Thermal expansion problem

(D (ScNdErYbLu), SiO, (ScNdErYbLu), 510, Yb,SLO, SIC Matrix Linear CTE, x10" /C SI CTE 3 400 500 600 700 800 900 1000 1100 1200 Temperature, *C Figure 1: Thermal expansion coefficient of rare earth silicates. Problem 2: Thermal Expansion. (20 points) Environmental/thermal barrier coatings have been successfully employed in the hot zone of gas turbine engines, allowing for high fuel burn temperatures and increased flight efficiency. The objective in the design and discov- cry of environmental barrier coatings is to identify materials with both low thermal conductivity, providing good thermal insulation, and low coefficient of thermal expansion (CTE), which matches the substrate or matrix. In a study that was published in December of 2022 (Materialia, 26, 101557, 2022), Drs. Elizabeth Opila and Patrick Hopkins showed how multi-component rare earth silicates offer a unique solution for simultaneously co- optimizing thermal expansion and thermal conductivity. How do chemical bond strength and atomic mass impact thermal expansion coofficiant, or CTE? As shown in Figure 1, rare earth mono-silicate (Scog Ndo2Ero2 YbogLun.2)2Si0; has a significantly larger CTE than di-silicate (Sco.2 NdogEro2 YbozLun.2)2SigO, and YbeSigO, (the latter is known as the coating materials in Rolls-Royce en- gines). Why