**1. Introduction**

Thermal barrier coatings (TBCs) with low thermal conductivity provide excellent thermal protection and have been widely used to protect hot-components in aero-engines from high-temperature environment [1–3]. The thermal and mechanical properties of TBCs have a significant effect on the lifetime of TBCs. Therefore, the measurements for thermal and mechanical properties are essential. In addition, the thermal and mechanical properties of materials are closely related to their microstructures, so it is worth investigating microstructures of TBCs.

Studies have shown that improvement in physical, thermal, and mechanical properties of new materials can be attributed to improvement of microstructure when compared with conventional materials [4]. For plasma sprayed coatings, particle size of the feedstock powders [5–8] and spray parameters [9–11] have a grea<sup>t</sup> effect on the microstructure (such as porosity, micro-crack content, and grain size) of the coatings. Liang et al. reported that the feedstock powders used for depositing nanostructured coating (particle size of agglomerated powders ranged in 30–50 μm, the size of nanoparticles inside the agglomerated powders varied from 50 to 80 nm) was smaller than the powders used for depositing conventional coating (particle size ranged in 60–100 μm), which contributed to the improvement of microstructure (such as reduction of grain size and contents of pores and micro-cracks) of the nanostructured coating [6]. Bai et al. investigated the e ffect of spray parameters on the particles temperature and velocity which determined the melting state of the particles, and found that the spray distance had the greatest impact [9]. Their results showed that the content of unmelted nanoparticles decreased from 12% to 6% when the temperature and velocity of in-flight particles increased by 10% and 14%, respectively.

Recently, a grea<sup>t</sup> deal of research with respect to the e ffect of microstructure on thermal properties such as thermal shock (oxidation) resistances [6–8,12,13] and thermal insulation [9,14], and mechanical properties such as hardness and modulus [5,14–22] have been done. Wang et al. found that the nanostructured zirconia coating possessed a better thermal shock resistance than that of the conventional zirconia coating [7]. The enhanced toughness and decreased porosity and micro-cracks in the nanostructured coating contribute to improvement of thermal shock resistance, which is consistent with what Liang reported [6]. Fan et al. discovered the small grain size had a positive influence on thermal fatigue life, and the columnar crystal microstructure had a grea<sup>t</sup> e ffect on thermal shock resistance of TBCs [13]. Wu et al. found that the reduction of porosity resulted in increase of thermal di ffusivity, suggesting a significant degradation in the thermal barrier e ffect [14]. Some researchers have studied the e ffect of microstructure on hardness and modulus at high temperature [14–18]. They all discovered that the hardness and modulus of TBCs increased with the decrease of porosity caused by sintering of coating at high temperature. Nath et al. evaluated the resistance to plastic deformation of TBC at room temperature and with thermal exposure [15]. Baiamonte et al. indicated that nanostructured coating had larger hardness and modulus than the conventional coating by dynamic indentation tests at room and high temperatures [18]. The e ffect of microstructure on hardness and modulus at room temperature have also been investigated [19–22]. Jang et al. discovered that the hardness and Young's moduli at the side regions of TBCs decreased with increasing the porosity [19], which is consistent with reference [20]. Lima et al. studied the e ffect of roughness on the microhardness and elastic modulus of nanostructured zirconia coatings, their results showed that the microhardness and elastic modulus increased with decreasing roughness [21]. Zeng et al. found that the nanocrystalline zirconia coating had a larger microhardness than that of conventional coating, and they used the Hall–Petch model assuming that a dislocation network density slipped through the grain boundaries to explain the phenomenon [22].

In order to study the mechanical properties (hardness and modulus) of TBCs, several tests have been presented and widely used, such as beam bending tests [18,23–25] and indentation tests [5,14–23,26,27]. Thompson et al. indicated that the modulus given by indentation test was much higher than the value based on the beam bending technique [23], which is consistent with Baiamonte reported [18], because indentation test gave an indication of local modulus, and beam bending test gave a global value which contained the e ffects of micro-crack and porosity. All modulus values measured by beam bending methods were relatively small for TBCs [24,25].

The measured mechanical properties based on beam bending tests are average values on macroscopic scales. However, the measured mechanical properties based on the nanoindentation tests are local values on microscopic scales. The above two types of mechanical properties obtained by the above two scale tests are extremely di fferent. Many studies have shown that an apparent indentation size e ffect (ISE) of hardness for di fferent kinds of materials was observed, such as brittle materials [26,27], metal materials [28,29], and biomaterials [30]. In order to describe the ISE, a series of di fferent theoretical methods were presented. Li et al. proposed an energy balance analysis based on elastic/plastic indentation model to analyze the apparent ISE of hardness [26]. Zotov et al. used a new empirical equation based on the concept of elastic recovery to explain the phenomenon of ISE [27]. Wei et al. presented the strain gradient plasticity theory based on the thermodynamics frame

to describe the ISE and cross-scale fracture [28,29], and they predicted the micrometer-sized parameter of strain gradient plasticity theory by the comparison of theoretical predictions with experimental measurements. Song et al. [30] used the trans-scale mechanics theory presented by Wu et al. [31] to model the nanoindentation size effect for limnetic shell, and they considered both the strain gradient effect and surface/interface effects.

In this study, the microstructures of micron-/nano-grain coatings were observed by using scanning electron microscopy (SEM) and atomic force microscopy (AFM); the porosity and grain size of micron-/nano-grain coatings were calculated by quantitative image analysis using Image-Pro Plus software. The mechanical properties (hardness and modulus) of micron-/nano-grain coatings were measured by using nanoindentation tests. The effect of microstructure on mechanical properties was analyzed by comparing the microstructure of micron-grain coating with that of nano-grain coating. The trans-scale mechanics theory presented by Wu et al. [31] was adopted to characterize the nanoindentation size effect for the micron-/nano-grain coatings.
