The fractional change in length when the temperature rises by 1 K. It arises from the anharmonicity of the interatomic potential and tends to be smaller in strongly bonded materials with high melting points.
Japanese name: 線膨張係数
Coefficient of linear thermal expansion appears in 10 practice questions across 6 topics, including Thermal properties of materials, Thin films, surfaces and nanomaterials, Ceramics and glasses.
Answer: A. About 77 K
Eα = 380×10⁹ × 8.0×10⁻⁶ = 3.04×10⁶ Pa/K and σf(1 − ν) = 300×10⁶ × 0.78 = 2.34×10⁸ Pa, so ΔTc = 2.34×10⁸/(3.04×10⁶) ≈ 77 K. About 99 K forgets to multiply by (1 − ν), and about 127 K divides by (1 − ν) instead. Thermal shock resistance is greater the higher the strength and the lower the Young's modulus and thermal expansion coefficient. Fused silica, with a very small thermal expansion coefficient of about 0.5×10⁻⁶ K⁻¹, is extremely resistant to thermal shock. A high thermal conductivity also helps, because it keeps the temperature difference between the surface and the interior small.
Answer: C. Tensile, about 220 MPa
Δα = 23×10⁻⁶ − 2.6×10⁻⁶ = 20.4×10⁻⁶ K⁻¹ and ΔT = 100 K, so σ = 70×10⁹ × 20.4×10⁻⁶ × 100/(1 − 0.35) ≈ 2.2×10⁸ Pa, about 220 MPa. On cooling, aluminum tries to shrink more than silicon, but constrained by the substrate it cannot, so the film is pulled into tension. Calling it compressive gets the sign wrong. About 143 MPa forgets to divide by (1 − ν). The film is in a biaxial stress state, constrained simultaneously in both in-plane directions, so the biaxial modulus E/(1 − ν) must be used. Thermal stresses like this cause stress migration and voids in interconnects.
Thermal shock resistance is greater the higher the strength and the lower the Young's modulus and thermal expansion coefficient.
A ceramic has a flexural strength of 300 MPa, a Young's mod…The sign of thermal stress can be judged this way: if the film's thermal expansion coefficient is larger than the substrate's, the film is in tension after cooling; if smaller, in compression.
A thermal oxide film (SiO₂, linear thermal expansion coeffi…As a result, the linear expansion coefficient is as small as about 1×10⁻⁶ K⁻¹ below the Curie temperature, and Invar is used in precision measuring instruments, containers for liquefied natural gas and the like.
Which statement correctly explains why the linear thermal e…By the Grüneisen relation β = γC_v/(BV) (β is the volume expansion coefficient, γ the Grüneisen parameter, C_v the constant-volume molar heat capacity, B the bulk modulus and V the molar volume), the thermal expansion coefficient follows nearly the same temperature dependence as the heat capacity.
According to the Grüneisen relation, the volume expansion c…Adding SiC particles, which have a high Young's modulus of about 400 GPa and a low coefficient of thermal expansion of about 4×10⁻⁶ K⁻¹, makes the Young's modulus and wear resistance of the composite higher than those of the aluminum alloy matrix and its thermal expansion coefficient lower.
Which correctly describes the properties of a metal matrix …Thermal stress Young's modulus Invar Curie temperature Debye temperature Metal matrix composite Fracture toughness Non-bridging oxygen Glass transition temperature Thermal barrier coating