Microstructural evolution and martensitic transformation mechanisms during solidification processes of liquid metal Pb

The microstructural evolution and the martensitic transformation (bcc–hcp and bcc–fcc) mechanisms during the solidification process of liquid metal Pb were studied by molecular dynamics simulation. Results indicate that, with the decrease of temperature, the system undergoes two phase transitions: from the liquid state into a metastable bcc phase first and then from the bcc phase into a coexisting crystal structure of hcp and fcc phases. Moreover, the complicated martensitic transformation processes are clearly observed by cluster type index method (CTIM) and the tracing method. The two transformation mechanisms are very analogous at the atomic level; the essential difference between them is that, in the bcc–hcp transformation, two adjacent layers shift in opposite directions, whereas in the bcc–fcc transformation, the top layer and bottom layer shift in opposite directions relative to the middle layer. The specific mechanisms for the bcc–hcp and bcc–fcc transformations are confirmed to correspond to the revised Burgers mechanism and Bain mechanism, respectively.     

第一性原理计算Fe从bcc到hcp结构的相变路径及其磁性边界

本文采用基于密度泛函理论的第一性原理方法,计算了压力作用下Fe从bcc到hcp结构相变的势能面、相变路径以及相变过程中的磁性相边界.结果表明:与Burgers路径不同,相变过程中bcc结构(110)bcc面的剪切和相对滑移相互耦合,并伴随有(110)bcc面间距的减小;这一相变机制可以解释Fe的静高压实验中在相变初期观察到的hcp结构异常.因此,并不需要像Wang和Ingalls提出的那样,在相变过程中引入一个亚稳定的fcc相来解释这些实验结果.对相变势能面的计算表明剪切对相变的发生有激活作用.此外,分析表明相变过程中涉及复杂的磁性转变,相变过渡态位置正好位于磁性相边界上,并对原子磁性对结构转变影响的物理机制进行了讨论.     

一维应变加载下单晶铁结构转变的微观研究

采用嵌入原子势和分子动力学方法,模拟了单晶铁在一维应变条件下由体心立方（bcc）转变为六角密排（hcp）结构的微观过程. 当应变加载至相变临界值时,hcp相开始均匀形核并沿{011}晶面长大为薄片状体系.弹性常数C₃₁和C₃₂在相变前被逐渐硬化,C₃₃则在相变前出现软化行为;当体系完全相变后,上述各弹性常数显示开始随体积压缩而迅速硬化,温度效应对晶格具有软化作用,可削弱C₃₃的硬化和软化过程;样品在压缩过程可出现孪晶结构,孪晶结构使晶格发生剪切变形.混合相中,hcp相势能比bcc相高,最大剪应力方向与bcc相反向;系统的偏应力与hcp相质量分数近似呈线性关系. 关键词： 结构转变 分子动力学 一维应变     

Monte Carlo and cell model calculations for the solid—fluid phase behaviour of the triangle-well model

Monte Carlo simulations and cell model calculations are reported for the vapour-liquid and solid-liquid phase behaviour of the triangle-well model system. The behaviour is examined as a function of the range of the triangle-well attraction, from 1.05 to 2.5 times the diameter of the hard core of the potential. Cell model calculations indicate that the stable solid is almost always face-centred cubic (fcc), except for a small set of conditions where hexagonal close-packed (hcp) is favoured. This outcome differs markedly from a much earlier study performed for the square-well model potential, where a much richer phase diagram was observed, with significant regions of stability for hep and body-centred cubic (bcc) phases. Monte Carlo simulations indicate that the cell model calculations represent well the true phase behaviour for this model system. The differing behaviour between the triangle-well and square-well models indicates an important role for the flatness of the potential well in governing the stability of hcp and bcc phases relative to the fcc phase.     

Lattice dynamics and phase diagram of aluminum at high temperatures

The dispersion of phonons in the fcc, hcp, and bcc phases of aluminum is calculated at ultrahigh pressures by the method of small displacements in a supercell. The stability of the phonon subsystem is studied. The thermodynamic characteristics are calculated in the quasi-harmonic approximation, and a phase diagram of aluminum is plotted. As compared to the Debye model, the use of a phonon spectrum calculated in the quasi-harmonic approximation significantly broadens the hcp phase field and strongly shifts the phase boundary between the fcc and bcc phases. The normal isentrope is calculated at megabar pressures. It is shown to intersect the fcc-hcp and hcp-bcc phase boundaries. The sound velocity along the normal isentrope is calculated. It is shown to have a nonmonotonic character.     

Structural and phase transformations in ferromanganese alloys during deformation under pressure

Using optical metallographic, TEM, Mössbauer spectroscopy, and X-ray analysis the structural and phase transformations in Fe-(3–55) wt % Mn alloys during shear deformation under pressure were investigated. It is established that a large deformation under high pressure causes the formation of a nanocrystalline structure with grain sizes of 40–60 nm. Nanostructure increases the hysteresis of inverse (hcp-fcc) transformation and stabilizes the (hcp) ? phase in alloys containing more than 40 wt % Mn, up to normal conditions. The Fe-3 wt % Mn alloy after shear under pressure treatment became nanostructured, retaining the original bcc phase state.     

Novel gamma-phase of titanium metal at megabar pressures

Group IV transition metals titanium, zirconium, and hafnium are expected to transform from an ambient hexagonal close packed (hcp, alpha-phase) to a body centered cubic (bcc, beta-phase) at high pressures. This transition path is usually facilitated by the occurrence of an intermediate hexagonal phase (distorted bcc, omega-phase). The existence of a bcc phase in zirconium and hafnium at high pressures has been known for the past ten years; however, its occurrence in titanium has been theoretically predicted but never observed. We report a novel unexpected transformation in titanium metal from an omega phase to an orthorhombic phase (distorted hcp, gamma-phase) at a pressure of 116+/-4 GPa.     

非静水压条件下铁从α到ε结构相变的第一性原理计算

采用基于密度泛函理论的平面波赝势方法,研究了三轴加载的非静水压力和静水压力对铁从体心立方结构（bcc,α相）到六角密排结构（hcp,ε相）相变压力和磁性的影响,结果发现：在0—18 GPa压力范围内,相对静水压力条件,随着压力的升高,bcc结构的原子磁矩在非静水压力下降低得更快;在非静水压力下,相变更容易发生,相变压力随着非静水压力程度的增加而降低;并且对非静水压力对相变压力影响的物理机理进行了讨论. 关键词： 相变 非静水压力 第一性原理 铁     

Theory of the crystal structures of cerium and the light actinides

First-principles theory, based on the density-functional approach, is used to study the crystal structures of Ce and the light actinides (Th-Pu) at low temperatures as a function of hydrostatic pressure. Calculated ground-state properties, such as crystal structure, atomic volume and bulk modulus, are shown to be very well described within this theory. We present the following pressureinduced phase transitions: Ce, fcc -> bct -> hcp; Th, fcc -> bct -> hcp; Pa, bct -> alphaU bct -> hcp; U, alpha-U -> bct -> bcc; Np, alpha-Np -> beta-Np -> bcc; Pu, alpha-Pu -> alphaNp -> beta-Np -> bcc. We explain the occurrence of low-symmetry (complex) structures in these metals as a consequence of a symmetry-breaking mechanism that shows similarities to a Peierls distortion. The ultimate high-pressure phases are well accounted for in a canonical model for the f bands for these metals.     

单轴应变驱动铁bcc—hcp相转变的微观模拟

用分子动力学方法模拟了沿〈001〉晶向应变加载和卸载情况下单晶铁中体心立方(bcc)与六方密排(hcp)结构的相互转变,分析了相变的可逆性和微结构演化特征.微观应力的变化显示样品具有超弹性性质,而温度变化表明在相变和逆相变过程中均出现放热现象.相变起始于爆发式均匀形核,晶核由块状颗粒迅速生长为沿{011}晶面的片状分层结构; 而卸载逆相变则从形核开始就呈现片状形态,且相界面晶面指数与加载相变完全一致,表现出形态记忆效应.在两hcp晶核生长的交界面易形成面心立方(fcc)堆垛层错. fcc通过在hcp晶粒内     

The effect of silicon impurities on the phase diagram of iron and possible implications for the Earth's core structure

The hexagonal-close-packed (hcp) structure is the accepted stable form of pure iron (Fe) under Earth's core conditions. Recently, however, a body-centred-cubic (bcc) phase of iron alloyed with lighter elements has been proposed. At relatively modest conditions, experiments have shown that small amounts of silicon (Si) can stabilise the bcc phase with respect to the hcp phase. This result has motivated our present study examining the effect of silicon on the bcc-hcp phase transition. We have performed ab initio calculations on both phases at zero Kelvin; our results are in good agreement with experiment. Extending our results to core pressures and taking into account previous studies of pure iron at core temperatures, we conclude that the bcc phase of iron alloyed with silicon is likely to be the stable crystalline phase in the inner core.     

Reconstructive structural phase transitions in dense Mg

The question raised recently about whether the high-pressure phase transitions of Mg follow a hexagonal close-packed (hcp) → body centered cubic (bcc) or hcp → double hexagonal close-packed (dhcp) → bcc sequence at room temperature is examined by the use of first principles density functional methods. Enthalpy calculations show that the bcc structure replaces the hcp structure to become the most stable structure near 48 GPa, whereas the dhcp structure is never the most stable structure in the pressure range of interest. The characterized phase-transition mechanisms indicate that the hcp → dhcp transition is also associated with a higher enthalpy barrier. At room temperature, the structural sequence hcp → bcc is therefore more energetically favorable for Mg. The same conclusion is also reached from the simulations of the phase transitions using metadynamics methods. At room temperature, the metadynamics simulations predict the onset of a hcp → bcc transition at 40 GPa and the transition becomes more prominent upon further compression. At high temperatures, the metadynamics simulations reveal a structural fluctuation among the hcp, dhcp, and bcc structures at 15 GPa. With increasing pressure, the structural evolution at high temperatures becomes more unambiguous and eventually settles to a bcc structure once sufficient pressure is applied.     

Prediction of a bcc-hcp phase transition for Sn: A first-principles study

The high-pressure structural transformation of elemental Sn is studied using an ab initio density functional theory implementation of the metadynamics method that predicts with sufficient compression, Sn will transform from the bcc structure into an hcp structure. The low-free-energy pathway associated with this phase transition is characterized as the Burgers transition mechanism. The superconducting properties of Sn under pressure are also investigated. Both bcc and hcp structures of Sn exhibit very weak electron-phonon coupling and therefore would not sustain superconductivity at high pressure.     

Crystal structure analysis in (3+d) dimensions

Inelastic neutron scattering on in situ grown bcc single crystals of the group 4 metals Ti, Zr and Hf show a band of low energy and strongly damped phonons. Geometrical considerations show how these damped lattice vibrations achieve the displacements necessary for the two martensitic phase transitions from bcc to ω (under pressure) and from bcc to hcp (upon lowering the temperature). The low energy and temperature dependent phonons are precursor fluctuations of the hcp or ω phase within the bcc phase.     

X-ray diffraction study of thermal vacancies in solid helium-3

Thermal vacancy concentrations in solid ³He have been directly measured by x-rays over a wide range of molar volumes in the bcc phase and one molar volume in the hcp phase. Values of the vacancy free energies and free volumes of formation have been obtained, and comparison with NMR and ultrasonic studies yields information about vacancy motion in the two phases of the solid.     

Elastic properties of the Ta–V system: bcc Ta0.33V0.67 and C15 TaV2

Resonant ultrasound spectroscopy was used to measure the elastic constants of bcc Ta_0.33V_0.67 over the temperature range 3.5–300?K; the results were compared to earlier measurements on C15 TaV₂. The temperature dependence of the polycrystalline shear modulus is completely different in the two phases; that of the bcc phase decreases with temperature whereas that of the C15 phases increases in an anomalous fashion. This difference is consistent with a model involving doubly-degenerate levels at the X point of the Brillouin zone in the C15 phase with the Fermi level lying near the doubly degenerate level. This model accounted for the unusual behaviour of the C15 phase. Debye temperatures were determined from the ultrasonic measurements: 295?K for the C15 phase and 315?K for the bcc phase.     

室温下压致铁钴镍合金的bcc→hcp相变

 本文采用高压X光衍射方法在金刚石对顶压砧中在位地（in situ）研究了Fe₆₈Co₂₄Ni₈（wt%）合金在室温下的压致bcc→hcp结构相变和直到40.5 GPa的等温压缩行为。实验结果表明该合金在常压下为bcc结构，晶格常数a₀=(0.287 0±0.000 1) nm，体积V₀=(7.119±0.007) cm³/mol，密度ρ₀=(7.981±0.008) g/cm³；在20.9 GPa附近出现bcc→hcp结构相变，两相共存压力区约10 GPa，在此区域内有晶面间距d(002)_hcp=d(110)_bcc，且原子平面(002)_hcp//(110)_bcc，hcp相比bcc相体积减小(0.33±0.02) cm³/mol；高压相hcp结构的晶格参数比值c/a=1.608±0.004；相变后原子配位数的增加使得hcp相(002)平面内及(002)平面间的最近邻原子间距比bcc相最近邻原子间距分别增大约1.6%和0.5%；用Murnaghan状态方程对实验数据进行最小二乘法拟合，得到bcc相B₀=(130±13) GPa，B₀'=12.6±0.5；hcp相V₀=(6.62±0.04) cm³/mol，B₀=(243±21) GPa，B₀'=6.8±0.3；对于该合金的bcc→fcp相变时的结构转变机制做了详细的讨论。     

Band structure and Fermi surfaces of alternate structural phases of Co and Rh

In this work, first-principles DFT scalar-relativistic calculations using the GGA functionals were performed to study the equilibrium properties of alternate structural phases of Co and Rh. The results show that cobalt orders ferromagnetically in the bcc, fcc and hcp phases, where the Co atoms carry magnetic moments of 1.80 μ_B, 1.71 μ_B and 1.69 μ_B, respectively. Rhodium is ferromagnetic only in the bcc phase where the Rh atoms carry a moment of 0.56 μ_B. The results yield evidence for the influence of the crystal symmetry in establishing ferromagnetic order in transition metals.     

Evidence of a medium-range ordered phase and mechanical instabilities in strontium under high pressure

We provided the first theoretical evidence for a medium-range ordered phase in high pressure strontium from the first-principles calculations. At the absolute zero temperature, the enthalpy–pressure relation shows that the bcc and hcp are energetically more favorable than the other experimentally observed phases between 24 and 27 GPa. In the present work, we concentrate on the bcc phase because we found a link to a medium-range ordered phase. Our results reveal that the bcc phonon dispersion at the N and H points starts softening at around 24.1 GPa. The ab initio molecular dynamics at 300 K and 27 GPa showed that the bcc is quickly transformed into a lower energy structure with R3c symmetry and distorted basis. The simulated diffraction patterns showed that the R3c structure has only a single major peak at low angle. The R3c peak locates near the first peak of the bcc structure. This is the evidence of the so-called medium-range ordered phase. This structure is a strong candidate for the unsolved S-phase reported by experiments.