Compressibility of FeNiP under High Pressure
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摘要: 利用金刚石压腔技术和原位同步辐射X射线衍射技术，对FeNiP（
$P\bar 62m$ ）的压缩性进行了实验研究。常温下，FeNiP在0～23.4 GPa压力范围内保持$P\bar 62m$ 结构不变。用Birch-Murnaghan状态方程对单位晶胞体积随压力的变化关系（p-V关系）进行拟合，得到：体积模量K0=153(2) GPa，体积模量微商$K'_0 $ = 5.7(2)，零压下晶胞体积V0 = 101.6(1) Å3；或K0 = 167(1) GPa，$K'_0 $ = 4.0（固定值），V0 = 101.5(1) Å3。与Fe2P相比，FeNiP的体积模量更小，呈现出与Fe2P相反、与Ni2P相同的轴向压缩各向异性，据此探讨了Ni对(Fe,Ni)2P压缩性的影响。应用当前实验结果，估算了FeNiP、Fe2P、Fe3P、Fe2.15Ni0.85P和Fe3S在月球外核温压条件下的密度，通过与γ-Fe及月球外核密度的比较，得出Ni的加入会使“Fe-轻元素”体系的密度更接近月球外核密度，进一步阐释以多元合金体系（如Fe-Ni-S-P）为对象来研究行星核部物质组成更具合理性。Abstract: Compressibility of FeNiP ($P\bar 62m$ ) has been studied up to 23.4 GPa by using diamond anvil cells (DAC) combined with in situ synchrotron X-ray diffraction (XRD) at room temperature. FeNiP remains the hexagonal structure at experimental pressure range. The pressure-volume (p-V) data has been fitted by the Birch-Murnaghan (B-M) equation of state, yielding K0 = 153(2) GPa,$K'_0 $ = 5.7(2), V0 = 101.6(1) Å3 or K0 = 167(1) GPa,$K'_0 $ = 4.0 (fixed), V0 = 101.5(1) Å3. FeNiP has smaller bulk modulus than Fe2P, and shows analogous axial compressibility to Ni2P. This might result from nickel’s doping effect on elastic properties of (Fe,Ni)2P. The densities of FeNiP, Fe2P, Fe3P, Fe2.15Ni0.85P and Fe3S have been estimated under the pressure-temperature conditions commensurate to the Moon’s outer core. The comparison shows that the doping of nickel could make (Fe,Ni)2P and (Fe,Ni)3P’s density approaching that of the Moon’s outer core.-
Key words:
- FeNiP /
- diamond anvil cell /
- X-ray diffraction /
- Moon /
- outer core
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图 1 FeNiP在Run 1（a）和Run 2（b）两次原位高压同步辐射XRD实验中部分压力条件下的衍射图谱（星号表示铼的衍射峰）
Figure 1. Representative synchrotron radiation XRD patterns of FeNiP at various pressures in Run 1 (a) and Run 2 (b)(The asterisks mark diffraction peaks of rhenium)
图 2 FeNiP的归一化轴长（a/a0和c/c0）及归一化轴长比值（（c/c0）/（a/a0））随压力的变化关系（Fe2P和Ni2P的p-（c/c0）/（a/a0）数据[23–24]也被列出用于比较）
Figure 2. Normalized axis length of FeNiP (a/a0 and c/c0) and normalized ratio of axis length ((c/c0)/(a/a0)) with the change of pressure (p-(c/c0)/(a/a0) data of Fe2P and Ni2P[23–24] are plotted for comparison.)
图 4 FeNiP的欧拉应变-标准化应力（εE-FE）关系
Figure 4. Eularian strain-normalized stress (εE-FE) plot of the p-V data based on the B-M equation of state
图 5 月球外核温压（4.8～5.0 GPa，1 800 K）条件下FeNiP、Fe2P、Fe3P、Fe2.15Ni0.85P、Fe3P和Fe3S的估算密度（γ-Fe和月球外核密度也绘出用以比较）
Figure 5. Calculated density of FeNiP, Fe2P, Fe3P, Fe2.15Ni0.85P, Fe3P, and Fe3S under the pressure-temperature conditions commensurate to the Moon’s outer core（4.8–5.0 GPa, 1 800 K）（Density of γ-Fe and the Moon’s outer core are plotted for comparison.）
表 1 FeNiP在不同压力下的晶胞参数
Table 1. Pressure dependence of unit-cell parameters of FeNiP
p/GPa a/Å c/Å V/Å3 p/GPa a/Å c/Å V/Å3 0.000 1 5.845（1） 3.433（1） 101.6（1） 7.9（1） 5.760（1） 3.379（1） 97.1（1） 1.0（1） 5.829（1） 3.426（1） 100.8（1） 9.1（1） 5.750（1） 3.372（1） 96.6（1） 2.8（1） 5.811（1） 3.413（1） 99.8（1） 10.5（1） 5.737（1） 3.362（1） 95.8（1） 3.3（1） 5.806（1） 3.410（1） 99.5（1） 11.6（1） 5.729（2） 3.353（2） 95.3（1） 3.8（1） 5.798（1） 3.406（1） 99.2（1） 13.5（1） 5.713（1） 3.346（1） 94.6（1） 4.8（1） 5.790（1） 3.400（1） 98.7（1） 18.1（1） 5.682（1） 3.320（1） 92.8（1） 5.7（1） 5.783（1） 3.392（1） 98.2（1） 20.7（1） 5.660（1） 3.306（1） 91.7（1） 6.6（1） 5.772（1） 3.385（1） 97.7（1） 23.4（1） 5.647（1） 3.292（1） 90.9（1） Note: Data of 1.0–9.1 GPa are from Run1, and data of 10.5–23.4 GPa are from Run 2; numbers in parentheses represent errors in the last digit. 
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表 3 FeNiP、Fe2P、Fe3P、Fe2.15Ni0.85P和Fe3S的高温B-M状态方程参数
Table 3. High-temperature B-M equation of state parameters for FeNiP, Fe2P, Fe3P, Fe2.15Ni0.85P, and Fe3S
Material T0/K ${V_{{0,T}_0}}$/Å3 ${K_{{0T}_0}}$/GPa ${K'_{{0T}_0}}$ ${{\left( {\dfrac{{\partial {K_T}}}{{\partial T}}} \right)_p}}/({\rm{GPa}}\cdot{\rm K}^{-1})$ α0/（10–5 K–1） α1/（10–8 K–2） FeNiP 300 101.5 167 4.0 –3.75×10–2[54] 3.0[54] 2.8[54] Fe2P 300[23] 103.16[23] 175[23] 4.0[23] –3.75×10–2[54] 3.0[54] 2.8[54] Fe3P 300[20] 366.9[20] 161[20] 4.0[20] –3.75×10–2[54] 3.0[54] 2.8[54] Fe2.15Ni0.85P 300[21] 365.8[21] 185[21] 4.0[21] –3.75×10–2[54] 3.0[54] 2.8[54] Fe3S 300[54] 377.01[54] 150[54] 4.0[54] –3.75×10–2[54] 3.0[54] 2.8[54]
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