zirconate has become a very promising candidate for thermal barrier coating applications, because it has low thermal conductivity and high-temperature phase stability. A transmission electron microscopy (TEM) image of La2Zr2O7 coating powder is shown in Fig. 1.
For thermal barrier coating materials, one of the most important material properties is thermal conductivity. There are several experimental methods to measure thermal conductivity. The most common one is flash method, which was first proposed by Parker et al. [7]. Three thermal properties – thermal diffusivity, specific heat capacity and thermal conductivity – can be deduced simultaneously using one sample [7]. The flash method is designated as the standard thermal diffusivity method specified in ASTM E1461-11. The measurement error of the standard flash method is less than 5% [8]. Using flash method, Vassen et al. measured the thermal conductivity of hot pressed fully dense La2Zr2O7 disk samples to be 1.5–2.0 W/m/K in a temperature range of 200–1500 °C [5]. Zhu et al. did similar studies for hot pressed disk samples using La2Zr2O7 spray-dried La2Zr2O7 powders [9], [10]. The measured thermal conductivities were 1.9–3.0 W/m/K in a temperature range of 200–1600 °C. We measured thermal conductivities for porous 8 wt% yttria stabilized zirconia (8YSZ) coating and porous La2Zr2O7 coating using flash method in our previous work [11]. The measured average thermal conductivity of La2Zr2O7 (porosity 11.54%) was about 0.59–0.68 W/m/K at the temperature range of 297 to 1172 K (24–899 °C), which was about 25% lower than that of porous 8YSZ at the same temperature range.
In parallel to experimental technique, molecular dynamics (MD) method can also be used to investigate the thermal conductivity. For single crystals, there are two common molecular dynamics methods for thermal conductivity calculations, i.e., direct method [12], [13] and Green–Kubo method [14], [15]. The direct method is a non-equilibrium molecular dynamics (NEMD) method, which imposes a temperature gradient to the system. The Green–Kubo method is an equilibrium MD (EMD) method, which uses the current fluctuation to calculate the thermal conductivity according to the fluctuation–dissipation theorem [16]. Schelling et al. predicted the thermal conductivities of several dozens of single crystal pyrochlores with composition of A2B2O7 (A is a rare element, and B = Ti, Mo, Sn, Zr or Pb) using the NEMD methods with Buckingham potentials [12]. The calculated thermal conductivity of single crystal La2Zr2O7 was 1.98 W/m/K at 1200 °C [12]. A more reliable method to compute thermal conductivity is the reverse NEMD (RNEMD) method [17]. In RNEMD method, the Muller-Plathe algorithm [18] is used to exchange kinetic energy between two atoms in different regions of the simulation box every finite steps to induce a temperature gradient in the system. It works by exchanging velocities between two atoms in different parts of the simulation cell. At set intervals, the velocity of the fastest atom in one region is replaced by the velocity of the slowest atom in another region, and vice versa. Consequently, the first region become colder, whereas the second region increases in temperature. The system will react by flowing energy from the hot to the cold region. Eventually a steady state sets in when the energy exchanged offsets the energy flowing back with a temperature gradient over the space between the two regions. This enables the thermal conductivity of a material to be calculated. The usual NEMD approach is to impose a temperature gradient on the system and measure the response as the resulting heat flux. In RNEMD using the Muller-Plathe algorithm, the heat flux is imposed, and the temperature gradient is the system’s response. The advantage of NEMD over traditional NEMD is that there are no artificial ‘‘temperature walls’’ in the simulated system, since these cause a fluid structure different from the bulk. Additionally, energy and momentum are conserved, and there are no thermostat issues [17]. We have calculated thermal properties of La2Zr2O7 such as specific heat and coefficient of thermal expansion (CTE) in our previous work [19], [20]. In this work, we will compute temperature-dependent thermal conductivity of La2Zr2O7 single crystal using RNEMD method to provide data in later finite element model in order to compare against experimental data. As shown in the TEM image in Fig. 1, there are very few defects in the crystal, therefore La2Zr2O7 single crystal can be described by using molecular dynamics model.
Finite element (FE) method can be used to simulate the heat conduction process of coating structures with cracks and pores [21]. In addition, quantitative imaging analysis method has been used to investigate the non-uniformity properties of the porous coating with polycrystalline microstructure [22], [23]. Pore and crack morphology of thermal barrier coating are important parameters affecting the mechanical and thermal properties [24], [25]. The thermal properties of non-uniform porous polycrystalline coatings can be calculated using image based FE method. Image based FE method uses scanning electron microscope (SEM) images to generate microstructures and import into a FE model [26]. Arai et al. studied the thermal conductivities of TBCs with different porosities using SEM image based FE modeling [25]. They found that the presence of the pores disturbed heat flow in materials. In addition, the thermal conductivity of plasma sprayed porous yttria-stabilized zirconia (YSZ) was investigated by several researchers using FE method [27], [28]. The calculated effective thermal conductivities were in good agreement with experimental results.
In this paper, we propose a novel image-based multi-scale simulation framework combining molecular dynamics and finite element calculations to study the thermal conductivity of La2Zr2O7 thermal barrier coating. Since there is no experimental thermal conductivity data of La2Zr2O7 single crystal, a reverse non-equilibrium molecular dynamics approach is first used to compute the temperature-dependent thermal conductivity of La2Zr2O7 single crystal. The single crystal data is then passed to a FE model with realistic thermal barrier coating microstructures generated using SEM images. The predicted thermal conductivities from the FE model are compared against experimentally measured thermal conductivity using both flash laser technique and pulsed thermal imaging-multilayer analysis.
Section snippets
Multi-scale simulation of thermal conductivity
For La2Zr2O7 single crystal, the RNEMD method is used to predict temperature-dependent thermal conductivity. The La2Zr2O7 unit cell is a face-centered cubic pyrochlore structure with a lattice parameter of 10.8 Å [19]. A La2Zr2O7 supercell model with the dimension of 324 × 21.6 × 21.6 Å3 has total 10,560 atoms, including 6720 O atoms, 1920 La atoms and 1920 Zr atoms. The supercell model is sliced into 30 layers with equal thickness. A temperature decay constant 0.1 ps is imposed in each layer. The
La2Zr2O7 single crystal RNEMD thermal conductivity calculation
The optimized La2Zr2O7 single crystal unit cell has a lattice parameter of 10.8 Å which is used to in construction of a supercell in the RNEMD thermal conductivity calculations. The calculated temperature distribution in the supercell is shown in Fig. 2. There are two high temperature hot zones at the ends, and a low temperature cold zone in the middle for generating a temperature gradient. The target temperature in Fig. 2 is 1273 K which is the average temperature in the supercell.
The
Conclusions
In this work, a novel image based multi-scale simulation framework combining molecular dynamics and finite element calculations has been proposed to study the thermal conductivity of La2Zr2O7 coatings. Experimental validations include the flash method and pulsed thermal image-multilayer analysis technique to measure the coating thermal conductivity. The main conclusions are summarized below:
- 1.
The calculated thermal conductivity of La2Zr2O7 single crystal ranges from 1.25 to 1.39 W/m/K in the
Acknowledgements
J.Z. acknowledges the financial support provided by the U.S. Department of Energy (Award Number: DE-FE0008868; Project Title: Novel Functionally Graded Thermal Barrier Coatings in Coal-fired Power Plant Turbines; Program Manager: Richard Dunst) and Indiana University Research Support Funds Grant (RSFG) and International Research Development Fund (IRDF). Y.J. acknowledges the financial support provided by a National Research Foundation of Korea (NRF) grant funded by the Korean Government (MEST)
References (33)
- et al.
Lanthanum zirconate thermal barrier coatings deposited by spray pyrolysis
Surf. Coat. Technol.
(2013) - et al.
Effects of doping on thermal conductivity of pyrochlore oxides for advanced thermal barrier coatings
Mater. Sci. Eng. A
(2007) - et al.
Dynamical simulations of nonequilibrium processes — Heat flow and the Kapitza resistance across grain boundaries
Solid State Commun.
(1997) - et al.
First principles study of thermodynamic properties of lanthanum zirconate
Mater. Today Proc.
(2014) - et al.
Modeling of thermal properties and failure of thermal barrier coatings with the use of finite element methods: a review
J. Eur. Ceram. Soc.
(2016) - et al.
Microstructural non-uniformity and mechanical property of air plasma-sprayed dense lanthanum zirconate thermal barrier coating
Mater. Today Proc.
(2014) - et al.
Influence of pores on the surface microcompression mechanical response of thermal barrier coatings fabricated by atmospheric plasma spray—finite element simulation
Appl. Surf. Sci.
(2011) - et al.
A novel low-thermal-conductivity plasma-sprayed thermal barrier coating controlled by large pores
Surf. Coat. Technol.
(2016) - et al.
Automated three-dimensional finite element modelling of bone: a new method
J. Biomed. Eng.
(1990) - et al.
Effects of pores and interfaces on effective properties of plasma sprayed zirconia coatings
Acta Mater.
(2003)
Melting index characterization and thermal conductivity model of plasma sprayed YSZ coatings
J. Eur. Ceram. Soc.
Thermal barrier coatings for gas-turbine engine applications
Science
Thermal-barrier coatings for more efficient gas-turbine engines
MRS Bull.
Materials design for the next generation thermal barrier coatings
Annu. Rev. Mater. Res.
Zirconates as new materials for thermal barrier coatings
J. Am. Ceram. Soc.
Thermal stability of lanthanum zirconate plasma-sprayed coating
J. Am. Ceram. Soc.
Cited by (15)
The effect of the molecular weight and polydispersity index on the thermal conductivity of Polyamide 6: A molecular dynamics study
2020, International Journal of Heat and Mass TransferModeling of the temperature field in a porous thermal barrier coating
2019, Ceramics InternationalCitation Excerpt :Although several methods have been developed to investigate the influence of micro-pores, the modeled results did not match the experimental data well [6,7]. For typical porous microstructures in TBCs, random geometric models are better than those with a periodic array geometry as the former contains information about the heat transfer paths [8–10]. Shakhova calculated the thermal conductivity of as-sprayed coatings, where the properties of the micro-pores were set as a vacuum state.
Performance of plasma-sprayed thermal barrier coating with engineered unmelted nano-particle contents
2019, Surface and Coatings TechnologyLanthanum zirconate based thermal barrier coatings: A review
2017, Surface and Coatings TechnologyCitation Excerpt :% YSZ and La2Zr2O7 layers deposited by the EB-PVD method [31]. All of the experimental data and a modeling result [51] (see Section 8.1 for thermal conductivity modeling details) are compiled in Fig. 9. As shown in Fig. 9, the thermal conductivities of the LZ coating decrease with the increase of temperature till 1200 K due to lattice scattering, and the conductivities increase again above 1200 K due to radiation contribution.