Melting Temperatures of Fe92.5O2.2S5.3 under High Pressure
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摘要: 采用反向碰撞法与光分析技术，测量了Fe92.5O2.2S5.3(质量分数比)在208 GPa下的声速，发现固态Fe92.5O2.2S5.3的纵波声速在144 GPa下开始减小，直到165 GPa完全转变为液态体波声速，表明样品的完全熔化温度为(3 500±400)K。将该熔化温度作为参考点，应用Lindeman定律并外推至地球内外核边界可知，Fe92.5O2.2S5.3的熔化温度为(5 000±400)K。通过比较Fe、Fe-O、Fe-S以及Fe-O-S的熔化温度，发现O元素对Fe熔化温度的影响很小，S元素对Fe熔化温度的降低与其含量成正比。如果外地核中S的质量分数为2%~6%，则地球内外核界面温度为5 000~5 400 K。Abstract: In the present work we determined the sound velocities of shocked Fe92.5O2.2S5.3 (in weight percent) under pressures up to 208 GPa using the reverse-impact method and the optical analyzer technique.We found that the longitudinal sound velocities of the solid Fe92.5O2.2S5.3 began to decrease at 144 GPa and completely transformed to bulk sound velocity of liquid at 165 GPa, indicating that the completely melting temperature of the sample is about (3 500±400)K based on the energy conservation relation.With respect to this point as reference, the melting temperature of Fe92.5O2.2S5.3 is about (5 000±400)K when extrapolated to the boundary of the inner/outer core using the Lindeman Law.Compared with the already measured melting temperatures of Fe, Fe-O, Fe-S and Fe-O-S, it shows that the oxygen has little effect on the melting of iron, and the melting depression of iron increases with sulfur content in the sample.If the mass fraction of the sulfur in the outer core is 2%-6%, the temperature is about 5 000-5 400 K at the inner core/outer core boundary of the Earth.
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Key words:
- Fe-O-S /
- sound velocity /
- melting temperature /
- Earth's outer core
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1. 引言
众所周知，地核是由固态内核和液态外核组成，因此地球内外核界面温度等于地核物质在此压强(330 GPa)下的熔化温度，而该温度也是构建地球温度剖面的重要参考温度。根据地震波数据和高压实验结果可知，外核物质由铁和轻元素(质量分数约10%)组成[1-4]，其中可能的轻元素包括氧(O)、硫(S)、硅(Si)、碳(C)、氢(H)，而O和S被认为是主要的候选轻元素[5-14]。因此，为了构建地核的温度剖面，十分有必要研究O和S元素在高压下对Fe熔化温度的影响。
对于Fe-O体系，实验研究发现：在低于50 GPa的压强范围内，共晶点温度比Fe的熔化温度低50~350 K，并且当O的含量小于共晶含量时，Fe-O体系的液相温度与Fe的熔化温度非常接近[15-19]，即O对Fe熔化温度的影响很小。此外，通过实验研究还发现：Fe-S体系的共晶温度比纯Fe的熔化温度低1 000~1 500 K，并且随着压强的增大，共晶体成分向S减少的方向偏移[6-9, 20-26]；随着S含量的增大，Fe-S体系的液相温度急剧降低。对于Fe-O-S三元体系，Urakawa等[11]和Tsuno等[27]使用大腔体压机分别在15 GPa和15~27 GPa压强下实验研究了Fe-O-S体系的熔化行为。Urakawa等[11]发现Fe-O-S共晶体系中存在液体不互溶区，并且随着压强的增大，这种不互溶区逐渐消失；且在15 GPa时，Fe-O-S共析线(共晶点的连线)在Fe-S轴上的投影与Fe-S在18.5 GPa下的液相线非常一致[19]，说明O元素对Fe-S体系液相线温度的影响可以忽略。在更高的压强下，Huang等[14]利用冲击波压缩技术在低于230 GPa的压强范围内研究了富氧体系的Fe-O-S(Fe、O、S的质量分数比w(Fe)：w(O)：w(S)=90：8：2)的熔化行为，其液相线外推到内外核边界的温度为5 400 K。利用金刚石对顶砧与X射线同步辐射技术，Terasaki等[28]在0~157 GPa压强范围内测量了富硫体系的Fe-O-S(w(Fe)：w(O)：w(S)=85：2：13)的固相线和液相线温度，在误差范围内其液相线温度与Huang等[14]的测量结果非常接近。如果在高压下O对Fe-S体系液相线的影响非常小，那么由Huang等[14]和Terasaki等[28]的研究结果可知高压下S的含量对Fe-S体系液相线温度的影响将变得很小，与低压下的实验结论[6-9, 20-26]不同。而此结论是否正确，还需要进行进一步的高压实验。为此，本研究选择富硫体系的Fe-O-S样品作为研究对象，利用冲击波压缩技术研究其在高压下的熔化行为。
2. 实验
初始原料为高纯Fe、FeS和Fe2O3粉末，按质量比78.15：14.53：7.32在玛瑙研钵中研磨1 h。将干燥后的混合物压制成片，并密封于钼“杯”中，以杜绝Fe在高温下被氧化的可能性。将钼“杯”放置在大腔体压机的样品腔中进行烧结，压强约为2 GPa，温度为850 ℃。X射线衍射(XRD)分析发现，样品中不存在Fe2O3相，表明Fe2O3已经完全还原成FeO。根据混合物中Fe、FeS和Fe2O3的质量比，计算得到样品中Fe、O、S的质量分数比w(Fe)：w(O)：w(S)=92.5：2.2：5.3，以下将样品表示为Fe92.5O2.2S5.3。样品的平均密度为6.88(0.02)g/cm3，与理论密度6.89 g/cm3非常接近。
为了判断样品在冲击压缩过程中是否完全熔融，即在冲击加载下纵波声速是否变为体波声速，必须测量样品在冲击加载过程中的声速。尽管Huang等[13]已经报道了Fe92.5O2.2S5.3在高压下的声速数据，但是受篇幅限制，对测量方法和数据处理过程只进行了简单介绍，并未详细说明，为此本研究将对此进行详细论述。在测量Fe92.5O2.2S5.3的声速时，本研究采用了反向碰撞技术[29-30]和光分析技术[14]。反向碰撞技术可以在较低的压强下同时测出纵波声速和体波声速，而光分析技术可在较高的压强下测量样品熔融前的纵波声速和熔融后的体波速度。图 1(a)为反向碰撞技术的原理图。Fe92.5O2.2S5.3样品作为飞片，直接高速碰撞镀有铝膜的LiF单晶窗口。为了避免前冲气体对测量信号产生影响，在铝膜表面用环氧树脂粘贴一层8 μm厚的铝箔。碰撞后，在样品和铝箔中分别产生冲击波DsL和DAlL(波速分别为DsL和DAlL)，如图 1(b)所示。当铝箔中的冲击波DAlL在t0时刻到达铝膜/LiF单晶界面时，全光纤位移干涉仪(Displacement Interferometer System for Any Reflector，DISAR)[31]会观测到其粒子速度突然增加，并保持不变。样品中的冲击波DsL传播到样品后表面时，会反射稀疏波CsL。当铝箔中的稀疏波CAlL在t1时刻到达铝膜/LiF窗口界面时，粒子速度会缓慢减小。上述粒子速度的变化过程如图 2所示。
图 1 反向碰撞法实验装置图(a)和反向碰撞法波系作用图(b)Figure 1. Sample configuration (a) and wave interaction (b) for sound velocity measurements in the reverse impact method
图 2 实验No.081225和No.081226的界面粒子速度历史Figure 2. Particle velocity histories at the impact interface for experiments No.081225 and No.081226在拉格朗日坐标系中，样品中的纵波声速CL采用如下公式计算
CL=dst1−t0−ds/DLsρ0ρ (1) 式中：ds为样品厚度，ρ0和ρ分别为样品的初始密度和压缩后密度。在卸载过程中，如果可以确定弹性-塑性转变点在t2时刻，则体波声速CB可由下式确定
CB=dst2−t0−ds/DLsρ0ρ (2) 然而，根据粒子速度历史(见图 2)，很难准确判定t2的值。Asay等[32]发现样品在弹塑性卸载过程中，拉格朗日声速与粒子速度呈线性变化，他们将这种线性关系外推到卸载前的粒子速度，由此得到样品在卸载前的体波声速(见图 3)。
光分析技术实验装置如图 4所示。样品靶由3个不同厚度的样品构成，样品后表面为LiF单晶窗口，为了避免样品与窗口间的空隙在冲击过程中发出强光对测量信号产生干扰，在LiF表面粘贴一层金属钽箔。光分析技术中波系的相互作用见图 5。当飞片与样品高速碰撞时，在飞片与样品中分别产生两个传播方向相反的冲击波(DfL和DsL，波速分别为DfL和DsL)，当样品中的冲击波DsL在B1时刻到达样品/LiF窗口界面时，DISAR会监测到粒子速度突然增加，同时在界面向样品内部反射一个稀疏波Cs′L。飞片中的冲击波DfL传播到飞片后表面时，会反射一个向前传播的稀疏波，它们经过飞片和样品时的速度分别为CfL和CsL。当稀疏波CsL与来自样品后表面的稀疏波Cs′L相遇时，其稀疏波速度变为Cs1L，并在E1时刻到达样品/LiF窗口界面，此时会观测到界面粒子速度缓慢减小。在其他样品/窗口界面也会观测到类似的现象。由于稀疏波在样品中传播的速度CsL大于冲击波速度DsL，如果样品足够厚，稀疏波总会在样品中追赶上冲击波，如图 5中A点所示(所对应的厚度d为追赶厚度)。由于△A1B1E1∽△A2B2E2，因此Δt1/Δt2=(d-d1)/(d-d2)，其中d1和d2分别为样品1和样品2的厚度。如果在实验中可以布置更多厚度不同的样品，可以发现Δti与厚度di呈线性变化，当Δt=0即可得到追赶厚度。图 6显示了实验No.110505的粒子速度历史，样品厚度分别为1.535、2.336和3.065 mm，测量的时间间隔分别为579、536和500 ns，通过线性拟合得出样品的追赶厚度d=(12.74±0.06)mm，如图 7所示。
图 4 采用光分析技术测量声速的实验装置Figure 4. Experimental configuration for sound velocity measurements using optical analyzer technique
图 5 光分析技术测量声速实验中波的传播Figure 5. Wave interaction for sound velocity measurements in optical analyzer technique
图 6 实验No.110505在198 GPa下的粒子速度历史Figure 6. Particle velocity history for experiment No.110505 at 198 GPa
图 7 实验No.110505在198 GPa下的时间差Δt与样品厚度的关系Figure 7. Time intervals Δt vs.sample thickness for experiment No.110505 at 198 GPa在拉格朗日坐标下声速为
dDLs=dfDLf+dfCLf+dCLs (3) 式中：df为飞片厚度。在本实验过程中，为了在更高压力下获得声速，飞片材料采用Ta。在拉格朗日坐标系中，飞片和样品中的冲击波速度可采用以下公式计算
DLf=C0,Ta+λTa(W−u) (4) DLs=C0,s+λsu (5) 式中：C0和λ为Hugoniot参数，W为飞片速度，u为粒子速度。对于Fe92.5O2.2S5.3样品，C0，s=(3.71±0.12)km/s，λs=1.61±0.04[13]；对于Ta飞片，C0，Ta=3.293 km/s，λTa=1.307[33]。粒子速度u由冲击阻抗匹配法得到，Ta飞片的CfL取Brown等[34]给出的欧拉声速Cf，样品的欧拉声速为CsL与ρ0/ρ的乘积。
3. 结果讨论
Fe92.5O2.2S5.3的纵波声速和体波声速的测量结果如图 8所示。当冲击压强为142 GPa时，反向碰撞法测得的样品卸载信号不理想，根据实验数据计算得到的体波声速有很大误差，因此图 8中没有给出142 GPa下的体波声速。在144~165 GPa压强范围内，声速测量值沿Hugoniot线出现不连续性；而当压强高于165 GPa时，体波声速测量值与理论计算值[13]一致，表明样品在165 GPa下已经完全熔化，转变为液体。根据能量守恒关系，Fe92.5O2.2S5.3的液相线温度由(6)式和(7)式得到[35]
EH=12(V0−V)pH+E0=Ex+∫Tm0cVdT+TmΔS (6) pH=ρ0C20(1−ρ0/ρ)[1−λ(1−ρ0/ρ)]2 (7) 
图 8 Fe92.5O2.2S5.3的声速与冲击压强的关系Figure 8. Sound velocity of Fe92.5O2.2S5.3 vs.shock pressure式中：E为比内能，V为比容，p为压强，T为温度，Tm为熔化温度；下标“H”代表沿Hugoniot线，“x”代表沿0 K等温线，“0”代表室温；ΔS为熔融熵，ΔS=0.19R[36]，其中R为气体常数；cV为定容比热容，包括晶格比热容(cVl)和电子比热容(cVe)。Fe92.5O2.2S5.3的cV可根据Fe、FeO、FeS的定容比热容，通过可加性原理得到，即
cV=∑iwicVli+∑iwiβ0i(ρ0i/ρi)κiT (8) 式中：wi为组分i的质量分数；β0i和κi为组分i的电子热参数；ρ0i和ρi分别为组分i的初始密度和密度；cVli为组分i的晶格比热容贡献，在高温下满足Dulong-Petit定律，近似等于3R/μ(μ为摩尔质量)。组分Fe、FeO、FeS的详细参数如表 1所示。在(6)式中，固态下冷能Ex的计算方程为
Ex=EH−∫T0cVdT (9) 表 1 Fe、FeO、FeS和Fe-O-S体系参数Table 1. Parameters for Fe, FeO, FeS and Fe-O-S systemMaterial ρ0/(g/cm3) C0/(km/s) λ γ0 q β0/(J·kg-1·K-2) κ E0/(kJ) α-Fe 7.85[43] 3.935[43] 1.578[43] ε-Fe 8.298[44] 4.720* 1.523* 1.76* 0.76* 0.091[45] 1.34[45] 76.268 4[44] FeO(B1) 5.71[46] 5.83* 0.99* 57.796 7[47] FeO(B8) 6.05[46, 48] 4.486* 1.699* 1.8[48] 1[48] 0[49] 0[49] FeS 4.602[50] 2.947[50] 1.578[50] 1.54[50] 1[50] 0.25[51] 1.34[51] 33.707 5[52] Fe90O8S2 6.69[14] 3.97[14] 1.58[14] 1.85[14] 0.87[14] 0.075[14] 1.39[14] 67.315 Fe92.5O2.2S5.3 6.88 3.71 1.61 1.82 0.85 0.119 1.407 68.258 Note:The asterisk * represents the fitted results from the Hugoniot data. 固态样品的冲击温度可由下式给出[37]
dT=−T(γeffV)dV+12cV[(V0−V)dp+(p−p0)dV] (10) 式中：γeff为Grüneisen参数，包括晶格的贡献γl和电子的贡献γe。γeff的计算公式为
γeff=(cVlγl+cVeγe)/cV (11) Fe92.5O2.2S5.3的晶格参数γl=γ0(ρ0/ρ)q，其中γ0为常温下的Grüneisen参数，q为参数；由可加性原理及表 1中Fe、FeO、FeS的晶格参数可计算得到γl。Fe92.5O2.2S5.3的电子参数γe与纯Fe的γe较为接近，γe=2[38]。将以上参数代入(6)式中，计算得出Fe92.5O2.2S5.3样品在165 GPa压强下的熔化温度为(3 500±400)K。基于熔化温度的计算值，应用Lindeman原理，得出Fe92.5O2.2S5.3样品的熔化曲线，如图 9所示。
ΔTm=2Tm(γeff−13)Δρρ (12) 
图 9 Fe、Fe-O、Fe-S、Fe-O-S体系在高压下的熔化温度和液相线温度随压强的变化(红色实线为本研究得到的Fe92.5O2.2S5.3的熔化温度。Fe：Ma等[40]，标记为M04；Anzellini等[39]，标记为A13。Fe-O-S体系：Terasaki等[28]，标记为T11；Huang等[14]，标记为H10。Fe-S体系：Kamada等[26]，标记为K12。)Figure 9. Melting temperature of Fe-O-S system compared with those of Fe, Fe-O and Fe-S (The red solid line shows the melting temperature of Fe92.5O2.2S5.3 from this study.The lines labeled as M04 and A13 represent the melting temperatures of Fe from Ref.[40] and Ref.[39] respectively.The dashed lines labeled as H10 and T11 represent the melting temperature of Fe90O8S2[14] and the liquidus and solidus temperature of Fe-O-S[28].K12 represent the melting relationships in the Fe-Fe3S system up to the outer core conditions[26].)为了研究O元素与S元素对纯Fe熔化温度的影响，将Fe92.5O2.2S5.3的熔化温度与已发表的Fe、Fe-O-S、Fe-O、Fe-S体系的熔化温度和液相线温度进行比较，如图 9所示。对于Fe，最近Anzellini等[39]通过快速XRD研究了Fe在高压下的熔化温度，在实验误差范围内比Ma等[40]和Shen等[41]利用XRD得到的测量结果以及Huang等[42]利用动高压实验得到的计算结果高300 K。对于Fe-O体系，Seagle等[18]测量的Fe-FeO液相线温度非常接近，说明高压下O对Fe熔化温度的影响很小。对于Fe-O-S体系，由冲击波实验测得的Fe90O8S2[14]和Fe92.5O2.2S5.3的液相线温度均低于Fe的熔化温度，并且随着S含量的增大，Fe-O-S体系的液相线温度越来越低，但高于Fe-FeS的熔化温度[21-26]。在图 9中，对于Fe85O2S13，Terasaki等[28]用激光加热金刚石压砧和原位XRD技术测得的液相线温度比较高，由于其S含量超过共晶点S的含量，因此所测结果有可能是Fe3S在高压下的液相线温度。以上仅定性分析了O和S在高压下对Fe熔化温度的影响。为了进一步说明O和S对Fe熔化温度的影响，将Fe-O-S的液相线温度投影到Fe-S相图上，如图 10所示。Fe-O-S在15 GPa下的液相线[11]与Fe-S在18.5 GPa下的液相线[19]非常一致，说明O元素对Fe-S液相线的影响很小。Kamada等[26]测量了123 GPa下Fe-Fe3S的共晶点温度和液相温度，发现Fe90O8S2、Fe92.5O2.2S5.3的液相线温度恰好在Fe的熔化温度与Fe-Fe3S的共晶点温度连线之间，并低于Fe-Fe3S在液相区的温度。在330 GPa下，Fe90O8S2和Fe92.5O2.2S5.3的液相温度低于Fe的熔化温度，并高于Kamada等[26]依据实验数据估算的Fe92S8(质量分数比)的熔化温度。综合图 10所示相图可知，Fe-O-S与Fe-S的液相线在高压下基本一致；O对Fe熔化温度的影响很小，而S对Fe熔化温度的降低与其含量成正比。如果外地核是Fe-O-S体系，根据地球化学估算，地核中S的质量分数在2%~6%之间[53-54]，则内外核边界温度为5 000~5 400 K，与根据核幔边界所推算的温度5 200~5 700 K[55]在误差范围内非常接近。
图 10 高压下Fe-S与Fe-O-S体系液相线温度的比较Figure 10. Comparison of liquid-phase temperature between Fe-S and Fe-O-S system under high pressure4. 结论
测量了Fe92.5O2.2S5.3在208 GPa压强下的声速，发现其纵波声速在144 GPa下开始逐渐减小，到165 GPa时完全转变为液态体波声速。通过计算得到样品完全熔化温度为(3 500±400)K。将该熔化温度作为参考点，应用Lindeman定律并外推至地球内外核边界可知，Fe92.5O2.2S5.3的熔化温度为(5 000±400)K。通过比较Fe、Fe-O、Fe-S以及Fe-O-S的熔化温度发现，Fe-O-S体系与Fe-S体系的液相线温度非常接近，说明O元素对Fe熔化温度的影响很小，而S元素对Fe熔化温度的降低与其含量成正比。如果外地核中S元素的质量分数在2%~6%之间，则内外核界面温度为5 000~5 400 K。
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图 1 反向碰撞法实验装置图(a)和反向碰撞法波系作用图(b)
Figure 1. Sample configuration (a) and wave interaction (b) for sound velocity measurements in the reverse impact method
图 2 实验No.081225和No.081226的界面粒子速度历史
Figure 2. Particle velocity histories at the impact interface for experiments No.081225 and No.081226
图 4 采用光分析技术测量声速的实验装置
Figure 4. Experimental configuration for sound velocity measurements using optical analyzer technique
图 5 光分析技术测量声速实验中波的传播
Figure 5. Wave interaction for sound velocity measurements in optical analyzer technique
图 6 实验No.110505在198 GPa下的粒子速度历史
Figure 6. Particle velocity history for experiment No.110505 at 198 GPa
图 7 实验No.110505在198 GPa下的时间差Δt与样品厚度的关系
Figure 7. Time intervals Δt vs.sample thickness for experiment No.110505 at 198 GPa
图 8 Fe92.5O2.2S5.3的声速与冲击压强的关系
Figure 8. Sound velocity of Fe92.5O2.2S5.3 vs.shock pressure
图 9 Fe、Fe-O、Fe-S、Fe-O-S体系在高压下的熔化温度和液相线温度随压强的变化(红色实线为本研究得到的Fe92.5O2.2S5.3的熔化温度。Fe：Ma等[40]，标记为M04；Anzellini等[39]，标记为A13。Fe-O-S体系：Terasaki等[28]，标记为T11；Huang等[14]，标记为H10。Fe-S体系：Kamada等[26]，标记为K12。)
Figure 9. Melting temperature of Fe-O-S system compared with those of Fe, Fe-O and Fe-S (The red solid line shows the melting temperature of Fe92.5O2.2S5.3 from this study.The lines labeled as M04 and A13 represent the melting temperatures of Fe from Ref.[40] and Ref.[39] respectively.The dashed lines labeled as H10 and T11 represent the melting temperature of Fe90O8S2[14] and the liquidus and solidus temperature of Fe-O-S[28].K12 represent the melting relationships in the Fe-Fe3S system up to the outer core conditions[26].)
图 10 高压下Fe-S与Fe-O-S体系液相线温度的比较
Figure 10. Comparison of liquid-phase temperature between Fe-S and Fe-O-S system under high pressure
表 1 Fe、FeO、FeS和Fe-O-S体系参数
Table 1. Parameters for Fe, FeO, FeS and Fe-O-S system
Material ρ0/(g/cm3) C0/(km/s) λ γ0 q β0/(J·kg-1·K-2) κ E0/(kJ) α-Fe 7.85[43] 3.935[43] 1.578[43] ε-Fe 8.298[44] 4.720* 1.523* 1.76* 0.76* 0.091[45] 1.34[45] 76.268 4[44] FeO(B1) 5.71[46] 5.83* 0.99* 57.796 7[47] FeO(B8) 6.05[46, 48] 4.486* 1.699* 1.8[48] 1[48] 0[49] 0[49] FeS 4.602[50] 2.947[50] 1.578[50] 1.54[50] 1[50] 0.25[51] 1.34[51] 33.707 5[52] Fe90O8S2 6.69[14] 3.97[14] 1.58[14] 1.85[14] 0.87[14] 0.075[14] 1.39[14] 67.315 Fe92.5O2.2S5.3 6.88 3.71 1.61 1.82 0.85 0.119 1.407 68.258 Note:The asterisk * represents the fitted results from the Hugoniot data. 
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