伯奇高温定律
Birch's law at elevated temperatures
摘要：
高压物理学中的伯奇定律假定弹性波的速度和密度之间存在线性关系，其最著名的应用之一是使用初步参考地球模型作为约束的主要来源来研究地球内核的组成。然而，即使在适度升高的温度下，它也从未接受过高精度测试。在这里，我们利用计算电子结构的密度泛函理论和计算声子色散关系的密度泛函微扰理论来进行这样的测试。我们表明，最近提出的修改伯奇定律是一贯满意更准确地比原来的版本。这个修改版本指出，弹性波速度与密度的三分之一次方的乘积应该是密度的线性函数。我们研究了铂、钯、钼和铑的立方晶胞和铁的六方密排晶胞的情况，温度高达1500K，压力高达360GPa。我们还研究了最近提出的扩展的伯奇定律的有效性的通用性，根据该定律，弹性波的速度是温度在给定密度的线性函数。在我们计算的误差条内，我们发现这与我们在高达3300 K的温度下对四种立方材料的数据一致。
英文摘要：
Birch's law in high pressure physics postulates a linear relationship between elastic wave speed and density and one of its most well known applications is in investigations into the composition of the inner core of the Earth using the Preliminary Reference Earth Model as the primary source of constraints. However, it has never been subjected to high precision tests even at moderately elevated temperatures. Here we carry out such a test by making use of the Density Functional Theory of electronic structure calculation and the Density Functional Perturbation Theory of calculating the phonon dispersion relation. We show that a recently proposed modification to the Birch's law is consistently satisfied more accurately than its original version. This modified version states that it is the product of elastic wave speed and one-third power of density that should be a linear function of density. We have studied the cases of platinum, palladium, molybdenum and rhodium with cubic unit cell and iron with hexagonal-close-packed unit cell with temperatures up to 1500K and pressures up to about 360 GPa. We also examine the genericity of the validity of a recently proposed extension of the Birch's law according to which elastic wave speed is a linear function of temperature at a given density. Within the error bars of our calculation, we find that this is consistent with our data for the four cubic materials at temperatures up to 3300 K.
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