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(
Pˉ62m )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Pˉ62m 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 (Pˉ62m ) 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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地球、火星和月球的核部被认为主要由铁镍合金和少量轻元素组成[1-3],其中研究较为广泛的轻元素有C、H、O、Si、S等[4-6]。P作为一种重要的轻元素,也得到了越来越多的关注。首先,铁陨石和石铁陨石被认为是能够反映行星核部物质组成的天然样本,其中广泛存在的金属磷化物(如schreibersite(Fe,Ni)3P[7]、barringerite(Fe,Ni)2P[8]、allabogdanite(Fe,Ni)2P[9]、melliniite(Ni,Fe)4P[10]、perryite(Ni,Fe)8(Si,P)3[11]、monipite MoNiP[12]等)为P在行星核部的赋存提供了证据。其次,核幔分异是行星演化历史上制约核幔元素丰度的最重要事件[13],虽然P可能在高温下挥发散失,但是作为一种亲铁元素,其在地球和月球早期岩浆海中的核幔分异系数分别高达20~50[14]和40~200[15],使其能够在核幔分异和再平衡作用过程中被金属相大量攫取而进入核部。再者,高温高压实验也证实了P在铁中具有较高的溶解度:在与月球核幔边界相当的压力(3 GPa)条件下,P在固相Fe和Fe-P液相中的溶解度(质量分数)分别高达2.9%和10.1%[15],而在与火星核部相当的压力(23 GPa,1 275 ℃)条件下,在Fe-S-P三元体系中P在Fe中的溶解度达4%[16],说明P在固态Fe中的溶解度随着压力的增加而增大。P在地核中的丰度约为0.2%(质量分数),超过地球上P总含量的90%[4];P在火星核部的丰度约为0.32%[17];而在完全凝固的纯铁月核中,P含量(以下如无特别说明,均为质量分数)最高可达(0.85±0.15)%[15]。
宇宙天体化学研究显示,Ni在地核、火星核部和月球核部的质量分数分别为5%~15%、7.6%[2]和(17.4±6.5)%[18],是行星核部一种重要的合金元素,对Fe-Ni-P体系高温高压性质的影响不可忽视。基于以上因素,近年来研究者对陨石中常见的几种铁镍磷化合物展开了高温高压实验和理论计算研究。在压缩性方面:Fe3P(
Iˉ4 )在20~40 GPa范围内发生Fe3+电子自旋态转变[19],从而引起原子磁矩坍塌,在20 GPa出现晶胞体积随压力的不连续变化,同时由轴向压缩各向同性转变为各向异性[20];而Ni的置换式固溶弱化了这种效应,使Fe2.15Ni0.85P在0~50 GPa内始终保持轴向压缩各向同性;此外,Ni含量的增加还会增大(Fe,Ni)3P和(Fe,Ni)2P(Pnma)的体积模量[21-22]。在晶体结构方面,(Fe,Ni)2P是目前已知陨石中唯一具有同质多象的铁镍磷化合物(Pˉ62m 结构barringerite和Pnma结构allabogdanite)。Dera等[23-24]分别对两端元化合物Fe2P和Ni2P进行了研究,发现Fe2P在8 GPa、1 400 K条件下由Pˉ62m 结构转变为Pnma结构,后者可在常温常压条件下以亚稳相形式存在,但在加热后又会转变为六方相结构。根据此现象,通过分析陨石中(Fe,Ni)2P的晶体结构,便可反演出陨石热动力学史的相关信息。但Ni2P却与Fe2P形成鲜明对比,在6.5 GPa、1 400 K条件下,Ni2P分解为Ni和NiP2,表明Ni显著影响(Fe,Ni)2P的高温高压晶体结构。在波速和密度方面,Ni的加入会增大(Fe,Ni)4P纵波和横波波速的各向异性[25],降低Fe3P在火星核部温压条件下的密度,使其更接近火星核部密度[21]。本研究选取(Fe1–xNix)2P(0 ≤ x ≤ 1.0)固溶体系中x = 0.5的中间组分化合物FeNiP为研究对象,利用金刚石压腔(Diamond Anvil Cell, DAC)技术和原位同步辐射X射线衍射(X-Ray Diffraction, XRD)实验对样品在0~25 GPa压力范围内的压缩性进行研究,以探究Ni对(Fe,Ni)2P压缩性的影响;根据状态方程参数对FeNiP、Fe2P、Fe3P、Fe2.15Ni0.85P和Fe3S在月球外核温压条件下的密度进行估算,讨论Ni、P两种元素对月球外核物质组成密度的影响。
1. 实验方法
FeNiP(
Pˉ62m )样品由高温固相法合成。首先按照化学计量比1∶1∶1称量一定量的铁粉(纯度99.99%)、镍粉(纯度99.99%)和红磷(纯度99.99%)作为起始反应物,混合研磨并压片,装入石英管中并抽真空密封;然后,将石英管置于管式炉中,于1 000 ℃保温6 h后,逐渐冷却至室温。将生成物研磨成颗粒直径约5 μm的粉末,用XRD实验(Cu Kα)进行物相分析。对衍射图谱进行精修,得到样品的晶胞参数a = 5.845 2(3) Å,c = 3.432 9(2) Å,单位晶胞体积V = 101.58(2) Å3。原位高压同步辐射XRD实验分两次进行,分别称为“Run 1”和“Run 2”。Run 1在中国科学院上海应用物理研究所上海光源(SSRF)硬X射线微聚焦及应用光束线站(BL15U1线站)完成。所用高压装置为Symmetry型DAC,砧面直径为400 μm。封垫材料为T304不锈钢,封垫起始厚度为203 μm,预压后厚度为41 μm,样品腔孔径约为200 μm。首先将FeNiP样品粉末压制成厚度约10 μm的薄片,随后选取尺寸约为50 μm× 40 μm× 10 μm的样品与压标物质Au箔片[26]一同置于样品腔中,并加入体积比为4∶1的甲醇-乙醇混合溶液作为传压介质。样品腔内的初始压力为1.0 GPa,最高实验压力为9.1 GPa。压力误差由Au的111和200衍射峰分别计算出的轴长a的标准差得出。X射线的波长为0.619 9 Å,聚焦光斑尺寸约为3 μm × 10 μm。衍射信号由MarXperts-SX-165型CCD采集记录,每张图谱的采谱时间为75 s。用FIT2D软件[27]对衍射图谱进行积分,转换为衍射强度-二倍衍射角(Intensity-2θ)关系图谱。Run 2在日本高能加速器研究机构(High Energy Accelerator Research Organization,KEK)PF(Photon Factory)的BL-18C线站完成。所用高压装置为Clamp型DAC,砧面直径为300 μm。封垫材料为铼,封垫起始厚度为263 μm,预压后厚度为51 μm,样品腔孔径约为170 μm。将尺寸约为50 μm×40 μm×10 μm的样品薄片与一颗红宝石球[28]一同置于样品腔中,并充入液氦作为传压介质。此时样品腔孔径缩小至约80 μm,腔内初始压力为10.5 GPa,最高实验压力为23.4 GPa。X射线的波长为0.610 7 Å,聚焦光斑尺寸
∅40 μm。衍射信号由FUJIFILM BAS-IP MS 2025感光板采集记录,每张图谱的采谱时间为20 min。用IPAnalyzer软件[29]对衍射图谱进行积分,转换为衍射强度-二倍衍射角关系图谱。用EXPGUI软件[30](Model biased法)对所有图谱进行全谱拟合,得到FeNiP在各实验压力条件下的晶胞参数。2. 结果与讨论
2.1 轴向压缩性
FeNiP在各实验压力条件下的XRD图谱显示,随着压力p升高,晶面间距减小,各衍射峰逐渐向高角度方向漂移,但其相对强弱及数目未发生变化,说明FeNiP在实验压力范围内保持
Pˉ62m 结构不变(见图1)。不同压力下的晶胞参数(a、c、V)列于表1。FeNiP的归一化轴长随压力的变化关系(p-a/a0和p-c/c0关系)显示其为轴向压缩各向异性,如图2所示。用线性二阶Birch-Murnaghan(B-M)状态方程(EOS)[31]拟合得到a、c两轴向的线性模量Ma = 525(6) GPa,Mc = 442(2) GPa。根据线性模量的定义式表 1 FeNiP在不同压力下的晶胞参数Table 1. Pressure dependence of unit-cell parameters of FeNiPp/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. Mi=−xi(∂p∂xi)T=1βi (1) 计算得到线性压缩系数βa=1.90(2)× 10–3 GPa–1,βc=2.26(1)×10–3 GPa–1,说明沿c轴方向比沿a轴方向更易压缩。
据Dera等[23-24]的研究结果,Fe2P和Ni2P也呈现轴向压缩各向异性。为直观比较三者的差异,本研究计算了归一化轴长比值随压力的变化关系(p-(c/c0)和p-(a/a0)关系),如图2所示。可以看出,FeNiP和Ni2P的各向异性与Fe2P相反:FeNiP和Ni2P沿c轴方向更易压缩,而Fe2P沿a轴方向更软;但FeNiP的p-(c/c0)或p-(a/a0)斜率明显小于Ni2P。综合以上结果可知,在(Fe1–xNix)2P(0 ≤ x ≤ 1.0)固溶体系中,当Ni的含量x达0.5时,在轴向压缩各向异性上就已经表现为Ni端元的性质,但程度仍弱于Ni2P。
Fe2P和Ni2P在轴向压缩上的差异来自于二者不同的磁性和磁矩排列。Fe2P为铁磁性,沿c轴方向相邻Fe原子之间的磁矩相互作用使得c轴比a轴更难压缩。而Ni2P为泡利顺磁性,磁矩取向无序,沿c轴方向没有阻碍压缩的相互作用,因而表现出与Fe2P相反的各向异性[24, 32]。在(Fe1–xNix)2P中,Ni原子具有晶格占位择优性。穆斯堡尔谱研究表明,当0 ≤ x < 0.3时,Ni倾向于优先占据四面体中心位置(MⅠ位置),当x>0.7时则优先占据五面体中心位置(MⅡ位置)[33]。当Ni占据MⅡ位置时,固溶体的铁磁性会明显减弱,在x ≥ 0.8时呈顺磁性[32]。在Ni含量x = 0.5的FeNiP中,可以认为Ni原子同时占据MⅠ和MⅡ位置。故虽然FeNiP在整体上仍呈铁磁性,但已弱于Fe2P。Ni的置换型固溶会减弱Fe2P在c轴方向上铁磁性磁矩之间的相互作用,使得c轴的抗压缩能力降低,因而FeNiP表现为与顺磁性Ni2P一致的轴向压缩各向异性。
2.2 体积压缩性
FeNiP的归一化晶胞体积随压力的变化关系(p-V/V0关系)如图3所示。使用EoSFit7c软件[31],用B-M状态方程(EOS)[34]
p(V)=32K0[(V0V)73−(V0V)53]{1+34(K′0−4)[(V0V)23−1]} (2) 对p-V关系进行拟合(考虑压力和晶胞体积的误差值),可得: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(三阶状态方程拟合结果);或者K0 = 167(1) GPa,K′0 = 4.0(固定值),V0 = 101.5(1) Å3(二阶状态方程拟合结果)。根据欧拉应变(εE=[(V/V0)−3/2−1]/2 )和标准化应力(FE = p/[3εE(1+2εE)5/2])的线性关系曲线斜率为正,说明体积模量微商值大于4(见图4),故三阶B-M状态方程的拟合结果K′0 = 5.7(2)合理[35]。将FeNiP的状态方程参数与(Fe,Ni)2P固溶体中两纯组分端元Fe2P(K0 = 175(8)GPa)和Ni2P(K0 = 201(8)GPa)进行比较,可以得到K0(FeNiP)< K0(Fe2P)< K0(Ni2P),见表2。FeNiP的体积模量小于Fe2P,经分析可能有以下几点原因。首先,本研究采用的传压介质与前人不同。本研究在1.0~9.1 GPa(Run 1)和10.5~23.5 GPa(Run 2)分别采用体积比为4∶1的甲醇-乙醇混合溶液(静水压极限10.5 GPa)和氦作为传压介质(静水压极限60 GPa),最高实验压力均处于传压介质的静水压极限范围内[36-39]。而Dera等[23]采用体积比为16∶4∶1的甲醇-乙醇-水混合溶液,其静水压极限约为14 GPa,在25 GPa的准静水压条件下,压力误差约为0.15 GPa[39],其p-V数据点在15 GPa后的散乱度明显增大[23],可能是受到传压介质性能变化的影响。第二,由于fcc镍的体积模量(K0 = 180 GPa)仅略大于hcp铁(K0 =165 GPa)[39-40],因而Dera等[24]认为Ni的置换型固溶对增加(Fe1–xNix)2P体积模量的作用很小;加之Ni减弱了铁磁性,从而降低了a轴的抗压缩能力,对降低FeNiP的体积模量亦具有一定影响。
3. 对月球外核的指示意义
地震学、激光测距和转动惯量等多方面的研究表明,月球的内部结构与地球相似,且具有较小的金属核[41-43]。其半径在250~430 km,占月球半径的15%~25%,且由固态内核和液态外核两部分构成[44]。月核的主要成分为铁镍合金,并含有质量分数不超过6%的轻元素[45-47],其中研究较为广泛的为S和C[3, 18, 48-50]。前人用多种方法对两种元素的丰度进行了估算:一些基于Fe-S或Fe-FeS二元体系的研究认为,S的丰度(质量分数)为(4±3)%[49],不超过6%[47]或6%~11%[3];还有研究认为C是月核中主要的轻元素。Steenstra等[6]认为月核中C的质量分数为0.6%~4.8%,而S则低于0.16%;Righter等[51]基于Fe-Ni-0.357%S-0.5%C四元体系研究显示,外核中C的质量分数为1.7%~2.4%,S为3.8%~11.8%,内核中C和S的质量分数分别约为1.2%和0.02%。
除了S和C之外,P也被认为是存在于月球核部的一种重要轻元素。P的核幔分异系数高达40~200[15],表明其在月球演化早期岩浆海的核幔分异过程中逐渐在核部富集[45-46, 52-53]。高温高压实验结果显示,在完全凝固的纯铁月核中,P的含量最高可达(0.85±0.15)%;而在有Ni和C存在的条件下,P的含量有所降低,为(0.4±0.1)%[15]。此外,月核中Ni的含量为(17.4±6.5)%[18],也是重要的合金元素。
根据Fe2P(
Pˉ62m )和Ni2P的稳定温压区间,(Fe,Ni)2P(Pˉ62m )在月球、木卫一(Io)、木卫二(Europa)和木卫三(Ganymede)等小行星核部(压力在6 GPa左右)存在的可能性较大[54-55]。为探讨P和Ni含量对月核密度的影响,并与S进行比较,本研究基于高温B-M状态方程[35]和实验结果,参考前人研究所得Fe3S的状态方程参数[20-21, 23, 56](见表3),估算了FeNiP、Fe2P、Fe3P、Fe2.15Ni0.85P和Fe3S在月球外核温压条件下(4.8~5.0 GPa,1 800 K)[3]的密度,并与γ-Fe[57]和月球外核密度((6.75±0.25)g/cm3)[3]进行比较,如图5所示。高温B-M状态方程为[35]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 Fe3SMaterial T0/K V0,T0/Å3 K0T0/GPa K′0T0 (∂KT∂T)p/(GPa⋅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] 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.)p(V,T)=32K0T[(V0TV)73−(V0TV)53]{1+34(K′0T−4)[(V0TV)23−1]} (3) K0T=K0T0+(∂KT∂T)p(T−T0) (4) K′0T=K′0T0 (5) V0T=V0,T0exp(∫TT0αTdT) (6) αT=α0+α1T (7) 式中:K0T、
K′0T 和V0T为温度T下的等温体积模量、体积模量微商和晶胞体积;K0T0 、K′0T0 和V0T0 为温度T0下的等温体积模量、体积模量微商和晶胞体积;(∂KT∂T)p 为等温体积模量随温度变化的偏导数;αT为热膨胀系数,由经验系数α0和α1表示。考虑到月球外核为液态,本研究还对以上几种物质进行了体积修正,即认为其在月球外核温压条件下发生熔融时,液态体积相较固态增大1%[58]。首先,虽然Fe2P(21.7% P)和FeNiP(21.3% P)中轻元素的质量分数相较Fe3P(15.6% P)、Fe2.15Ni0.85P(15.4% P)和Fe3S(16.1% S)更高,但密度却比后三者高,这一方面与常温常压下的物质密度有关,另一方面也受体积模量等状态方程参数的影响,说明物质在行星核部的密度受多种因素共同控制。其次,虽然Fe2P、Fe3P和Fe3S的密度低于外核密度,但FeNiP(40.3% Ni)和Fe2.15Ni0.85P(24.8% Ni)的密度均高于其对应的纯铁端元,特别是FeNiP的密度与月球外核密度相当,说明Ni的加入会使(Fe,Ni)2P和(Fe,Ni)3P的密度更接近月球外核密度,阐释了在未来的工作中以多元合金体系(如Fe-Ni-S-P)为对象来研究行星核部物质组成的重要性。4. 结 论
FeNiP作为中间组分化合物,对于研究Ni对(Fe1–xNix)2P(0 ≤ x ≤ 1.0)固溶体压缩性的影响具有重要意义。原位同步辐射XRD实验表明,FeNiP在0~23.4 GPa压力范围内保持
Pˉ62m 晶体结构不变。FeNiP的体积模量低于Fe2P,并表现出与Fe2P相反、与Ni2P一致的轴向压缩各向异性。通过估算和比较FeNiP、Fe2P、Fe3P、Fe2.15Ni0.85P和Fe3S在月球外核温压条件下的密度,发现Ni的加入可使(Fe,Ni)2P和(Fe,Ni)3P的密度更接近月球外核密度,阐释了以多元合金体系(如Fe-Ni-S-P)为对象来研究行星核部物质组成的重要性。 -
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 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. 表 2 Fe2P、Ni2P和FeNiP的B-M状态方程参数
Table 2. B-M EOS parameters of Fe2P, Ni2P, and FeNiP
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 V0,T0/Å3 K0T0/GPa K′0T0 (∂KT∂T)p/(GPa⋅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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