The thermal expansion of gold: point defect concentrations and pre-melting in a face-centred cubic metal.
The thermal expansion of gold: point defect concentrations and pre-melting in a face-centred cubic metal.
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DOI：
10.1107/s1600576718002248
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发表时间：
2018-04-01
影响因子：
6.1
通讯作者：
Vočadlo L
中科院分区：
文献类型：
--
作者：
Pamato MG;Wood IG;Dobson DP;Hunt SA;Vočadlo L
用X射线粉末衍射法测定了金在40 K至1337 K之间的热膨胀系数。 金显示出非线性的热膨胀增加，这与熔化前的相关Grüneisen-Debye模型不同，这已经在点缺陷的产生方面进行了量化。基于从头计算的计算机模拟，预熔化现象已被建议发生在六方密堆积铁的弹性性能的条件下的地球内核的熔化之前。这些预熔化效应在多大程度上也可能发生在面心立方金属的物理性质已在这里进行了研究，在更多的实验条件下的黄金，允许与未来的计算机模拟这种材料进行比较。用X射线粉末衍射法测定了金在40 K至1337 K之间的热膨胀系数。 对于整个温度范围内的研究，晶胞体积可以用以下方式表示：二阶Grüneisen近似的零压体积状态方程，通过德拜模型计算的内能，用于表示“完美晶体”的热膨胀。金在熔化之前表现出非线性的热膨胀增加，这与Grüneisen-Debye模型不同，这可能是在大范围温度下产生点缺陷的结果，从T/Tm> 0.75开始（类似于在Au的弹性模量中观察到软化的同源T）。因此，利用点缺陷的热力学理论来考虑空位在高温下的附加体积（“真实晶体”），得到以下拟合参数：Q =（V 0 K 0）/γ = 4.04 （1） × 10−18 J，V 0 = 67.1671 （3） B =（K 0′ − 1）/2 = 3.84 （9），θD = 182 （2） K，（v f/Ω）exp（s f/k B）= 1.8 （23）和h f = 0.9 （2） eV，其中V 0是0 K时的晶胞体积 ，K 0和K 0′是等温不可压缩性及其对压力的一阶导数（在零压力下计算），γ是Grüneisen参数，θ D是德拜温度，v f、h f和s f分别是空位形成体积、焓和熵，Ω是每个原子的平均体积，k B是玻尔兹曼常数。
The thermal expansion of gold has been determined by X-ray powder diffraction from 40 K up to the melting point (1337 K). Gold shows a nonlinear increase in thermal expansion that departs from the associated Grüneisen–Debye model prior to melting, which has been quantified in terms of the generation of point defects. On the basis of ab initio computer simulations, pre-melting phenomena have been suggested to occur in the elastic properties of hexagonal close-packed iron under the conditions of the Earth’s inner core just before melting. The extent to which these pre-melting effects might also occur in the physical properties of face-centred cubic metals has been investigated here under more experimentally accessible conditions for gold, allowing for comparison with future computer simulations of this material. The thermal expansion of gold has been determined by X-ray powder diffraction from 40 K up to the melting point (1337 K). For the entire temperature range investigated, the unit-cell volume can be represented in the following way: a second-order Grüneisen approximation to the zero-pressure volumetric equation of state, with the internal energy calculated via a Debye model, is used to represent the thermal expansion of the ‘perfect crystal’. Gold shows a nonlinear increase in thermal expansion that departs from this Grüneisen–Debye model prior to melting, which is probably a result of the generation of point defects over a large range of temperatures, beginning at T/T m > 0.75 (a similar homologous T to where softening has been observed in the elastic moduli of Au). Therefore, the thermodynamic theory of point defects was used to include the additional volume of the vacancies at high temperatures (‘real crystal’), resulting in the following fitted parameters: Q = (V 0 K 0)/γ = 4.04 (1) × 10−18 J, V 0 = 67.1671 (3) Å3, b = (K 0′ − 1)/2 = 3.84 (9), θD = 182 (2) K, (v f/Ω)exp(s f/k B) = 1.8 (23) and h f = 0.9 (2) eV, where V 0 is the unit-cell volume at 0 K, K 0 and K 0′ are the isothermal incompressibility and its first derivative with respect to pressure (evaluated at zero pressure), γ is a Grüneisen parameter, θ D is the Debye temperature, v f, h f and s f are the vacancy formation volume, enthalpy and entropy, respectively, Ω is the average volume per atom, and k B is Boltzmann’s constant.