Grüneisen Parameter for a Solid under Finite Strain
Grüneisen Parameter for a Solid under Finite Strain
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有限应变下固体的 Grüneisen 参数
DOI：
10.1103/physrev.102.331
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发表时间：
1956
期刊：
影响因子：
--
通讯作者：
J. Gilvarry
中科院分区：
文献类型：
--
作者：
J. Gilvarry
Druyvesteyn和Meyering在有限应变理论的基础上，从固体状态方程中求得了Gr unesisen参数（或常数）。结果与洛伦兹和斯莱特给出的德拜理论的相应评价不同（相差$\ensuremath{-}\frac{1}{3}$）。Druyvesteyn和Meyering的值在这里推导出来，而不使用有限应变的形式理论，并显示出物理上对应于一个独立的最近邻原子对的模型，而不是耦合原子振动的德拜模型。这一事实解决了达格代尔和麦克唐纳提出的一个与理想调和固体有关的悖论，并被他们归因于忽略有限应变。利用Murnaghan的有限应变理论，考虑了有限静水压力状态的存在，在此状态下施加弹性波或无限小振幅的压力变化，得到了由德拜模型和Druyvesteyn-Meyering固体的状态方程计算的Gr“uneisen参数.这两种情况下的结果与不使用有限应变的形式理论得到的相应值是相同的。因此，Dugdale和MacDonald提出的在有限压力下对德拜理论中的Gr“uneisen参数进行修正是没有根据的。比较了相对大量元素的平均值、根据Gr Uneisen定律计算的Gr Uneisen常数和德拜模型状态方程计算的Gr Uneisen常数，结果表明，在正常温度和熔化温度下，Gr Uneisen常数具有很好的一致性。
An evaluation of the Gr\"unesisen parameter (or constant) from the equation of state of a solid has been obtained by Druyvesteyn and Meyering on the basis of the theory of finite strain. The result differs (by $\ensuremath{-}\frac{1}{3}$) from the corresponding evaluation on the Debye theory, as given by Lorentz and by Slater. The value of Druyvesteyn and Meyering is derived here without use of the formal theory of finite strain, and shown to correspond physically to a model of independent pairs of nearest neighbor atoms, rather than to the Debye model of coupled atomic vibrations. This fact resolves a paradox raised by Dugdale and MacDonald in connection with an ideal harmonic solid, and ascribed by them to neglect of finite strain. The presence of a state of finite hydrostatic pressure, upon which elastic waves or pressure changes of infinitesimal amplitude are impressed, is taken into account explicitly by means of Murnaghan's theory of finite strain, to obtain the Gr\"uneisen parameter, as evaluated from the equation of state, on the Debye model and for a Druyvesteyn-Meyering solid. The results are identical in the two cases with the corresponding values obtained without use of the formal theory of finite strain. Hence, no basis exists for the modification at finite pressure in the Gr\"uneisen parameter from the Debye theory, as proposed by Dugdale and MacDonald. A comparison of average values over a relatively large number of elements, of Gr\"uneisen constants as evaluated from Gr\"uneisen's law and from the equation of state on the Debye model, shows excellent agreement at normal and at melting temperature.