非简谐效应下的晶格热膨胀的讨论  

Discussion on lattice thermal expansion with nonharmonic effect

作　　者：朴林鹤[1] 成泰民[2] 周永军[1] 

机构地区：[1]沈阳航空工业学院基础科学部,辽宁沈阳110034 [2]东北大学物理系,辽宁沈阳110006

出　　处：《沈阳师范大学学报（自然科学版）》2004年第2期95-98,共4页Journal of Shenyang Normal University:Natural Science Edition

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.In this paper,we have a study on lattice thermal expansion with nonharmonic effect.While expanding Taylor series of potential energy U(r_0+δ) at equilibrium r_0,we learn that the relation between lattice thermal expansion and temperature T is linear,=3gk_BT/(4f\+2),when we keep section of δ~3.But it is nonlinear,=3gk_BT/(4f\+2-3ghk_BT),when we keep section of δ~4.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 δ~4 in the expand formula of Taylor series.

关 键 词：非简谐效应 热膨胀 热膨胀系数 MORSE势 

分 类 号：O482.2[理学—固体物理]