【摘要】 在非简谐效应下讨论了晶格的热膨胀.把势能U(r0+δ)相对于平衡位置r0泰勒级数展开,只保留到δ3项时晶格热膨胀是与温度T是线性的 δ=3gkBT/(4f2)关系,但只保留到δ4项时我们得到晶格热膨胀是与温度T是非线性的 δ=3gkBT/(4f2-3ghkBT)关系.讨论了非简谐效应下的热膨胀系数.原子对势具有Morse势[5]的形式下计算了镁的线热膨胀系数及 δ.从而看出 δ=3gkBT/(4f2)仅适用于低温情况,在高温熔点附近有明显的偏离.因此讨论在高温下的晶格热膨胀至少要保留U(r0+δ)的泰勒级数展开式中的δ4项.更多还原

【Abstract】 In this paper,we have a study on lattice thermal expansion with nonharmonic effect.While expanding Taylor series of potential energy U（r₀+δ） at equilibrium r₀,we learn that the relation between lattice thermal expansion and temperature T is linear,=3gk_BT/（4f\+2）,when we keep section of δ³.But it is nonlinear,=3gk_BT/（4f\+2-3ghk_BT）,when we keep section of δ⁴.We also discuss the lattice thermal expansion coefficient.Under the format of atomic between cohesive energy possess Morse potential,we calculate linear thermal expansion coefficient of magnesium （Mg）.Thereby we come to the conclusion that =3gk_BT/（4f\+2） only works at low temperature but not absolutely reliable at high temperature melting point.Therefore when we discuss lattice thermal expansion,we must have at least δ⁴ in the expand formula of Taylor series.更多还原