地核温压条件下铁的深度学习分子动力学模拟

铁(Fe)是地核中的主要元素，研究铁在地核温压条件下的状态方程及热力学性质对理解地核至关重要。为高效地构建出准确和稳健的势能面模型，本文使用第一性原理数据为初始数据，利用深度势能生成器对地核内温压下构型进行采样，通过深度神经网络训练出深度学习势，完成对大体系超胞的深度学习分子动力学高精度模拟。所构建的地核温压下铁的深度势能，与第一性原理计算结果相吻合。利用该势能，可实现内核温压下超过10000原子体系的高精度分子动力学模拟，计算出密堆六方(hcp)和体心立方(bcc)结构铁的密度和状态方程。本文利用深度势能方法提高了计算效率、保证了计算精度同时可利用于大规模体系、多晶体系，为更接近地球内部条件物质状态、性质的模拟打下基础。     

超临界态甲烷密度研究

超临界甲烷密度不仅是非常规天然气资源量计算与吸附能力测定的重要参数,同时也是衡量超临界甲烷扩散效率与溶解有机物能力的主要指标。通过对比分析各种气体状态方程的适用性,认为基于亥姆霍兹能量基本状态方程可以准确计算0~30 MPa、270~360 K条件下甲烷的密度。利用Microsoft Office Excel编写了甲烷密度的计算程序,与NIST （美国国家标准与技术研究院）商业软件计算结果相比,误差小于0.05%。分析了0~100 MPa、270~360 K范围内甲烷密度的变化规律。结果表明,甲烷密度随压力增大而增大,在低于30 MPa时增速较大且对温度的敏感性较强,高于30 MPa时增速逐渐变缓,且敏感性减弱。在煤层原位条件下随着埋深的增大,甲烷密度随温度升高而减小,随压力增大而增大;在温度与压力共同作用下,甲烷密度呈先增速不变、近似线性增加,后增速逐渐减小、凸曲线形增加的变化规律。游离态甲烷密度受温度的影响比吸附态甲烷小,是深部煤层气资源增量的主要贡献者。研究结果为深部煤层气赋存及其潜力预测提供了基础参数。      

通过第一性原理预测内地核的成分与结构

内地核成分与结构的确定一直是地球深部研究的重要课题。目前地核的公认成分是铁和少量的镍。但由于地核密度低于纯粹的铁镍合金(固态内核2%～3%,液态外核6%～7%),其中必定掺杂有一定量的轻元素,其种类与浓度有待确定。除成分外,地核条件下铁的晶体结构也存在争议。根据地震学观测,声波沿地轴方向的传播速度比赤道平面方向快大约3%～4%。这意味着内地核是各向异性的;但在极端高压下,晶体结构中的原子应该按致密的密排六方结构(h.c.p)排列,而h.c.p结构对声波传输是高度各向同性的,这就需要确定地核条件下铁的晶体结构。根据第一性原理计算得到的高压下体系能量以及爱因斯坦谐振子模型,本项研究估算了给定结构的自由能以及掺杂轻元素后的影响。根据计算结果可以定性的分析得出,在高压OK下致密的h.c.p结构显然比疏松的体心立方(b.c.c)更稳定;而随着温度的升高,原子核的振动造成b.c.c结构的自由能比h.c.p结构下降得更快,因此在高温下b.c.c结构更稳定;掺杂轻元素后,这种优势变得更加明显,而3.6at.%的Si则恰好同时解释了2%～3%的密度缺失和b.c.c结构在内地核条件下的稳定性。因此我们建议内地核的基本结构与成分应为以体心立方结构存在的铁,掺杂约3.6at.%的硅元素,内地核温度至少在5500K以上。这一结论与其它更复杂的方法得到的结果一致。     

外核液态铁粘滞度的分子动力学研究

地球外核液态铁的不断流动造成了地球磁场 ,决定这一流动的基本性质之一是剪切粘滞度。研究外核液态铁的剪切粘滞度对认识地球磁场的运转机制具有非常重要的意义。地震波和大地测量研究表明地球内部除了剪切衰减外 ,还具有体积衰减。研究外核液态铁的体粘滞度对认识地球内部非弹性性质具有重要意义。由于外核所处的温度和压力状态 ,目前还无法从实验的角度对外核的粘滞度进行测量 ,因此必须采用实际观测和理论模拟计算相结合的方法。在考察了地球外核的主要成分和所处的温压状态后 ,简要介绍了研究外核的一种有效的理论方法———分子动力学。在此基础上 ,重点评述了国际上对外核液态铁剪切粘滞度和体粘滞度的研究现状。在剪切粘滞度方面 ,理论计算值位于实际地球观测值区间的下限。在体粘滞度方面 ,理论计算与实际地球观测之间均存在巨大的差别。这一巨大差异的解决将加深人们对地球内部非弹性性质的认识。     

H2O-CH4-H2-CO2-CO-O2在高温、高压和高密度条件下的状态方程

为了计算高温，高压和高密度流体的热力学性质，提出了一个具有19个参数的维里型状态方程，其中参数与温度间的函数关系采用由Sutherland位能函数导出的维里系数近似式。除临界点附近以外，在已报道的pVT数据所覆盖的大部分超临界区域内，该方程均可适用。用该方程对H2O，CH4，H2，CO2，CO和O2等流体pVT关系的计算结果令人满意，其中pVT上限分别为：91-610GPa,1.6-11.0cm^3/mol,4000-5000K。计算体积的平均偏 小于0．8％，最大偏差小于5．4％。     

钙钛矿结构MgSiO3的分子动力学研究——体系大小对弹性性质与状态方程的影响

本文利用分子动力学模拟方法,研究了300~3000K、0.1~100GPa条件下,MgSiO3钙钛矿大小两个体系的平衡状况和热力学性质,并将大小两个体系的模拟结果与高温高压实验结果进行比较,验证体系大小对哪些物理性质有影响以及影响有多大,为后续工作选择合适的模拟体系进行模拟研究工作提供参考。研究发现,无论在模拟的平衡过程中还是利用模拟数据对状态方程参数的拟合中,大体系的拟合结果都比小体系的计算结果接近高温高压实验结果。大体系的各项模拟结果与高温高压实验结果相比,相差均在1%左右。因此,在计算条件允许的情况下,尽量模拟较大的体系有助于得到更精确的分子动力学研究结果。     

气体(CH4、H2S、CO2等)在水溶液中的溶解度模型

本文介绍一个通过状态方程和特定粒子相互作用理论建立起来的气体在水溶液中的溶解度模型,用以计算气体(CH4、H2S、CO2)在纯水和含盐水溶液中的溶解度、流体包裹体的均一条件、成矿热液沸腾、流体不混溶性、水合物形成条件、CO2地质储藏量等.该模型不仅重现了上百套实验数据(约8000多个数据点),而且具有很强的外延能力.因此适用宽广的温度、压力和盐度范围(CH4:273～523K,1～2000bar,0～6m;H2S:273～500K,0～200bar,O～6m;CO2:273～533K,0～2000bar,0～4.5m),而且精度高、形式简洁.由于使用状态方程和特定粒子相互作用理论相结合的方法,这一模型在无需实验数据的情况下能够拓展到诸如海水和地下热卤水等更为复杂的体系.该模型在国际上得到日益广泛的应用,已被许多国家的同行用以多方面的研究工作,如计算CH4、H2S和CO2气体在水、卤水和海水等天然水溶液不同温度、压力和盐度条件下的溶解度(即水溶液中最大允许的气体含量),分析矿物流体包裹体的PVTX条件(根据包裹体中气体的总含量和均一温度,用该模型就会很方便得到均一化压力,在此基础上还可以迸一步通过状态方程得到密度和等容线)、计算成矿流体的不混溶性或沸腾点、计算CO2地质储藏量、实验校正等方面.相关研究可进行在线计算:www.geochem-model.     

超临界水的热力学模拟:一种可用到4273K、2GPa的立方型状态方程

根据水的高精度热力学模型IAPWS-95和IAPWS-IF97产生的压力-体积-温度(PVT)数据,本文建立了超临界水的一种高精度立方型状态方程。在723.15~2273.15K和0~1.4GPa范围内,该方程的平均体积偏差只有0.26%;在此范围之外,直到4273.15K和2GPa,方程的平均体积偏差不到2%。该方程在精度和适用范围方面均明显优于以前的立方型方程。在可比的温压条件下,该方程也明显优于一些常用的多参数非立方型方程(多数是高次维里型方程)。本文根据上述立方型方程和有关的热力学原理导出了膨胀系数、压缩系数、逸度系数、剩余焓和剩余熵的解析表达式,其计算结果与IAPWS-95模型的结果均吻合得很好。在此基础上很容易计算出许多其它的热力学性质。     

天然铁闪锌矿的热状态方程及相变

利用金刚石压腔及其外加温技术,对天然铁闪锌矿(Zn0.76Fe0.23S)进行了高压(17GPa)同时高温(300～623 K)下的原位能量色散X射线衍射实验研究.依据高温高压下获得的p-V-T数据进行了Birch-Murnaghan状态方程拟合.结果表明,铁闪锌矿晶体中Fe对Zn的类质同象替换可能导致其体积模量增大.获得了铁闪锌矿的体积模量的温度导数为((a)K/(a)T)P=-0.044(23)GPa/K.     

高温高压下黄铁矿热力学性质的第一性原理研究

黄铁矿是自然界中分布最为广泛的硫化物矿物,同时也是重要的造矿矿物,在金属矿床、沉积岩、变质岩、花岗岩、基性-超基性岩浆岩、以及地幔岩中都有大量出现。因此,研究黄铁矿在不同温度压力下的热力学性质可以为深入探讨与黄铁矿有关的成岩、成矿、成藏问题提供有用的矿物学依据。本文利用基于密度泛函微扰理论的第一性原理方法,采用准谐近似计算了黄铁矿在高温高压下的热力学性质。我们计算的黄铁矿的晶格常数、零压下的体积模量及其对压力的导数与前人的实验及理论计算结果吻合得很好,零压下等压热容和熵随温度的变化与实验结果有很好的一致性。尤其是,本文计算了直至2500K、100GPa的高温高压下黄铁矿的等温体积模量、热膨胀系数、热容和熵等热力学性质。这为在有硫参与的情况下,人们开展下地壳-岩石圈地幔深度的地球动力学模拟和建立地球物理模型提供了有用的信息。     

Thermodynamics, structure, dynamics, and freezing of Mg2SiO4 liquid at high pressure

We perform first principles molecular dynamics simulations of Mg₂SiO₄ liquid and crystalline forsterite. On compression by a factor of two, we find that the Grüneisen parameter of the liquid increases linearly from 0.6 to 1.2. Comparison of liquid and forsterite equations of state reveals a temperature-dependent density crossover at pressures of ∼12-17 GPa. Along the melting curve, which we calculate by integration of the Clapeyron equation, the density crossover occurs within the forsterite stability field at P = 13 GPa and T = 2550 K. The melting curve obtained from the root mean-square atomic displacement in forsterite using the Lindemann law fails to match experimental or calculated melting curves. We attribute this failure to the liquid structure that differs significantly from that of forsterite, and which changes markedly upon compression, with increases in the degree of polymerization and coordination. The mean Si coordination increases from 4 in the uncompressed system to 6 upon twofold compression. The self-diffusion coefficients increase with temperature and decrease monotonically with pressure, and are well described by the Arrhenian relation. We compare our equation of state to the available highpressure shock wave data for forsterite and wadsleyite. Our theoretical liquid Hugoniot is consistent with partial melting along the forsterite Hugoniot at pressures 150-170 GPa, and complete melting at 170 GPa. The wadsleyite Hugoniot is likely sub-liquidus at the highest experimental pressure to date (200 GPa).     

Experimental study of reaction between perovskite and molten iron to 146 GPa and implications for chemically distinct buoyant layer at the top of the core

Partitioning of oxygen and silicon between molten iron and (Mg,Fe)SiO₃ perovskite was investigated by a combination of laser-heated diamond-anvil cell (LHDAC) and analytical transmission electron microscope (TEM) to 146 GPa and 3,500 K. The chemical compositions of co-existing quenched molten iron and perovskite were determined quantitatively with energy-dispersive X-ray spectrometry (EDS) and electron energy loss spectroscopy (EELS). The results demonstrate that the quenched liquid iron in contact with perovskite contained substantial amounts of oxygen and silicon at such high pressure and temperature (P–T). The chemical equilibrium between perovskite, ferropericlase, and molten iron at the P–T conditions of the core–mantle boundary (CMB) was calculated in Mg–Fe–Si–O system from these experimental results and previous data on partitioning of oxygen between molten iron and ferropericlase. We found that molten iron should include oxygen and silicon more than required to account for the core density deficit (<10%) when co-existing with both perovskite and ferropericlase at the CMB. This suggests that the very bottom of the mantle may consist of either one of perovskite or ferropericlase. Alternatively, it is also possible that the bulk outer core liquid is not in direct contact with the mantle. Seismological observations of a small P-wave velocity reduction in the topmost core suggest the presence of chemically-distinct buoyant liquid layer. Such layer physically separates the mantle from the bulk outer core liquid, hindering the chemical reaction between them.     

Thermal equation of state of iron and Fe0.91Si0.09

We have carried out an in situ synchrotron X-ray diffraction study on iron and an iron-silicon alloy Fe_0.91Si_0.09 at simultaneously high pressure and temperature. Unit-cell volumes, measured up to 8.9 GPa and 773 K on the bcc phases of iron and Fe_0.91Si_0.09, are analyzed using the Birch-Murnaghan equation of state and thermal pressure approach of Anderson. Equation of state parameters on iron are found to be in agreement with results of previous studies. For both iron and Fe_0.91Si_0.09, thermal pressures show strong dependence on volume; the (∂K_T/∂T)_V values are considerably larger than those previously reported for other solids. The present results, in combination with our previous results on ɛ-FeSi, suggest a small dependency of the room-temperature bulk modulus upon the silicon content, less than 0.3 GPa for 1 wt.% silicon. We also find that substitution of silicon in iron would not appreciably change the thermoelastic properties of iron-rich Fe−Si alloys. If this behavior persists over large pressure and temperature ranges, the relative density contrast between iron and iron-rich Fe−Si alloys at conditions of the outer core of the Earth could be close to that measured at ambient conditions, i.e., 0.6% for 1 wt.% Si. Received: 13 January 1998 / Revised, accepted: 8 May 1998     

Hot degenerate dwarfs in a two-phase model

The characteristics of degenerate dwarfs-core radius, mass, and energy, thickness of their outer layers-are calculated based on a mechanical-equilibrium equation in a five-parameter, two-phase compositemodel with an isothermal core and a non-degenerate outer region. An accurate equation of state for the partially degenerate, ideal, relativistic electron gas of the core is used together with a polytropic approximation for the outer layers. The model parameters are determined using the known masses, radii, and luminosities of observed DA white dwarfs. A region where dwarfs can exist is identified in a plot of core temperature vs. the relativity parameter at the center of the star, and the dependence of the core temperature on the effective temperature of the photosphere is constructed.     

Density measurements of liquid Fe–Si alloys at high pressure using the sink–float method

The compositional dependence on the density of liquid Fe alloys under high pressure is important for estimating the amount of light elements in the Earth’s outer core. Here, we report on the density of liquid Fe–Si at 4 GPa and 1,923 K measured using the sink–float method and our investigation on the effect of the Si content on the density of the liquid. Our experiments show that the density of liquid Fe–Si decreases from 7.43 to 2.71 g/cm³ non-linearly with increasing Si content (0–100 at%). The molar volume of liquid Fe–Si calculated from the measured density gradually decreases in the compositional range 0–50 at% Si, and increases in the range 50–100 at% Si. It should be noted that the estimated molar volume of the alloys shows a negative volume of mixing between Fe and Si. This behaviour is similar to Fe–S liquid (Nishida et al. in Phys Chem Miner 35:417–423, 2008). However, the excess molar volume of mixing for the liquid Fe–Si is smaller than that of liquid Fe–S. The light element contents in the outer core estimated previously may be an underestimation if we take into account the possible negative value of the excess mixing volume of iron–light element alloys in the outer core.     

The effect of sulfur content on density of the liquid Fe–S at high pressure

The density of liquid Fe–S was measured at 4 GPa and 1,923 K using a sink/float method with a composite density marker. The density marker consisted of a Pt rod core and an Al₂O₃ tube surrounding. The uncertainty in the density of the composite marker is much smaller than that of the composite sphere, which had been used in previous density measurements. The density of liquid Fe–S decreases nonlinearly with increasing sulfur content at 4 GPa and 1,923 K. This tendency is consistent with the results measured at ambient pressure. The molar volume of FeS calculated from the measured density gradually increases with sulfur content. The excess molar volume from ideal mixing of Fe and S at 4 GPa was negative value. The new method proposed here is applicable to the density measurement of other Fe alloys at high pressure. The tendency of the molar volume and the excess molar volume with sulfur content at ambient pressure is consistent with these at high pressure at least up to 4 GPa. The excess molar volume at high pressure is essential for estimating the amount of light elements in the outer core.