Phase transition From Wikipedia, the free encyclopedia. In physics, a phase transition is the transformation of a thermodynamic system from one phase to another. The distinguishing characteristic of a phase transition is an abrupt sudden change in one or more physical properties, in particular the heat capacity, with a small change in a thermodynamic variable such as the temperature. Examples of phase transitions are: The transitions between the solid, liquid, and gaseous phases (evaporation, boiling, melting, freezing, sublimation, etc.; see also vapor pressure) The transition between the ferromagnetic and paramagnetic phases of magnetic materials at the Curie point. The emergence of superconductivity in certain metals when cooled below a critical temperature. Quantum condensation of bosonic fluids, such as Bose-Einstein condensation and the superfluid transition in liquid helium. The breaking of symmetries in the laws of physics during the early history of the universe as its temperature cooled. Phase transitions happen when the free energy of a system is non-analytic for some choice of thermodynamic variables - see phases. This non-analyticity generally stems from the interactions of an extremely large number of particles in a system, and does not appear in systems that are too small. It's sometimes possible to change the state of a system non-adiabatically in such a way that it can be brought past a phase transition without undergoing a phase transition. The resulting state is metastable i.e. not theoretically stable, but quasistable. See superheating and supercooling and supersaturation. Contents 1 Classification of phase transitions 1.1 Ehrenfest classification 1.2 Modern classification of phase transitions 2 Properties of phase transitions 2.1 Critical points 2.2 Symmetry 2.3 Critical exponents and universality classes 3 References 4 External links Classification of phase transitions Ehrenfest classification The first attempt at classifying phase transitions was the Ehrenfest classification scheme, which grouped phase transitions based on the degree of non-analyticity involved. Though useful, Ehrenfest's classification is flawed, as we will discuss in the next section. Under this scheme, phase transitions were labelled by the lowest derivative of the free energy that is discontinuous at the transition. First-order phase transitions exhibit a discontinuity in the first derivative of the free energy with a thermodynamic variable. The various solid/liquid/gas transitions are classified as first-order transitions because they involve a discontinuous change in density (which is the first derivative of the free energy with respect to chemical potential.) Second-order phase transitions have a discontinuity in a second derivative of the free energy. These include the ferromagnetic phase transition in materials such as iron, where the magnetization, which is the first derivative of the free energy with the applied magnetic field strength, increases continuously from zero as the temperature is lowered below the Curie temperature. The magnetic susceptibility, the second derivative of the free energy with the field, changes discontinuously. Under the Ehrenfest classication scheme, there could in principle be third, fourth, and higher-order phase transitions. Modern classification of phase transitions The Ehrenfest scheme is an inaccurate method of classifying phase transitions, for it is based on the mean field theory of phases (to be described in a later section.) Mean field theory is inaccurate in the vicinity of phase transitions, as it neglects the role of thermodynamic fluctuations. For instance, it predicts a finite discontinuity in the heat capacity at the ferromagnetic transition, which is implied by Ehrenfest's definition of "second-order" transitions. In real ferromagnets, the heat capacity diverges to infinity at the transition. In the modern classification scheme, phase transitions are divided into two broad categories, named similarly to the Ehrenfest classes: The first-order phase transitions are those that involve a latent heat. During such a transition, a system either absorbs or releases a fixed (and typically large) amount of energy. Because energy cannot be instantaneously transferred between the system and its environment, first-order transitions are associated with "mixed-phase regimes" in which some parts of the system have completed the transition and others have not. This phenomenon is familiar to anyone who has boiled a pot of water: the water does not instantly turn into gas, but forms a turbulent mixture of water and water vapor bubbles. Mixed-phase systems are difficult to study, because their dynamics are violent and hard to control. However, many important phase transitions fall in this category, including the solid/liquid/gas transitions. The second class of phase transitions are the continuous phase transitions, also called second-order phase transitions. These have no associated latent heat. Examples of second-order phase transitions are the ferromagnetic transition, the superfluid transition, and Bose-Einstein condensation. Several transitions are known as the infinite-order phase transitions. They are continuous but break no symmetries (see Symmetry below). The most famous example is the Berezinsky-Kosterlitz-Thouless transition in the two-dimensional XY model. Many quantum phase transitions in two-dimensional electron gases belong to this class. Properties of phase transitions Critical points In systems containing liquid and gaseous phases, there exist a special combination of pressure and temperature, known as the critical point, at which the transition between liquid and gas becomes a second-order transition. Near the critical point, the fluid is sufficiently hot and compressed that the distinction between the liquid and gaseous phases is almost non-existent. This is associated with the phenomenon of critical opalescence, a milky appearance of the liquid, due to density fluctuations at all possible wavelengths (including those of visible light). Symmetry Phase transitions often (but not always) take place between phases with different symmetry. Consider, for example, the transition between a fluid (i.e. liquid or gas) and a crystalline solid. A fluid, which is composed of atoms arranged in a disordered but homogenous manner, possesses continuous translational symmetry: each point inside the fluid has the same properties as any other point. A crystalline solid, on the other hand, is made up of atoms arranged in a regular lattice. Each point in the solid is not similar to other points, unless those points are displaced by an amount equal to some lattice spacing. Generally, we may speak of one phase in a phase transition as being more symmetrical than the other. The transition from the more symmetrical phase to the less symmetrical one is a symmetry-breaking process. In the fluid-solid transition, for example, we say that continuous translation symmetry is broken. The ferromagnetic transition is another example of a symmetry-breaking transition, in this case the symmetry under reversal of the direction of electric currents and magnetic field lines. This symmetry is referred to as "up-down symmetry" or "time-reversal symmetry". It is broken in the ferromagnetic phase due to the formation of magnetic domains containing aligned magnetic moments. Inside each domain, there is a magnetic field pointing in a fixed direction chosen spontaneously during the phase transition. The name "time-reversal symmetry" comes from the fact that electric currents reverse direction when the time coordinate is reversed. The presence of symmetry-breaking (or nonbreaking) is important to the behavior of phase transitions. It was pointed out by Landau that, given any state of a system, one may unequivocally say whether or not it possesses a given symmetry. Therefore, it cannot be possible to analytically deform a state in one phase into a phase possessing a different symmetry. This means, for example, that it is impossible for the solid-liquid phase boundary to end in a critical point like the liquid-gas boundary. However, symmetry-breaking transitions can still be either first or second order. Typically, the more symmetrical phase is on the high-temperature side of a phase transition, and the less symmetrical phase on the low-temperature side. This is certainly the case for the solid-fluid and ferromagnetic transitions. This happens because the Hamiltonian of a system usually exhibits all the possible symmetries of the system, whereas the low-energy states lack some of these symmetries (this phenomenon is known as spontaneous symmetry breaking.) At low temperatures, the system tends to be confined to the low-energy states. At higher temperatures, thermal fluctuations allow the system to access states in a broader range of energy, and thus more of the symmetries of the Hamiltonian. When symmetry is broken, one needs to introduce one or more extra variables to describe the state of the system. For example, in the ferromagnetic phase one must provide the net magnetization, whose direction was spontaneously chosen when the system cooled below the Curie point. Such variables are examples of order parameters, which will be described later. However, note that order parameters can also be defined for symmetry-nonbreaking transitions. There exist also dual descriptions of phase transitions in terms of disorder parameters. These indicate the presence of line-like excitations such as vortex- or defect lines. Symmetry-breaking phase transitions play an important role in cosmology. It has been speculated that, in the hot early universe, the vacuum (i.e. the various quantum fields that fill space) possessed a large number of symmetries. As the universe expanded and cooled, the vacuum underwent a series of symmetry-breaking phase transitions. For example, the electroweak transition broke the SU(2)×U(1) symmetry of the electroweak field into the U(1) symmetry of the present-day electromagnetic field. This transition is important to understanding the asymmetry between the amount of matter and antimatter in the present-day universe (see electroweak baryogenesis.) See order-disorder Critical exponents and universality classes Continuous phase transitions are easier to study than first-order transitions due to the absence of latent heat, and they have been discovered to have many interesting properties. The phenomena associated with continuous phase transitions are called critical phenomena, due to their association with critical points. It turns out that continuous phase transitions can be characterized by parameters known as critical exponents. For instance, let us examine the behavior of the heat capacity near such a transition. We vary the temperature T of the system while keeping all the other thermodynamic variables fixed, and find that the transition occurs at some critical temperature Tc. When T is near Tc, the heat capacity C typically has a power law behaviour: The constant α is the critical exponent associated with the heat capacity. It is not difficult to see that it must be less than 1 in order for the transition to have no latent heat. Its actual value depends on the type of phase transition we are considering. For -1 α 0, the heat capacity has a "kink" at the transition temperature. This is the behavior of liquid helium at the "lambda transition" from a normal state to the superfluid state, for which experiments have found α = -0.013±0.003. Experiment was performed in satellite to minimize pressure differences in sample (see here). Result agrees with theoretical prediction based on variational perturbation theory (see here). For 0 α 1, the heat capacity diverges at the transition temperature (though, since α 1, the divergence is not strong enough to produce a latent heat.) An example of such behavior is the 3-dimensional ferromagnetic phase transition. In the three-dimensional Ising model for uniaxial magnets, detailed theoretical studies have yielded the exponent α ～ 0.110. Some model systems do not obey this power law behavior. For example, mean field theory predicts a finite discontinuity of the heat capacity at the transition temperature, and the two-dimensional Ising model has a logarithmic divergence. However, these systems are an exception to the rule. Real phase transitions exhibit power law behavior. Several other critical exponents - β, γ, δ, ν, and η - are defined, examining the power law behavior of a measurable physical quantity near the phase transition. Exponents are related by scaling relations such as β = γ / (δ ? 1), ν = γ / (2 ? η). It is a remarkable fact that phase transitions arising in different systems often possess the same set of critical exponents. This phenomenon is known as universality. For example, the critical exponents at the liquid-gas critical point have been found to be independent of the chemical composition of the fluid. More amazingly, they are an exact match for the critical exponents of the ferromagnetic phase transition in uniaxial magnets. Such systems are said to be in the same universality class. Universality is a prediction of the renormalization group theory of phase transitions, which states that the thermodynamic properties of a system near a phase transition depend only on a small number of features, such as dimensionality and symmetry, and is insensitive to the underlying microscopic properties of the system. References Anderson, P.W., Basic Notions of Condensed Matter Physics, Perseus Publishing (1997). Goldenfeld, N., Lectures on Phase Transitions and the Renormalization Group, Perseus Publishing (1992). Landau, L.D. and Lifshitz, E.M., Statistical Physics Part 1, vol. 5 of Course of Theoretical Physics, Pergamon, 3rd Ed. (1994). Kleinert, H., Critical Properties of φ4-Theories, World Scientific (Singapore, 2001); Paperback ISBN 98102465876 (readable online here). Kleinert, H., Gauge Fields in Condensed Matter, Vol. I, "SUPERFLOW AND VORTEX LINES; Disorder Fields, Phase Transitions,", pp. 1--742, World Scientific (Singapur, 1989); Paperback ISBN 9971-50-210-0 (readable online here
洋壳和陆壳的深俯冲命运：来自地幔相变研究的观点(2) The Fate of Subducted Slabs：Perspectives from Studies of Phase Transitions in the Earth’s Mantle （续）接 《洋壳和陆壳的深俯冲命运：来自地幔相变研究的观点(1)》 http://bbs.sciencenet.cn/home.php?mod=spaceuid=92454do=blogid=422988 , 现为第3章和第4章。 3.大陆地壳(岩石圈)的深俯冲 大陆岩石圈（地壳）与大洋岩石圈具有较大的区别，其在年龄、物质、结构等方面均存在较大差异，地球化学组成上更加复杂。 目前对于大陆地壳的深俯冲研究资料比较有限，主要是针对代表性的大陆地壳物质成分进行高温高压实验，从矿物和岩石物性方面进行解释和分析。Irifune et al.(1994)]和Wu et al.(2009)分别对平均大陆上地壳成分（氧化物合成）和天然大陆上地壳岩石（副片麻岩）进行了高温高压相变实验。两者在物质成分上略有差异（参考Wu et al.,2009原文中的成分对比Table），区别是前者所使用的物质成分为化学合成样品，后者使用的是中国东部大别山双河地区的副片麻岩天然样品。 图14. Mineral proportion changes in the continental crust composition as a function of pressure. Point = the results of a mass-balance calculation using chemical composition data obtained in the present experiments; Cpx = clinopyroxene; Coe = coesite; Or = orthoclase; Ga = garnet; Ky = kyanite; Wd = K2Si4O9 wadeite; Hol = KAlSi3O8, hollandite; St = stishovite; CAS = unidentified Ca and Al-rich silicate; CaPv = CaSiO3 perovskite; CF = calcium ferrite-type phase. (Irifune et al.,1994) 图15. Mineral proportions of the subducted upper continental crust as a function of pressure. Ca–Pv, Ca pervoskite; Cs, coesite; Ep, epidote; C, graphite heater; Cpx, jadeite. Grt, garnet; Holl, KAlSi3O8-hollandite; Jd, jadeite; K-mica, K rich mica with unknown structure; Law, lawsonite; M, melt. Or, orthoclase; Phe, phengite; St, stishovite. (Wu et al.,2009) 随压力(深度)增加，所观测到的物相见图14和15，详细的相关系请参考原文叙述，在此不再赘述。Wu et al(2009)实验结果与 Irifune et al(1994)在氧化物体系的实验有如下两方面差异：（1）Wu et al(2009)的实验中未出现 CAS 相；（2）Wu et al(2009)研究中硬玉(Cpx)含量高于 Irifune et al(1994)的实验，且未观察到硬玉在约 24 GPa 分解为 NAL（NaAlSiO4）+斯石英。 图16. Zero-pressure density changes in the continental crust (CC) and pelagic sediment compositions (SIL = siliceous facies; ARG = argillaceous facies) as a function of pressure. Density changes in a pyrolite composition are also shown for comparison. (Irifune et al.,1994) 图17. Comparison of the calculated densities of the subducted continental crust and MORB (Aoki and Takahashi, 2004; Hirose et al., 1999) with respect to the density profile derived from PREM model (Dziewonski and Anderson, 1981). Density calculations were carried out along the three geotherms which are typical for cold and hot subduction and normal mantle. The thirdorder high-temperature Birch–Murnaghan equation of state was used in the density calculations.(from Wu et al.,2009) 结果发现，陆壳物质在8-9GPa以下其密度远远低于pyrolite的密度，但随后在斯石英和K-锰钡矿等高压矿物的形成以及连续的脱水作用下，陆壳物质的密度将超过pyrolite甚至MORB，在660km不连续面时pyrolite和俯冲陆壳物质的密度相近（图 16，17）；但随着压力继续增加进入下地幔时，林伍德石相变分解形成更高密度的钙钛矿和镁方铁矿，下地幔顶部岩石密度将再次远远大于深俯冲陆壳物质的密度。由此可见，大陆上地壳在深俯冲作用过程中或许至少可以俯冲到400km以下的地幔转换带中，这对于我们认识大陆俯冲动力学具有重要的意义。至于大陆上地壳岩石在更高压力的下地幔条件下行为如何，目前尚缺乏直接的高温高压实验数据。Irifune et al.(1994)推测，大陆上地壳物质的密度将会一直低于下地幔岩石的密度，致使俯冲陆壳板片被阻挡在地幔转换带底部处。 以上是对两个代表性的高温高压实验研究对大陆地壳深俯冲命运探索的介绍，下面继续介绍Komabayashi等（2009）对大陆代表性岩石的密度计算结果及其对大陆物质深俯冲命运的启示。 图18. Zero-pressure density profile to 27 GPa for TTG (this study), anorthosite (this study), MORB (Irifune and Ringwood, 1987; Hirose et al., 1999), pyrolite (Irifune and Ringwood, 1987), and harzburgite (Irifune and Ringwood, 1987). (from Komabayashi et al.,2009) Komabayashi等（2009）根据相关数据资料对大陆TTG岩石和斜长岩与MORB、pyrolite及方辉橄榄岩的密度对比计算表明（图18），TTG岩石在9-10 GPa左右斯石英矿物组合形成以后直至下地幔，其密度始终都是大于pyrolite；而斜长岩在9-10 GPa左右斯石英矿物组合形成以后直至转换带底部（24 GPa左右），其密度一直都大于pyrolite，但在转换带底部由于pyrolite中后尖晶石相变生成了更高密度的钙钛矿和镁方铁矿矿物组合，密度关系倒转；在25GPa左右斜长岩中的石榴石相变其密度再次短暂超过pyrolite，而在此深度以下，斜长岩的密度一直都略小于pyrolite。可见，大陆TTG岩石在深俯冲过程中是可以穿越660 km不连续面而进入下地幔甚至核幔边界；而对于斜长岩，预计中的大面积斜长岩目前在地表并未找到，可以认为大量的斜长岩在地质历史时期都发生深俯冲而进入了地幔中，由于俯冲物质具有相对较低的温度，这一温度效应可能使斜长岩在深俯冲过程中具有比周围地幔更高的密度，从而也可以穿越660 km不连续面而进入下地幔。 4. 小结 与大陆和大洋岩石圈深俯冲相关的岩石零压密度随深度的变化关系总结在图19中，在660km不连续面以上由于大陆地壳岩石和MORB中可以形成高密度的斯石英或者石榴石（榴辉岩），其密度将大于pyrolite，单从密度考虑有理由相信大陆岩石和玄武质岩洋壳可以发生深俯冲直到转换带底部。即使pyrolite中后尖晶石相变产生了更高密度的钙钛矿和镁方铁矿组合，但是俯冲带内由于具有相对较低的温度而使岩石密度可能更高，另外在下地幔顶部（700-800km）石榴石也逐渐完全转变成高密度的钙钛矿而产生拖拽力，从而使深俯冲的板块可以俯冲至下地幔。 虽然密度是非常重要的因素，然而影响板块俯冲的因素还需要考虑上下地幔的粘性以及相关的热力学因素，另外地球演化和地质历史时期中地幔内部的状态特征与目前的地幔亦有差异，这些因素对于研究古板块和现在的板块的深俯冲作用都具有重要影响作用。 图19. 几种代表性岩石零压密度随压力/深度变化的比较（周春银等，2010）.资料来源：Pyrolite（Irifune and Ringwood,1987）, MORB（Irifune and Ringwood,1987; Hirose et al.,1999）, 斜长岩（Komobayashi et al.,2009）, 副片麻岩（Wu et al.,2009）, TTG（Komobayashi et al.,2009）, 方辉橄榄岩（Irifune and Ringwood,1987）. 其中，副片麻岩在24GPa 以上压力条件下的密度变化目前尚缺乏相关的数据. 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Jamieson J.C., Fritz J.N., Manghnani M.H., Pressure measurement at high temperature in X-ray diffraction studies: gold as a primary standard, in: S. Akimoto, M.H. Manghnani (Eds.), High-Pressure Research in Geophysics, CAPJ, Tokyo, 1982, pp. 27– 48. Komabayashi, T., Maruyama, S. and Rino, S., 2009. A speculation on the structure of the D'' layer: The growth of anti-crust at the core-mantle boundary through the subduction history of the Earth. Gondwana Research, 15(3-4): 342-353. Ono, S., Ito, E. and Katsura, T., 2001. Mineralogy of subducted basaltic crust (MORB) from 25 to 37 GPa, and chemical heterogeneity of the lower mantle. Earth and Planetary Science Letters, 190(1-2): 57-63. Ono, S., Ohishi, Y., Isshiki, M. and Watanuki, T., 2005. In situ X-ray observations of phase assemblages in peridotite and basalt compositions at lower mantle conditions: Implications for density of subducted oceanic plate. J. Geophys. Res., 110: B02208,doi:10.1029/2004JB003196. Ringwood, A.E. and Irifune, T., 1988. Nature of the 650-km seismic discontinuity: implications for mantle dynamics and differentiation. Nature, 331(6152): 131-136. Tsuchiya T, First-principles prediction of the P–V–T equation of state of gold and the 660-km discontinuity in Earth’s mantle, J. Geophys. Res. 108 (2003) , doi:10.1029/2003JB002446. Wu, Y., Fei, Y., Jin, Z. and Liu, X., 2009. The fate of subducted Upper Continental Crust: An experimental study. Earth and Planetary Science Letters, 282(1-4): 275-284.
洋壳和陆壳的深俯冲命运：来自地幔相变研究的观点(1) The Fate of Subducted Slabs：Perspectives from Studies of Phase Transitions in the Earth’s Mantle 说明：由于本文插图众多，篇幅较长，不得不将原文章拆分为两部分，总共4章，第1章为前言和背景介绍，第2章讨论洋壳物质的深俯冲命运，第3章讨论陆壳物质的深俯冲命运，第4章小结。 1.前言 关于岩石圈（包括大陆岩石圈/地壳和大洋岩石圈/地壳）的深俯冲命运，是板块构造和地球动力学研究的永恒的话题。岩石圈的深俯冲命运，不可能单一地由某一地学学科（地球化学、地球物理、实验岩石学等）得到完整解释，必须结合多方面的研究成果来认识。本人学识有限，不可能面面俱到，在这里仅从地幔相变研究出发，来稍微做一点介绍。 由于本文讨论是以地幔相变为基础的，因此需要对基本的地幔矿物学知识有所了解才便于理解，大家可以参考本博《 地球内部的基本基本结构和物质组成 》 http://bbs.sciencenet.cn/home.php?mod=spaceuid=92454do=blogid=408337 及文后参考文献，以及费英伟（2002）的文章（见参考文献）；另外最重要的三类岩石的相变，即pyrolite（地幔岩）、方辉橄榄岩和玄武岩（MORB）体系的相变，本博上一篇文章《 地幔相变 Phase transitions in the Earth’s Mantle 》 http://bbs.sciencenet.cn/home.php?mod=spaceuid=92454do=blogid=419398 已经对此进行了介绍。需要强调地是，本文讨论是以《地幔转换带：地球深部研究的重要方向》一文中的3.5.2节“洋壳和陆壳的深俯冲命运”为主体而展开的，同时加入了更多的原始参考文献数据和图解，内容更加详实丰富。 本文将首先分别讨论洋壳和陆壳物质的深俯冲命运，然后结合Komabayashi等（2009）的文章对其他的代表性岩石的密度-深度剖面进行简单介绍。另外，由于实验条件有限，相关的岩石在下地幔条件下的高温高压相变实验报道很少，本文也将以作者所了解的文献为基础稍作说明。 2.大洋岩石圈的深俯冲 要认识大洋岩石圈的深俯冲命运，首先要对大洋岩石圈的基本结构有所了解。如图1所示，根据Ringwood的模型（e.g. Ringwood and Irifune,1988），大洋岩石圈顶部是一层几公里的相对较薄的玄武岩层（MORB），玄武岩层下面为20多公里厚的方辉橄榄岩层，更下部的为二辉橄榄岩以及“亏损”地幔岩成分物质。在大洋岩石圈深俯冲过程中，二辉橄榄岩以及“亏损”地幔岩层由于物质组成和性质与周围地幔相近，而将会被吸收进入周围地幔环境中，因此，玄武质洋壳（MORB）和方辉橄榄岩的性质变化决定着大洋板块深俯冲的最终命运。 图1. 大洋岩石圈结构图（from Ringwood and Irifune,1988） 2.1玄武质洋壳（MORB）深俯冲命运 The fate of subducted basaltic crust 图2. Phase relations in MORB composition up to 27GPa. Solid lines represent solidus and liquidus temperatures.（Hirose et al.,1999） 图3. Mineral proportions (wt%) in MORB as a function of depth （Perrillat et al.,2006）. The solid circles represent the phase proportions estimated in this study from Rietveld refinement of the in situ XRD spectra at 2050 K. Previous estimates by Ono et al. (2001), Hirose et al. (1999) and Irifune and Ringwood (1993) are reported as squares, triangles and open circles, respectively. Mineral abundances at shallower depth region are taken from Irifune et al.(1986). 图4. Experimental conditions and schematic phase relation of NMORB （Ono et al.,2005）. Phase assemblages are solid circles, Mg perovskite + Ca perovskite + stishovite + CaFe2O4- type aluminous phase; solid triangle, Mg perovskite + Ca perovskite + CaCl2-type silica + CaFe2O4-type aluminous phase; solid square, CaIrO3-type (Mg,Fe)SiO3 + Ca perovskite + a-PbO2-type silica + CaTi2O4-type aluminous phase. Solid diamonds present results from previous multianvil experiments . Abbreviations in the diagram of phase relation are GA, majoritic garnet; CF, CaFe2O4-type aluminous phase; MP, Mg perovskite; CP, Ca perovskite; ST, stishovite; CC, CaCl2-type silica; CT, CaTi2O4-type aluminous phase; CI, CaIrO3-type (Mg,Fe)SiO3; AP, a-PbO2-type silica. 玄武质洋壳（MORB）体系在地幔中的相变可以参考图2（上地幔），3（下地幔上部）和4（下地幔）。 随着俯冲深度的增加，其中的辉石会逐渐转变为石榴石，玄武岩相变为榴辉岩，而榴辉岩的密度超过了地幔橄榄岩（pyrolite）的密度，驱动着洋壳进一步俯冲到更深的地幔转换带底部（图5；Irifune and Ringwood,1993; Ringwood and Irifune,1988）。但是在转换带底部660处，地幔中的矿物林伍德石相变分解形成更高压高密度的矿物集合体（钙钛矿和镁方铁矿），而MORB由于Al含量比pyrolite更高，致使其中石榴石（majorite）的能够保持稳定至800km深度，石榴石密度比钙钛矿密度低~10%，那么俯冲洋壳的密度将小于周围地幔的密度，成为洋壳穿越转换带底部不连续面的阻碍（图5，6，7）。但是当MORB中的石榴石在27GPa左右完全相变为钙钛矿后，下地幔中MORB的密度将再次大于周围地幔密度（图6，7）。如果俯冲洋壳在转换带底部/上地幔顶部堆积能够突破浮力阻碍而进入下地幔，将可能继续俯冲至核幔边界（图8）。 图5. Density differences between MORB and pyrolite compositions and between harzburgite and pyrolite compositions as a function of depth. (Irifune and Ringwood,1993) 图6. Comparison of zero-pressure density changes in MORB (solid line) and pyrolite (dashed line) (Hirose et al.,1999). Solid circles represent the calculated densities at 24, 26 and 27GPa from X-ray diffraction and microprobe data. The density profle of pyrolite is from a previous study(Irifune and Ringwood,1987). Pyrolite becomes denser than MORB at 660km depth because of the transformation to perovskitite lithology, but once MORB transforms to perovskitite at 720km depth, it is no longer buoyant in the deep mantle. 图7. Comparison of calculated densities in MORB, with average mantle densities based on seismic observations (Ono et al.,2001). It was assumed that the proportions of major phases remained constant for different temperatures. Solid lines represent the isothermal density profiles. The average mantle densities are from Dziewonski and Anderson (1981): PREM and Kennett et al.(1995): AK. 图8. Net density profile of MORB composition.(Hirose et al.,2005) Pressure was calculated based on EOS of gold proposed by (a) Tsuchiya (2003) and by (b) Jamieson et al. (1982). Circles, MgPv+St+CaPv+CF; triangles, MgPv+CaCl2-type SiO2+CaPv+CF; squares, MgPP+a-PbO2-type SiO2+CaPv+CF. Closed and open symbols indicate 300 K and high temperature (1750–2290 K) data, respectively. Broken lines indicate the PREM density. The error of density is typically 0.02 g/cm3, derived from the uncertainties in volumes of coexisting phases and in mineral proportion. (a) Solid line shows a density profile at 300 K for perovskite-dominant assembly fitted to the Birch–Murnaghan equation of state. (b) Data by Ono et al. (2005) using Jamieson’s gold scale were shown for comparison (pluses). Slightly lower density reported by Ono et al. (2005) is primarily due to the lower density of CaFe2O4-type Al-phase with a different chemical composition. 2.2 大洋岩石圈方辉橄榄岩层的深俯冲命运 The fate of subducted harzburgite layer 方辉橄榄岩是俯冲大洋岩石圈中的另一种重要的岩石，它在俯冲过程中与MORB的相变行为不同。方辉橄榄岩的相变见图9. 图9. Mineral proportion changes in a harzburgite compositions as a function of pressure. (Irifune and Ringwood,1987)Opx = orthoenstatite; Cpx = clinoenstatite; St =stishovite; llm = ilrnenite. 根据前人的研究结果(Irifune and Ringwood,1987; Ringwood and Irifune,1988)，在660以上，方辉橄榄岩密度始终都小于pyrolite（图 10），这是由于方辉橄榄岩比pyrolite中Fe和Al含量均相对较低，而Al是高密度的石榴石的主要成分之一。在下地幔顶部（24-26GPa），同样由于pyrolite中Al使石榴石稳定至更深部，方辉橄榄岩的密度才略大于周围地幔以及MORB的密度。但是随着pyrolite和MORB中石榴石在27GPa左右完全转变成钙钛矿，此后一直到核幔边界，方辉橄榄岩的密度将始终略微小于相同深度的下地幔岩石（图11）。但是这并不能简单地就此而认为方辉橄榄岩完全无俯冲至下地幔的可能，且看下面的分析。 图10. Density profiles in the harzburgite, MORB and pyrolite compositions along the geotherm as a function of depth. (Irifune and Ringwood,1987) 图11. Bulks density variations of pyrolite, hartzburgite, and MORB calculated, based on the PVT-EoS of constituent mineral phases and their proportions (refer to the paper for details). Broken lines at pressures lower than 30 GPa are results in Irifune (1993).(from Irifune and Tsuchiya,2007) 根据Ringwood的大洋岩石圈模型，Irifune和Ringwood（1987，1988）将玄武岩（MORB）和方辉橄榄岩以1：4的比例（图1，玄武岩和方辉橄榄岩层厚度比大约为1：4）混合来代表深俯冲洋壳的组分，研究俯冲洋壳与周围地幔的密度关系，结果发现在650km以上俯冲洋壳始终比pyrolite密度大，但在下地幔顶部密度关系又倒转过来，而在下地幔700km左右洋壳的密度将再次大于pyrolite，在此深度以下，二者的密度非常接近（图12）。以上结果表明，影响洋壳深俯冲最终命运的关键问题在于能否突破地幔转换带底部的浮力障碍。 图12. Density differences between subducted slab and surrounding mantle. (Ringwood and Irifune,1988) The slab is assumed to consist of 20% basalt and 80% harzburgite and to be cooler than surrounding mantle by 800°C at 400 km and by 400°C at 650 km, attaining thermal equilibrium with surrounding mantle at ~900 km. The surrounding mantle follows the geotherm of Brown and Shankland (1981) and consists of pyrolite above 600 and below 700 km. Between these depths the mantle consists of a pre-existing layer of basalt and harzburgite (图13). Ringwood和Irifune则提出在转换带底部，俯冲的洋壳物质（玄武岩和方辉橄榄岩）可能在660附近堆积而形成一个“巨石”（megalith）(图13；Ringwood and Irifune,1988)，这些堆积或残留在转换带底部的洋壳物质及“巨石”可以在横向和纵向上伸展，很可能与所观测到的地震波异常有关；温度相对较低的“巨石”由于高密度而将沉入下地幔中。但是俯冲的洋壳与周围地幔的密度关系非常复杂，相边界的压力-温度斜率此时具有重要意义：转换带底部的主要矿物相是林伍德石和石榴石（majorite），后尖晶石相变和石榴石-钙钛矿相变分别具有负的和正的P-T斜率(Clapeyron Slope)，而俯冲带内（或者“巨石”）温度相对周围地幔要低300-400℃，那么意味着在下地幔顶部pyrolite中林伍德石转变成高密度的钙钛矿和镁方铁矿矿物组合后，俯冲带内相对低密度的林伍德石(橄榄石组分)仍可能保持稳定而未发生分解，而石榴石成分则可能已经转变成更高密度的钙钛矿了，由此俯冲带内林伍德石和石榴石组分此时将分别产生正的和负的浮力，二者综合作用的效果尚需进一步的研究。 图13. Model showing subduction of a cool, thick plate of differentiated oceanic lithosphere. Previous subduction episodes involving thin, thermally equilibrated plates have produced a layer of former harzburgite and basalt ('ancient oceanic lithosphere') between 600 and 700 km. The tip of a cool, thick plate experiences buoyant resistance when it penetrates this layer and encounters the discontinuity at 650 km (the 670-km discontinuity in the above figure should read 650-km discontinuity). At that depth the fonner oceanic crust and harzburgite layers may plastically thicken and buckle to form a large melange (megalith) situated mainly below the seismic discontinuity. The megalith is a transient feature and ultimately becomes entrained in the convective regime of the lower mantle. The lower layer of ductile depleted pyrolite initially at the base of the descending plate of sub-oceanic lithosphere becomes resorbed into the upper mantle by convective circulation owing to its inability to penetrate the harzburgite-basalt layer at 600-700 km because of the buoyancy relationships. (from Ringwood and Irifune,1988) (未完，下文见《洋壳和陆壳的深俯冲命运 ：来自地幔相变研究的观点(2)》 http://bbs.sciencenet.cn/home.php?mod=spaceuid=92454do=blogid=423022 ) 参考文献： 费英伟, 2002. 地幔中的相变和地幔矿物学. In: 张有学 and 尹安 (Editors), 地球的结构、演化和动力学. 高等教育出版社, 北京, pp. 49-90. 周春银,金振民,章军锋,2010,地幔转换带:地球深部研究的重要方向,地学前缘, 17(3),90-113. Aoki, I. and Takahashi, E., 2004. Density of MORB eclogite in the upper mantle. Physics of the Earth and Planetary Interiors, 143-144: 129-143. Dziewonski, A.M. and Anderson, D.L., 1981. Preliminary reference Earth model. Physics of the Earth and Planetary Interiors, 25(4): 297-356. Kennett, B.L.N., Engdahl, E.R. and Buland, R., 1995. Constraints on seismic velocities in the Earth from traveltimes. Geophysical Journal International, 122(1): 108-124. Hirose, K., Fei, Y., Ma, Y. and Mao, H.-K., 1999. The fate of subducted basaltic crust in the Earth's lower mantle. Nature, 397(6714): 53-56. Irifune, T., Sekine, T., Ringwood, A.E. and Hibberson, W.O., 1986. The eclogite-garnetite transformation at high pressure and some geophysical implications. Earth and Planetary Science Letters, 77(2): 245-256. Irifune, T. and Ringwood, A.E., 1987. Phase transformations in a harzburgite composition to 26 GPa: implications for dynamical behaviour of the subducting slab. Earth and Planetary Science Letters, 86(2-4): 365-376. Irifune, T., 1993. Phase transformations in the earth's mantle and subducting slabs: Implications for their compositions, seismic velocity and density structures and dynamics. The Island Arc, 2(2): 55-71. Irifune, T. and Ringwood, A.E., 1993. Phase transformations in subducted oceanic crust and buoyancy relationships at depths of 600-800 km in the mantle. Earth and Planetary Science Letters, 117(1-2): 101-110. Irifune, T., Ringwood, A.E. and Hibberson, W.O., 1994. Subduction of continental crust and terrigenous and pelagic sediments: an experimental study. Earth and Planetary Science Letters, 126(4): 351-368. Irifune T, Tsuchiya T, 2007. Mineralogy of the Earth – Phase Transitions and Mineralogy of the Lower Mantle, Treatise on Geophysics,vol2,Mineral Physics,33-62. Jamieson J.C., Fritz J.N., Manghnani M.H., Pressure measurement at high temperature in X-ray diffraction studies: gold as a primary standard, in: S. Akimoto, M.H. Manghnani (Eds.), High-Pressure Research in Geophysics, CAPJ, Tokyo, 1982, pp. 27– 48. Komabayashi, T., Maruyama, S. and Rino, S., 2009. A speculation on the structure of the D'' layer: The growth of anti-crust at the core-mantle boundary through the subduction history of the Earth. Gondwana Research, 15(3-4): 342-353. Ono, S., Ito, E. and Katsura, T., 2001. Mineralogy of subducted basaltic crust (MORB) from 25 to 37 GPa, and chemical heterogeneity of the lower mantle. Earth and Planetary Science Letters, 190(1-2): 57-63. Ono, S., Ohishi, Y., Isshiki, M. and Watanuki, T., 2005. In situ X-ray observations of phase assemblages in peridotite and basalt compositions at lower mantle conditions: Implications for density of subducted oceanic plate. J. Geophys. Res., 110: B02208,doi:10.1029/2004JB003196. Ringwood, A.E. and Irifune, T., 1988. Nature of the 650-km seismic discontinuity: implications for mantle dynamics and differentiation. Nature, 331(6152): 131-136. Tsuchiya T, First-principles prediction of the P–V–T equation of state of gold and the 660-km discontinuity in Earth’s mantle, J. Geophys. Res. 108 (2003) , doi:10.1029/2003JB002446. Wu, Y., Fei, Y., Jin, Z. and Liu, X., 2009. The fate of subducted Upper Continental Crust: An experimental study. Earth and Planetary Science Letters, 282(1-4): 275-284.
ZrO 2 从高温液相冷却到室温的过程中将发生如下相变：液相（ L ）立方相（ c ）正方相（ t ）单斜相（ m ）。其中 t m （属于马氏体相变）转变时将产生约 5% 的体积膨胀。将 ZrO 2 t m 相变 Ms 点稳定到比室温稍低，而 Md 点比室温高，使其在承载时由应力诱发产生 t m 相变，由于相变产生的体积效应和形状效应而吸收大量的能量，从而表现出异常高的韧性，这就是二氧化锆 ZrO 2 相变增韧。
标签: 相变
