First-Principles Study of Spin State, Structure and Seismic Velocity of Ferrous-Bearing Post-Perovskite MgSiO3
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摘要: 运用基于密度泛函的第一性原理方法，对含Fe2+后钙钛矿相MgSiO3在高压下的性质进行了计算。计算结果表明, 在0~160 GPa的压强范围内Fe2+始终保持高自旋状态，但在高压下有转向中间自旋或低自旋的趋势。对于含有多个Fe2+的结构，通过比较可能结构的能量以及结合力学稳定性判据，发现Fe2+倾向于以最紧密方式替位占据Mg2+的位置。还计算了120 GPa(D〃层压强)下的弹性波速，表明无论压缩波(P波)还是剪切波(S波)，随着Fe2+浓度的增加，地震波速明显减小，并且S波的横向各向异性明显增强。Abstract: By using the first principles method based on density functional theory, the physical properties of ferrous-bearing post-perovskite MgSiO3 at high pressure were calculated.The results show that the high-spin state is conserved for ferrous irons from 0 to 160 GPa.The transition tendency from high-spin state to intermediate-spin or low-spin state at higher pressure was also presented.For those structures containing several Fe2+, from the comparison of total enthalpies and the mechanical stability criterion we can conclude that the ferrous irons tend to take the closest positions of Mg2+.Moreover, the seismic velocities at 120 GPa (pressure in D〃 layer) were calculated.The calculations show that both the compressional waves (P-waves) and the shear waves (S-waves) decrease obviously with the increasing concentration of Fe2+.Remarkably, the transverse anisotropy of shear wave increases significantly.
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Key words:
- post-perovskite /
- MgSiO3 /
- D〃 layer /
- spin /
- seismic velocity
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图 2 Fe2+不同自旋态的焓差随压强的变化关系
Figure 2. Pressure dependence of relative enthalpies(ΔH) of Fe2+ with different spin states
图 3 0和120 GPa时Fe2+的d电子的态密度图
Figure 3. Density of states of d electrons of Fe2+ at 0 and 120 GPa
图 4 Fe2+不同浓度时的不同结构(只给出了Fe和Mg元素(绿色为Mg原子、紫色为Fe原子)，(a)、(h)、(m)、(n)分别为浓度为37.5%、50.0%、67.5%、75.0%时的最稳定结构)
Figure 4. Different structures of various concentration of Fe2+(only the Fe and Mg atoms presented, and the green and purple balls denote Mg and Fe, respectively), where (a), (h), (m), (n) are the most stable structure for the concentration of 37.5%, 50.0%, 67.5%, 75.0%, respectively
图 5 体积模量B以及剪切模量G随Fe2+物质的量分数的变化
Figure 5. Bulk modulus (B) and shear modulus (G)as a function of mole fraction of Fe2+
图 6 压缩波和剪切波波速随Fe2+物质的量分数的变化
Figure 6. Compression waves and shear wavesas a function of mole fraction of Fe2+
图 7 Fe2+的物质的量分数分别为12.5%(a)和1(b)时P波和S波沿不同传播方向的波速
Figure 7. P-wave and S-wave velocities in different propagation directions for the Fe2+ mole fraction of 12.5%(a)and 1(b) respectively
表 1 Fe2+的不同自旋排列以及对应自旋态
Table 1. Various spin arrangement and corresponding spin states of Fe2+
Spin states Fe2+(3d6) HS(S=2) ↑↓ ↑ ↑ ↑ ↑ IS(S=1) ↑↓ ↑↓ ↑ ↑ LS(S=0) ↑↓ ↑↓ ↑↓ Note:↑ represents spin up, ↓ represents spin down. 
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表 2 120 GPa时含不同Fe2+浓度的pPv的弹性常数
Table 2. Elastic constants of pPv at 120 GPa with different concentrations of Fe2+
(GPa) Concentration C11 C22 C33 C12 C13 C23 C44 C55 C66 0 1 200 941 1 158 375 274 450 277 248 377 0.125 1 215 881 1 172 403 318 460 260 248 388 1 1 089 815 1 049 414 377 457 64 202 259
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