地球下地幔矿物结构和热力学参数的研究进展与展望
廖一帆, 孙宁宇, 毛竹*
地震和地球内部物理实验室,地球和空间学学院,中国科学技术大学,安徽 合肥 230026
*通信作者:毛竹(1982-),女,重庆人,教授,主要从事地球内部物质物理性质研究.E-mail:zhumao@ustc.edu.cn

作者简介:廖一帆(1993-),男,四川邛崃人,硕士研究生,主要从事地球内部物质物理性质研究.E-mail:lyfan123@mail.ustc.edu.cn

摘要

下地幔从660 km到2 891 km深度,占据整个地球质量的49.2%并处于极端高温高压的状态。在下地幔相应的温度压力条件下研究主要构成矿物的物理性质,尤其是结构、密度和波速,是理解下地幔结构、物质组成以及动力学过程的关键。通过回顾过去30年高温高压矿物学实验对下地幔矿物,包括布里基曼石、铁方镁石、Ca-钙钛矿以及硅酸盐—后钙钛矿结构和热力学状态方程的重要研究进展,探讨温压条件变化、成分变化以及Fe自旋变化对这些下地幔矿物(相)密度和体波波速的影响,指出现有研究结果的不足和需要解决的问题,并对未来的研究方向提出展望。

关键词: 下地幔高温高压条件; 结构; 热力学状态方程; 密度; 体波波速
中图分类号:P31 文献标志码:A 文章编号:1001-8166(2017)05-0465-16
Recent Advance and Prospects in the Structure and Thermal Elastic Properties of Lower Mantle Minerals
Liao Yifan, Sun Ningyu, Mao Zhu*
School of Earth and Space Sciences, University of Science and Techonology of China, Hefei 230026, China
*Corresponding author:Mao Zhu(1982-), female, Chongqing City, Professor. Research areas include physical properties in the Earth interior.E-mail:zhumao@ustc.edu.cn

First author:Liao Yifan(1993-), male, Qionglai City, Sichuan Province, Master student. Research areas include physical properties in the Earth interior.E-mail:lyfan123@mail.ustc.edu.cn

Abstract

Lower mantle, ranging from 660 km to 2 890 km depth, occupies 49.2% of the Earth by mass and is at extremely high pressure and temperature conditions. Experimental studies on the physical properties of the lower mantle minerals, particular the structure, density, and sound velocity, etc., are important to understand the structure, composition, and dynamic behavior of the region. Here we summarize the recent experimental results on the structure and thermal equation of states of the lower mantle minerals, including bridgmanite, ferropericlase, CaSiO3-perovskite, and silicate post-perovskite, and discuss the effect of pressure, temperature, composition, and Fe-spin transition on the density and bulk sound velocity of those minerals. This review aims to provide new insights into the lower-mantle structure and chemistry and help to understand the observed velocity anomalies in the lower mantle.

Keyword: Lower mantle high pressure-temperature condition; Structure; Thermal equation of state; Density; Bulk sound velocity.
1 引言

地球内部处于极度的高温高压状态。以下地幔为例, 从660 km至核幔边界的2 891 km深度, 压力从24 GPa急剧增加至136 GPa, 而温度从约1 900 K升高至2 800~4 000 K[1]。近期研究表明, 地球上、下地幔物质组成均符合地幔岩模型[2~5]。根据地幔岩模型, 地球下地幔由75 vol.%(vol.%为体积百分数)布里基曼石[(Mg, Fe)(Al, Fe, Si)O3], 17 vol.%铁方镁石[(Mg, Fe)O]以及8 vol.% Ca-钙钛矿(CaSiO3)组成(图1)[6]。在核幔边界D″区域, 布里基曼石由钙钛矿结构相变为后钙钛矿结构(后统称硅酸盐— 后钙钛矿)[7, 8]。因此, 在下地幔相应的温度和压力下研究主要构成矿物(相)的物理性质, 尤其是密度、弹性性质和波速, 对我们了解地球深内部的物质组成和结构, 理解观测到的波速异常和各向异性的形成机制以及认识地球内部的演化、发展及动力学过程具有重要意义[9~15]

矿物的密度、弹性性质以及波速主要受压力、温度、相变以及成分变化的影响。在实验室模拟下地幔高温高压状态主要由金刚石对顶砧与激光加热技术结合来实现[16]。作为下地幔含量最为丰富的矿物, 布里基曼石中Fe和Al含量约为10%[6, 17]。而铁方镁石中Fe含量为15%~20%[17]。但深俯冲至下地幔的大洋玄武岩可能带来更多的Fe和Al, 致使在核幔边界可能形成富Fe和/或Al的布里基曼石(或硅酸盐— 后钙钛矿)和铁方镁石[18~20]。富Fe和/或Al布里基曼石(或硅酸盐— 后钙钛矿)和铁方镁石在核幔边界的堆积也被认为可能与超低速带(Ultra Low Velocity Zone, ULVZ)和热化学异常(Large Low Shear Wave Velocity Zone, LLSVPs)的形成有关[9, 20]。除此以外, 高温高压实验和理论研究指出, 在下地幔温压条件下布里基曼石、铁方镁石和硅酸盐— 后钙钛矿中Fe的3d最外层电子会发生自旋转变并影响矿物的物理性质[9, 13~15, 21~24]。因此, 研究Fe自旋态变化对布里基曼石、铁方镁石以及硅酸盐— 后钙钛矿密度、弹性模量以及波速等物理性质的影响是过去十多年高温高压矿物学的重要研究课题之一[9, 13~15, 21, 22]。此外, 作为下地幔中含量较少的矿物, Ca-钙钛矿虽然可以含有一定量的Al2O3, 但相较于布里基曼石和铁方镁石, Ca-钙钛矿在下地幔成分变化较小[25, 26]。因此, 对Ca-钙钛矿的研究主要集中在压力和/或温度变化引起的结构相变对CaSiO3物理性质的影响[3, 25, 27~29]

图1 地幔岩物质组成[6]Fig.1 Mantle in a pyrolitic composition[6]

综上所述, 本文以下地幔主要构成矿物, 包括地幔岩模型中的铁方镁石、布里基曼石、Ca-钙钛矿和硅酸盐— 后钙钛矿为讨论对象, 总结了过去30年矿物学在下地幔相应的温度和压力下对这些矿物(相)结构和热力学状态方程的研究成果, 并对未来的研究方向进行了展望。由于实验技术的局限性和高温高压实验的困难性, 直接在下地幔相应温度和压力下测量矿物弹性性质的研究极为匮乏。因此, 本文的讨论集中在矿物的热力学状态方程。通过这些讨论, 以期对下地幔物质组成和结构带来新的认识。

2 热力学状态方程

三阶Birch-Murnaghan状态方程是最为常用的描述矿物压力和体积关系的状态方程。实验测量的压力和体积可以描述为[30]:

P=3/2K0T(T)[(V0T/V)7/3-(V0T/V)5/3]× {1-3/4(4-K0T')[(V0T/V)3/2-1]}(1)

式中:PV分别为实验测量的压力和体积, V0T为常压下温度T时的体积, K0T(T)为常压下温度T时的体积模量, K0T'为体积模量对压力的导数。

V0TK0T(T)可由常温常压下体积V0和体积模量K0计算获得:

V0T=V0exp 300Tα (T)dT

K0T(T)=K0+ KT/T)P(T-300)

α (T)01T+α 2/T (2)

式中:α (T), α 0, α 1α 2是热膨胀系数。通过拟合实验获得的P-V-T数据, 最终确定弹性模量K0, 体积模量分别对压力和温度的导数K0T'KT/T)P, 以及热膨胀系数α (T)。这些参数是确定矿物在下地幔温压条件下的密度和波速的关键。

除三阶Birch-Murnaghan状态方程之外, Mie-Grü neisen状态方程可以更为自洽地实现等温条件下获得的热力学参数向绝热状态下热力学参数转换, 并且在将结果外推至超越实验的温压范围时更为可靠[30]。在Mie-Grü neisen状态方程中, P-V-T关系可描述为:

P=P0+Pth(3)

式中:P0对应三阶Birch-Murnaghan状态方程中常温下的压强, 可表示为:

P0=3/2K0[(V0/V)7/3-(V0/V)5/3]× {1-3/4(4-K0T')[(V0/V)3/2-1]}(4)

公式(3)中的Pth为热压力, 与在温度T和300 K的热内能差相关, 可表示为:

Pth=γ /V[Eth(V, T)-Eth(V, 300)] (5)

式中:γ 是Grü neisen参数。公式(5)中的热内能与德拜温度(θ D)相关:

Eth(V, T)=9nRT(θ D/T)-3 $\int_0^{\theta_D/T}$x3/(ex-1)dx (6)

式中:n是一个分子式中的原子总数, R为气体常数。γ θ D又可表示为:

γ =γ 0(V/V0)q

θ DD0exp[-(γ -γ 0)/q] (7)

式中:γ 0θ D0分别为常温常压下的Grü neisen参数和德拜温度, q是一个与体积相关的常数。因此, 利用Mie-Grü neisen状态方程拟合获得的P-V-T数据, 最终需要确定K0, K0T', γ 0, θ D0q值。

3 结构和热力学参数
3.1 铁方镁石

铁方镁石[(Mg, Fe)O, Fp]属于立方晶系(Fm3m)。下地幔铁方镁石中Fe大部分以Fe2+形式存在, Fe3+的含量少于1%[17, 31, 32]。Badro等[33]利用同步辐射X光散射技术在2003年发现, 常温下铁方镁石中Fe2+在60~70 GPa时, 其最外层电子由高旋态转变为低旋态。随后大量的理论和实验研究表明, Fe2+自旋转变不仅引起铁方镁石的密度在下地幔温压下陡增, 还促发其他物理性质的突变, 尤其是弹性模量、波速以及波速各向异性[13~15, 21, 22, 34~38]。因此, 确定铁方镁石在下地幔的密度和波速, 必须考虑压力、温度、Fe含量变化以及Fe自旋转变的影响。

在常温常压下, 铁方镁石中的Fe2+处于高旋态。可以看到, 铁方镁石的密度(ρ )随Fe含量增加而线性变化(图2), 可表示为:

ρ HS=3.57+2.48× XFe(8)

式中:ρ HS为常温常压下铁方镁石的密度, XFe=Fe/(Fe+Mg)。当Fe的摩尔含量少于25%时, 考虑到实验误差, K0几乎与Fe含量不相关(图2)。而当Fe摩尔含量超过25%后, K0随铁含量增加而略微减小[40]表1总结了不同成分的铁方镁石的热力学参数。无论是Grü neisen参数γ 0, 德拜温度θ D0, 还是体积常数q, 与Fe含量变化并没有很强的相关性。尤其是q值, 通常难以用实验获得的P-V-T数据约束, 而多采用理论计算预测值[3, 41, 42]

图2 在常温常压下铁方镁石(Fp)的密度(ρ 0)(a)和等温体积模量(K0)(b)
(a)密度; (b)等温体积模量; 黄色:高自旋Fp[21, 22, 34~37, 39]; 蓝色:低自旋Fp[22, 34, 36, 37]
Fig.2 Variation in the density (ρ 0)(a) and isothermal bulk moduli (K0)(b) of ferropericlase (Fp) at ambient conditions with various Fe content
(a)Density; (b)Isothermal bulk moduli; Yellow:High spin Fp[21, 22, 34~37, 39]; Blue:Low spin Fp[22, 34, 36, 37]

表1 铁方镁石的热力学参数* Table 1 Thermoelastic parameters of ferropericlase*

在常温下对铁方镁石中Fe的自旋转变与Fe含量之间的关系仍存在较大争议[32]。由于不同研究组在高压实验中采用不同的传压介质和压标, 不同金刚石对顶砧样品中压力梯度和偏应力不同, 样品是否经过高温退火, 这些都对铁方镁石中Fe2+自旋转变发生的压力以及宽度产生影响。依据已有的实验结果, 当Fe摩尔含量少于20%, 自旋转变大多发生在40 GPa左右, 起始压力与Fe含量没有太强的相关性, 自旋转变宽度约为20 GPa[21, 22, 35, 36, 39]。而当Fe摩尔含量超过20%, Fe含量的增加会提升自旋转变发生的压力[34]。当高旋态Fe完全转变成低旋态Fe时, 压力已经在60~65 GPa以上[21, 22, 35, 36, 39]。因此, 大部分实验着重研究铁方镁石中Fe自旋转变的过程, 而对低旋态铁方镁石热力学状态方程的研究较为缺乏[22, 34, 37]。就为数不多的实验结果来看[22, 34, 37], 低旋态铁方镁石的密度和体积模量均随Fe摩尔含量的增加而增加(图2), 可表示为:

ρ LS=3.57+2.96× XFe

K0-LS=159+54× XFe(9)

温度的升高使铁方镁石Fe自旋转变发生在更高的压力[21, 22, 43, 44]。但在高温高压下原位研究铁方镁石自旋转变以及确定自旋转变对热力学状态方程影响的研究困难大, 致使研究结果较少。Komabayashi等[21]分别在300 K和1 600~1 900 K研究了含Fe量为19%的铁方镁石(Fp19)的P-V关系。但由于其实验数据少, 无法获取低旋态Fp19的热力学参数[21]。迄今, 仅Mao等[22]对Fe含量为25%的高旋和低旋态铁方镁石(Fp25)热力学状态方程进行了较为细致的研究。因此, Fe摩尔含量变化如何影响高温下自旋转变的起始压力和宽度以及对γ 0, θ D0q这3个参数的影响仍然未知。

利用实验获得的P-V关系及热力学参数可以计算铁方镁石随地温曲线的密度和体波波速(图3)。以Fp19和Fp25为例, 沿地温曲线低旋态铁方镁石在下地幔的密度比高旋态高1.0%~1.2%[21, 22, 45]。考虑到铁方镁石在地幔岩模型中的含量仅有17 vol.%, 自旋转变对下地幔地幔岩成分的密度影响仅为0.2%~0.3%。而Fp19和Fp25密度分别比MgO高约12%和约18%。这意味着在铁方镁石每增加1 mol.%(mol.%为摩尔百分数)的Fe[17], 则可使下地幔密度增加约0.1%。因此, 铁方镁石自旋转变对下地幔密度的影响与铁方镁石中Fe摩尔含量变化2 mol.%~3 mol.%相当。此外, 铁方镁石在下地幔的体波波速低于MgO。在经历自旋变化前, 高旋态Fp25体波波速比MgO低4.8%, 相当于每增加1 mol.% Fe使铁方镁石体波波速降低0.2%。而自旋转变则带来体波波速的大幅降低。自旋转变中的Fp25体波波速比其高旋态低14%[22]。在自旋转变完成后, 低旋态Fp25体波波速比其高旋态略有增加。

3.2 布里基曼石

布里基曼石作为下地幔含量最丰富的矿物, 在下地幔温压条件下对布里基曼石的密度和波速的研究一直受到较大关注。除了压力、温度以及Fe和Al含量会影响布里基曼石的密度和波速外, Fe是否在布里基曼石中经历自旋转变并如何影响布里基曼石的物理性质则是近年来的争论焦点。

在下地幔温压条件下确定布里基曼石中Fe的自旋态远比铁方镁石困难。首先, Fe既可以以二价, 也可以三价存在于布里基曼石中[32, 46, 47]。其次, 虽然Fe2+仅占据8配位位置, 但Fe3+既可以在8配位位置也可以在较小的6配位位置[32, 46]。而Fe的自旋态取决于其所处的晶格位置和价态[32]。至今, 实验和理论计算均认为, 位于6配位位置的Fe3+在15~32 GPa会经历高旋态至低旋态的转变, 而位于8配位位置的Fe3+则一直以高旋态存在于下地幔布里基曼石中[10, 23, 24, 48~50]。当位于6配位位置的Fe3+经历高旋态至低旋态的转变时会引发密度的陡增以及体积模量和体波波速的急速衰减[10, 24, 49, 50]。但考虑到下地幔布里基曼石中含有约10%的Al, 而Al的出现会致使Fe3+大多处于8配位位置, 因此在下地幔温压条件下, 布里基曼石中位于6配位位置的Fe3+极少。再考虑到从高旋至低旋转变压力间隔为7~15 GPa (200~500 km深度范围), 布里基曼石中Fe3+自旋转变对密度的影响仅约为0.5%, 因此布里基曼石中Fe的自旋转变对物理性质造成的影响可能在地震学无法观测到[10, 46, 51]

学界对布里基曼石中Fe2+的自旋态充满了争议。Badro等[52]2004年利用同步辐射X光非弹散射观测到Fe2+-布里基曼石中Fe的Kβ 卫星峰在70~120 GPa发生峰强部分坍塌。与铁方镁石进行对比后Badro等[52]认为峰强坍塌是由Fe2+的自旋转变导致。进一步的高压实验利用同步辐射穆斯堡尔技术在30 GPa时观测到Fe2+电四极矩分裂陡增至4 mm/s[53~57]。结合同步辐射X光非弹散射结果, 部分学者认为这一突变是由布里基曼石中的Fe2+经历高旋态至中旋态的自旋转变所引起的[53, 54, 57, 58]。而在120 GPa左右, 布里基曼石中Fe2+电四极矩分裂完全坍塌至0, 表明Fe2+从中旋态完全转变为低旋态[59]。理论计算对穆斯堡尔谱的实验结果提出了不同看法, 认为从能量的角度来看, 中旋态的Fe2+不可能稳定存在于下地幔温压状态[23, 60, 61]。观测到的Fe2+电四极矩分裂陡增是由局部晶格扭曲突然增加所致, 布里基曼石中的Fe2+应该以高旋态稳定存在于下地幔温压状态[23, 60, 61]。但理论计算无法解释在同步辐射X光非弹散射中观测到的Kβ 卫星峰强度的部分坍塌[9, 52, 62]。Mao等[63]在2014年提出了新的分析同步辐射X光非弹散射实验结果的IRD(Integrated Relative Difference)方法, 并认为之前所观测到的Kβ 卫星峰强度异常是由于压力增加导致Kβ 卫星峰宽度增加所致[63]。观测到的Kβ 卫星峰部分坍塌与Fe的自旋变化没有关系。将已有的同步辐射X光非弹散射结果进行重新分析并结合穆斯堡尔谱结果发现, 在下地幔温压条件下布里基曼石中的Fe2+不会经历自旋转变, 而是以高旋态稳定存在至核幔边界压力[63~65]。同时, 穆斯堡尔谱结合X光衍射实验结果显示Fe2+电四极矩分裂陡增不会对布里基曼石的P-V关系、密度和体积模量产生影响, 只会引起八面体倾斜角度、键长以及剪切应力的突变[66]。考虑到布里基曼石中位于6配位位置的Fe3+含量极少, 因此影响布里基曼石密度、弹性模量和波速的因素仅限于:压力、温度、Fe和Al含量。

图4总结了Fe和Al含量变化在常温常压下对布里基曼石ρ 0K0的影响。可以看到, 布里基曼石的密度主要受Fe含量变化影响。虽然Al含量变化对布里基曼石密度影响很小, 但已有的实验存在一定争议[49, 66~71]。考虑到大部分(Fe, Al)-布里基曼石[(Fe, Al)-Bm]的实验结果来自于粉晶X光衍射并存在较大误差, 这里我们考虑Al对布里基曼石密度的影响主要参考最近高质量的单晶实验结果[66]:

ρ 0=4.11+1.07XFe-0.31XAl(10)

式中:XAl=Al/(Al+Si), XFe= Fe/(Fe+Mg)。对于不含Al的布里基曼石(Fe-Bm), 考虑到实验误差, Fe对K0的影响基本可以忽略不计(图4)。(Fe, Al)-Bm实验结果较少。根据已有的实验结果, 只能近似的认为, 当Fe摩尔含量少于13%时, Fe和Al的同时出现将增加K0值, (Fe, Al)-Bm的K0为265 GPa; 而当Fe摩尔含量大于13%, Fe和Al的同时出现反而降低布里基曼石的K0值至237 GPa。需要注意的是, 未来需要更多的实验来确定Fe和Al对布里基曼石的密度和K0的影响。

同时在高温高压下对布里基曼石P-V关系的实验研究仍然十分缺乏。已有的3项高温高压实验仅限于(Mg, Fe)SiO3系统(Fe-Bm)[72~74]。可以看到, 利用已有的实验结果无法确定Fe含量变化对γ 0, θ D0和q这3个参数的影响(表2)。利用已有高温高压实验结果计算布里基曼石沿地温曲线的密度和体波波速表明含铁量为13 mol.%的Bm13[(Mg0.87Fe0.13)SiO3]比Bm0((Mg, Fe)SiO3)密度高4%, 体波波速低6%(图5)。因此, 在Fe-Bm中, 每增加1 mol.% Fe会引起0.3%密度升高和0.4%体波波速降低。在地幔相应的温度和压力条件下确定Fe和Al联合效应对布里基曼石密度和体波波速的影响则需要更多的实验研究。

3.3 硅酸盐— 后钙钛矿

布里基曼石在核幔边界温压条件下从钙钛矿结构向后钙钛矿(Post-Perovskite, PPv)结构的相变, 是过去10年深部地球物理研究最重要的发现之一[7, 8, 75]。Murakami等[7]和Oganov等[8]在2004年均采用高压实验和理论计算相结合的方法发现MgSiO3-布里基曼石在约120 GPa和2 400 K(约2 650 km深度)发生钙钛矿结构至PPv的结构相变。MgSiO3-PPv空间群为Cmcm, 结构与CaIrO3类似呈三维层状结构, 具有很强的空间波速各向异性[8, 76]。由于PPv结构中Mg2+所处的十二面体体积较钙钛矿结构相应位置小, 因此, MgSiO3-布里基曼石相变后将带来1%~1.5%的体积坍塌并引起密度增加[77~79]。此外, 这一结构相变同时带来横波波速的增加和纵波波速小幅增加, 而体波波速则下降[12, 77, 80]。再加上这一结构相变发生的深度正好对应D″层, 这一相变被认为与核幔边界D″层相关[77, 81, 82]。因此, 对布里基曼石由钙钛矿至PPv的相变以及PPv物理性质的研究受到了广泛关注。

图3 铁方镁石沿地温曲线[45]的密度(ρ )、等温体积模量(KT)和体波波速(VΦ )
(a); (b)密度; (c), (d)等温体积模量; (e), (f)体波波速; 红色:含Fe 25 mol.%(Fp25)[22]; 蓝色:含Fe 19 mol.%(Fp19)[21]; 绿色:MgO[17, 36]
Fig.3 Modeled density (ρ ), isothermal bulk moduli(KT), and bulk sound velocity (VΦ ) of ferropericlase along the lower mantle geotherm[45]
(a), (b)Density; (c), (d)Isothermal bulk moduli; (e), (f)Bulk sound velocity; Red:Fp25[22]; Blue:Fp19[21]; Green:MgO[17, 36]

迄今为止, 大量研究集中在布里基曼石钙钛矿相至PPv相变发生的温压条件[83~92]。尽管所有研究均表明, Fe, Al含量以及矿物组成的改变对相变发生的压力即深度有较大影响, 但对影响的幅度仍存在很大争议。这主要是因为不同研究组采用不同的压标以及定压标准[7, 86, 91, 93, 94]。以MgSiO3成分为例, 采用Pt做压标和Holmes等[95]的定压标准判定, MgSiO3在130 GPa和2 500 K发生至PPv的相变[84]; 而采用Au做压标和Tsuchiya等[96]的定压标准判定, 这一相变则发生在113 GPa和2 400 K[93]— — 相变发生的压力相差超过15 GPa。Fe对布里基曼石至PPv相变条件的影响也存在争议。部分实验和理论研究表明, 相对于布里基曼石, 含Fe-PPv结构更加稳定, 因为Fe的出现会降低布里基曼石钙钛矿至PPv的相变压力[83, 91, 97~99]。如Fe含量为38 mol.%的布里基曼石相变为PPv发生在87 GPa和2 150 K[91, 97], 远低于MgSiO3-PPv的形成压力[7]。但也有实验研究指出, 虽然含Fe钙钛矿结构的布里基曼石比PPv更加稳定, 但是Fe对布里基曼石钙钛矿至PPv的相变几乎没有影响[83]

图4 常温常压下布里基曼石(Bm)密度(ρ 0)(a)和等温体积模量(K0)(b)
(a)密度; (b) 等温体积模量; 蓝色:不含Al布里基曼石[49, 66~71]; 黄色:含Al布里基曼石[49, 66~71]
Fig.4 Density (ρ 0)(a) and isothermal bulk moduli (K0)(b), of bridgmanite (Bm) at ambient conditions
(a) Density:(ρ 0); (b) Isothermal bulk moduli; Blue: Al-free Bm[49, 66~71]; Yellow:Al-bearing Bm[49, 66~71]

图5 布里基曼石(Bm)沿地温曲线[45] 的密度(ρ )、等温体积模量(KT)和体波波速(VΦ )
(a), (b)密度; (c), (d)等温体积模量; (e), (f)体波波速; 蓝色:含Fe 13 mol.%(Bm13)[74]; 黄色:不含铁[72, 73]
Fig.5 Modeled density (ρ ), isothermal bulk moduli(KT), and bulk sound velocity (VΦ ) of bridgmanite (Bm) along the mantle geotherm[45]
(a), (b)Density; (c), (d)Isothermal bulk moduli; (e), (f)Bulk sound velocity; Blue:Bm with 13 mol.% Fe(Bm13)[74]; Yellow:Fe-free Bm[72, 73]

表2 布里基曼石的热力学参数 Table 2 Thermoelastic Parameters of Bridgmanite

不同于Fe, 大部分研究对于Al是如何影响布里基曼石至PPv相转变的温压条件结果基本趋于一致[89, 90, 98]。除Tsuchiya等[88], 实验和计算结果均表明相对于钙钛矿结构的布里基曼石, 含Al-PPv结构更加稳定[89, 90, 98]。例如, 在MgSiO3中加入25 mol.% Al2O3, 布里基曼石至PPv的相转变开始于140 GP和2500 K, 相变宽度为30 GPa[89, 90]。Hirose等[100]估计, 在地幔岩模型中每增加5 mol.% Al2O3将使布里基曼石从钙钛矿结构至PPv相变的起始压力提升约3 GPa, 将相变宽度增加6 GPa。Catalli等[86]采用同样的压标和定压标准比较了(Mg0.9Fe0.1)SiO3和(Mg0.9Fe0.1)(Al0.1Si0.9)O3 2种成分至PPv的相变条件, 发现含10 mol.% Al的(Mg0.9Fe0.1)(Al0.1Si0.9)O3在2 500 K时相变为PPv的起始压力为112 GPa, 比(Mg0.9Fe0.1)SiO3高约1 GPa, 相变宽度为27 GPa, 大于(Mg0.9Fe0.1)SiO3相变宽度的23 GPa。

需要注意的是, 地幔是一个多相共存体系。Sinmyo等[101]的高压实验结果就表明, 铁方镁石的出现虽然对布里基曼石至PPv的相变压力几乎没有影响, 但会显著减小其相变宽度。不少实验用天然橄榄石为研究对象[83~85, 87]。将这些实验结果均统一至Speziale等[41]的MgO定压标准, 尽管有的研究认为在2 500 K橄榄石体系中布里基曼石相变至PPv的起始压力为113~116 GPa[83, 87], 但也有部分结果显示相变起始压力可高达134~140 GPa[84, 85]。因此, 对在橄榄石体系中布里基曼石至PPv相变的压力条件仍存在很大争议。而在大洋玄武岩体系中若均采用Speziale等[41]的MgO定压标准, 不同研究组对这一相变的压力条件结果则较为统一, 均认为在2 500 K时的相变起始压力为108~112 GPa, 宽度为5~14 GPa[85, 87]。无论是在橄榄岩、大洋玄武岩还是纯MgSiO3体系, 若把不同实验的结果用Speziale等[41]MgO定压标准进行归一化处理, 相变的克拉珀龙斜率为11~13 MPa/K[100]

PPv中的Fe也一度被认为在下地幔压力下会发生自旋转变[53, 102]。与布里基曼石类似, 高压实验和理论计算均认为只有位于6配位位置的Fe3+在核幔边界压力下会处于低旋态[103, 104]。但拥有低旋态Fe3+的PPv和同样Fe2+含量PPv的压缩系数并无明显区别[103]。高压穆斯堡尔谱实验观测到位于8配位位置Fe2+的电四极矩分裂高达4 mm/s, 其X光散射光谱中的Kβ 卫星峰在高压下也存在峰强的部分坍塌— — 这也被认为是PPv中Fe处于中旋态的实验证据[53, 102]。但理论计算同样认为中旋态Fe2+不可能稳定存在于下地幔PPv中[104]。如前所述, 布里基曼石X光散射光谱中Kβ 卫星峰的部分坍塌可能仅仅是由于压力升高导致峰宽增加所致, 与Fe的自旋转变并无关系。但这是否同样适用于PPv, 仍需要进一步实验证明。

在常温下当压力低于80~100 GPa时, PPv将变为无定形态[78, 79, 99, 105, 106]。因此, 对PPv物理性质的实验研究只能在80~100 GPa以上进行, 实验结果相对较少[78, 79, 106, 107]。由于现阶段仍缺乏对MgSiO3-PPv热力学状态方程的研究, 这里仅以300 K的实验结果为例。将高压结果外推至常温常压下可以看到, MgSiO3-PPv的ρ 0K0随Fe含量增加线性增加(图6)。当Fe含量一定时, Al含量的增加将降低PPv的ρ 0, 但增加其K0。由于现阶段仍然缺乏对MgSiO3-PPv热力学方程的实验研究, 仅能根据现有实验结果计算300 K时PPv密度和体波波速(表3, 图7)。在(Mg, Fe)SiO3-PPv体系, 每增加1 mol.%Fe将使PPv密度在高压下增加0.5%。但Fe对PPv体波波速的影响仍存在争议。当PPv的Fe含量为9 mol.%~10 mol.%时, 含Fe-PPv的体波波速比MgSiO3-PPv低2%~3%[107, 108]; 但Mao等[20]的结果却显示, 富Fe PPv40(Fe含量为40 mol.%)的体波波速远大于MgSiO3-PPv0。当Fe和Al同时出现在PPv后, (Fe, Al)-PPv密度高于MgSiO3-PPv。含Fe量在13 mol.%~15 mol.%、含Al量在15 mol.%~50 mol.%的(Fe, Al)-PPv比MgSiO3-PPv密度高1%~3%[105, 106]。同时, (Fe, Al)-PPv的密度低于MgSiO3-PPv。含Fe 13%~15%、含Al 15%~28%的(Fe, Al)-PPv体波波速与PPv10相似。但当Al富集于PPv会引起PPv体波波速的大幅降低。含Al量为50 mol.%的Al50-PPv15体波波速比PPv0约低9%[104]。由于下沉的俯冲板片可能为核幔边界带来大量的Al并富集于PPv中[19, 109, 110], 富Al-PPv的聚集可能为理解核幔边界观测到的速度异常带来新的认识。

表3 后钙钛矿的弹性参数* Table 3 Elastic parameters of Post Perovskite*
3.4 Ca-钙钛矿

尽管在地幔岩模型中, 下地幔Ca-钙钛矿的含量仅为8 vol.%, 但其在俯冲至下地幔的大洋玄武岩中含量可高达22 vol.%~29 vol.%[19, 109]。有学者认为, Ca-钙钛矿在下地幔温压条件下的稳定相为四方晶系[111], 但近年来更多的实验和理论研究表明, Ca-钙钛矿沿地温曲线为立方晶系[3, 25, 27, 112~116]。但立方晶系的Ca-钙钛矿无法稳定存在于低温条件下, 而是相变为四方晶系结构[3, 25, 27]。四方和立方晶系的Ca-钙钛矿X光衍射谱最为显著的差别在于(200)和(110)峰是否分裂。但由于高温高压实验多采用粉晶为实验样品以及受金刚石对顶砧中的压力梯度和偏应力影响, 高压X光衍射峰宽度往往较宽, 致使很难从X光衍射谱判断(200)和(110)峰是否发生分裂[3, 25, 116, 117]。因此, 对四方和立方晶系在高压下的相变温度存在较大争议。例如, Adams等[118]和Stixrude等[114]就利用第一性原理计算认为Ca-钙钛矿从四方至立方晶系的相变温度在24 GPa为1 250 K, 以及100 GPa为2 000 K。这意味着Ca-钙钛矿沿地温曲线应以立方晶系稳定存在, 而在俯冲板片的洋壳中则是四方晶系。而Kurashina等[25]的高压实验却发现, Ca-钙钛矿在52 GPa、580 K已经从四方相变为立方晶系, 相变温度远远小于理论预测。近期Noguchi等[117]和Sun等[3]的实验均表明, 无论是沿地温曲线还是在俯冲板片中, Ca-钙钛矿均应为立方晶系结构。

Ca-钙钛矿的热力学参数列于表4。除Noguchi等[117]实验得到的K0值特别低, 只有208(8) GPa, 其余实验结果得到的K0均在237~249 GPa[3, 116, 119]。理论计算得到的K0值也存在一定分歧[120, 121]。Kawai等[121]计算K0值仅为227(1) GPa, 而Zhang等[120]的结果为250(1) GPa, 与实验结果更为吻合。

值得注意的是, 在不同的地幔物质组成中Ca-钙钛矿可含有一定量的Al2O3。例如, 地幔岩中的Ca-钙钛矿在下地幔Al2O3含量为0.7 wt.%~1.6 wt.%[122, 123](wt.%为重量百分含量); 而大洋玄武岩中的Ca-钙钛矿则可含有1.2 wt.%~4.5 wt.%的Al2 O319, 124, 125。Al2O3的出现对Ca-钙钛矿在下地幔的结构有较大影响。在高压低温如俯冲洋壳环境中, 含5.9 wt.% Al2O3的Ca-钙钛矿为 GdFeO3型(Pbnm)的正交晶系结构[25]。在32~34 GPa, 16 80~1 880 K和72 GPa, 1 820~2 220 K, 正交晶系的Al2O3-Ca-钙钛矿相变为立方晶系[25]。这意味着含有Al2O3的Ca-钙钛矿在俯冲板片和沿地温曲线的稳定结构分别为正交晶系和立方晶系[25]。但现在非常缺乏对正交和立方晶系Al2O3-Ca-钙钛矿热力学性质的实验和理论研究。仅有Yusa等[125]通过研究钙铝榴石的相变规律时确定了正交晶系的Ca3Al2Si3 O12高压相K0为283(7) GPa[25], 高于Ca-钙钛矿的237~249 GPa[3, 116, 119]。未来需要更多地对含Al2O3 Ca-钙钛矿正交晶系和立方晶系结构热力学状态方程的实验和理论研究。

图6 常温常压下硅酸盐— 后钙钛矿(PPv)的密度(ρ 0)(a)和等温体积模量(K0)(b)
(a)密度; (b)等温体积模量; 蓝色:不含Al硅酸盐— 后钙钛矿[79, 106]; 黄色: 含Al的硅酸盐— 后钙钛矿[78, 105, 107]
Fig.6 Density (ρ 0)(a) and isothermal bulk moduli (K0)(b) of post-perovskite (PPv) at ambient conditions
(a)Density; (b)Isothermal bulk moduli; Blue:Al-free PPv[79, 106]; Yellow: Al-bearing PPv[78, 105, 107]

图7 硅酸盐— 后钙钛矿(PPv)随地温曲线[45]的密度(ρ )、等温体积模量(KT)和体波波速(VΦ )
(a), (b)密度; (c), (d)等温体积模量; (e), (f)体波波速; 蓝色:不同含铁量的硅酸盐后钙钛矿[79, 106, 108]; 橙色:(Fe, Al)-硅酸盐后钙钛矿[20, 78, 105, 108]; 灰色:MgSiO3-硅酸盐— 后钙钛矿[107]
Fig.7 Density(ρ ), isothermal bulk moduli(KT), and bulk sound velocity (VΦ ) of Post-Perovskite (PPv) along the mantle geotherm[45]
(a), (b)Density; (c), (d)Isothermal bulk moduli; (e), (f)Bulk sound velocity; Blue: PPv with various Fe content[79, 106, 108]; Orange: PPv with various Fe and Al content[20, 78, 105, 108]; Gray: MgSiO3-PPv[107]

表4 Ca-钙钛矿的热力学参数 Table 4 Thermoelastic Parameters of CaSiO3 Perovskite
4 展 望

过去30年高温高压实验技术的进步极大地推动了对下地幔结构和物质组成的了解。尤其是2004年后, PPv的发现和下地幔布里基曼石、铁方镁石以及PPv中Fe自旋态的变化, 为认识下地幔、理解在下地幔观测到的波速异常打开了新的窗口。同时, 由于在下地幔相应温度压力条件下进行实验的困难性并且不同研究组结果存在一定矛盾, 现阶段对下地幔矿物和相物性的认识, 尤其是密度、波速等基本物理性质的认识仍存在较大局限性和不确定性。

尤其是以下问题亟待解决和厘清:

(1) 不同实验组的结果需要归一化到一个自洽的压标系统(如Fei等[127])再进行比较。这样可以尽量减小由于不同实验组采用不同压标带来的实验结果的误差。

(2) 仍需要在高温高压下对铁方镁石热力学状态方程进行进一步研究。在下地幔相应的温度和压力下Fe含量变化对铁方镁石自旋转变起始压力以及宽度的影响仍然不清楚, 缺乏足够的实验数据;

(3) 缺乏(Fe, Al)-布里基曼石和PPv的热力学状态方程研究, 导致无法正确判断Fe和Al的联合效应对下地幔布里基曼石和PPv密度以及波速的影响, 也无法在核幔边界相应温度压力下准确认识由(Fe, Al)-布里基曼石至PPv相变引起的密度和波速变化。

更为重要的是, 除热力学状态方程, 更需要从实验上在下地幔相应温压条件下对下地幔矿物的横波和纵波波速进行直接测量。而由于实验技术的限制, 仅有Murakami等[11]在40~124 GPa、300和2 700 K测量了布里基曼石和铁方镁石的横波波速。而对铁方镁石纵波波速的测量仅在300 K达到81 GPa[42], 布里基曼石纵波波速测量最大压力约为20 GPa[128], 目前还没有关于PPv纵波波速的研究。因此, 发展高温高压下直接测量下地幔矿物纵波和横波波速的新技术是进一步认识下地幔物质组成和结构的关键。

The authors have declared that no competing interests exist.

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