Universal relationships for the phonon spectra in BCC,FCC, and HCP crystals with a short-range interatomic interaction

The frequencies of the phonon branches that correspond to the vibrations of the close-packed atomic planes in bcc, fcc, and hcp crystals with short-range interatomic interaction are shown to be described by a universal relationship, which only contains two parameters for each branch, for any polarization λ. These phonon branches correspond to the (ξ, ξ, 0) direction in bcc crystals, the (ξ, ξ, ξ) direction in fcc crystals, and the (0, 0, ξ) direction in hcp crystals. This universal relationship can only be violated by long-range interactions, namely, the interactions outside the sixth coordination shell in a bcc crystal, the fifth coordination shell in an fcc crystal, and the eleventh or tenth coordination shell in an hcp crystal. The effect of these long-range interactions for each phonon branch can be quantitatively characterized by certain parameters Δ _nλ, which are simply expressed in terms of the frequencies of three phonons of the branch. The values of these parameters are presented for all bcc, fcc, and hcp metals whose phonon spectra are measured. In most cases, the proposed relationships for the frequencies are found to be fulfilled accurate to several percent. In the cases where the Δ _nλ parameters are not small, they can give substantial information on the type and scale of long-range interaction effects in various metals.     

Strain-induced interaction of interstitials in IVA group hcp metals

Strain-induced (elastic) interactions of oxygen, nitrogen and carbon atoms in IVA group metals, α-Ti, Zr, and -Hf, are calculated in the framework of the microscopic Krivoglaz-Kanzaki-Khachaturyan theory. The experimental elastic constants, lattice spacing of the host metal, and concentration expansion coefficients are used as the input numerical parameters. The resulting interactions are stronger in α-Ti than in α-Zr and α-Hf. A comparative analysis of interactions in the hcp IVA group metals with those in bcc and fcc solid solutions reveals the crystal structure effect. In general, the strain-induced interactions of O, N, and C in hcp IVA group metals are weaker than in bcc solid solutions and are stronger than in fcc solid solutions.     

Cold brittleness and fracture of metals with various crystal lattices: Dislocation mechanisms

The dislocation mechanisms of formation of the ductile–brittle transition temperature and the low-temperature brittle fracture of metals (single crystals, polycrystals) with various crystal lattices (bcc, fcc, hcp) are considered. The conditions of appearance of cold shortness and intracrystalline crack propagation (brittle fracture) are determined. These conditions can be met in bcc and some hcp metals and cannot be met in fcc and many hcp metals. The nondestructive internal friction (at 100 kHz) method is used to determine the temperature ranges of cold shortness (ductile–brittle transition temperatures) in bcc metals (ferritic–martensitic EK-181 steel, V–4Ti–4Cr alloy), which depend on their structure–phase state and strength (yield strength).     

平均键能Em的物理内涵探讨

在面心立方(fcc)、体心立方(bcc)和六角密堆积(hcp)3种不同结构晶体的自由电子能带模型中,发现4个最低能带与5个次低能带本征值的平均能量(称为平均键能,E_m)与费米能级(E_F)相当接近;并进一步在hcp结构的钛(Ti)、锆(Zr)和铪(Hf)以及bcc结构的铁(Fe)等金属中,采用从头赝势能带计算方法和平均键能计算方法,证实在这些金属的实际能带中,平均键能(E_m)值仍然非常接近于费米能级(E_F)值.该发现有助于进一步了解平均键能(E_m)的物理内涵. 关键词： 平均键能 费米能级 能带结构     

HIGH pressure structural investigations of zirconium using LMTO method

Abstract

The structural energy differences have been calculated for zirconium as a function of pressure at zero temperature using the Andersen force theorem and the linear muffin tin orbital method. The structures included are the following: α (hcp), the room temperature room pressure phase, ω- a three atom simple hexagonal, bcc and fcc. Our calculations show that the bcc structure would become energetically most favourable above 11 GPa. This results is in agreement with well known correlation between the crystal structure and the d-electron population in transition metals at normal volume. The diamond anvil cell based high pressure x-ray diffraction experiments are in progress to verify this result.     

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.     

高温高压下过渡金属Ru的结构相变

采用基于密度泛函理论的第一性原理和准简谐晶格动力学方法对Ru的六角密排 (hcp)、面心立方 (fcc)、体心四方 (bct) 和体心立方 (bcc) 结构的磁性、晶格结构稳定性和高温高压下的相变进行了系统的研究. 计算获得了各相结构的磁性基态及其稳定性范围, 结果表明: 零温下在计算的压力范围内, NM-hcp 结构是Ru最稳定的结构, 压力的单独作用下并没有相变的发生; NM-fcc结构是Ru的亚稳定结构, 而NM-bcc和FM-bct结构在动力学上并不稳定. 高温高压下Ru将发生从NM-hcp到NM-fcc结构的相变, 并给出了Ru的温度压力相图. 关键词： 相变 晶格稳定性 磁性 第一性原理     

First principles studies of the dependence of magnetism on the crystal phase in 4d and 5d late transition metals

We investigate the possibility of inducing ferromagnetic order in 4d and 5d late transition metals through crystal symmetry change. First principles, self-consistent density functional theory calculations, with spin-orbit coupling included, performed at 0 K show that ferromagnetism occurs in the bulk of Rh and Pd at the optimum lattice constant if Rh is in the bcc and Pd in the hcp/dhcp phase. The ferromagnetic order originates in the d-band occupancy of Rh or Pd which locates the Fermi energy at the top of the highest peak of the respective (paramagnetic) density of states induced by the bcc or hcp/dhcp structure. This peak in the density of states is caused by flat bands which lie at the surface of the respective Brillouin zone. For a bcc crystal these flat bands have the eg character and are positioned at the surface of the bcc Brillouin zone along the N-P line. The origin of the flatness of the bands was found to be the translation symmetry of the cubic lattice which causes the bands with the eg character to be narrow along the k-lines whose k-vector directions are furthest off the directions to which the orbitals of the eg symmetry point. Due to the d-band occupancy of Rh these flat bands lie in the paramagnetic state at the Fermi energy, whereas in the ferromagnetic state they exhibit the largest energetic split. This indicates that a smaller degree of orbital overlap narrows electronic bands enhancing the tendency of the system for ferromagnetic band split. For the hcp/dhcp structure the states contributing to the high density of para-magnetic states at the Fermi level of Pd lie in the vicinity of the M-L line of the hcp Brillouin zone boundary, which possesses a high number of symmetry (M and L) points. Moreover, the M-L line is aligned with the stacking sequence direction ([0001]) which is furthest off the densest-packed atomic chain direction of an hcp-crystal and, consequently, the weakest-bond direction in the crystal. This makes the narrow bands along the M-L line flat. The instability of the bcc and the meta-stability of the hcp crystal phase modifications for metals with native close-packed crystal structures is subsequently analysed in order to find whether they can be grown as films on suitable substrates.     

On the interaction between a vacancy and self-interstitial atom clusters in metals

Atomic-scale computer simulation is used to study the interaction between a vacancy and a cluster of self-interstitial atoms in metals with hcp, fcc and bcc crystal structure: α-zirconium, copper and α-iron. Effects of cluster size, atomic structure, dislocation nature of the cluster side and temperature are investigated. A vacancy can recombine with any interstitial in small clusters and this does not affect cluster mobility. With increasing sizes clusters develop dislocation character and their interaction with vacancies depends on whether the cluster sides dissociate into partial dislocations. A vacancy recombines only on undissociated sides and corners created with undissociated segments. Vacancies inside the cluster perimeter do not recombine but restrict cluster mobility. Temperature enhances recombination by either increasing the number of recombination sites or assisting vacancy diffusion towards such sites. The results are discussed with relevance to differences in irradiation microstructure evolution of bcc, fcc and hcp metals and higher level theoretical modelling techniques.     

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     

Structural properties of complex (dusty) plasma upon crystallization and melting

A change in the local order of a bounded complex (dusty) plasma in the process of its crystallization and melting has been examined by molecular dynamics simulations. The dynamics of microparticles is considered in the framework of a Langevin thermostat, the pair interaction between charged particles is described by a screened Coulomb potential (Yukawa potential) with the hard wall potential as a confinement. It has been shown that the beginning of the crystallization of such a system is accompanied by the formation of clusters with the hexagonal close packed (hcp) structure; a noticeable number of these clusters are then transformed to the face centered cubic (fcc) phase. A plasma crystal formed after crystallization consists of the metastable hcp phase, fcc clusters, and a small number of clusters with a body centered cubic (bcc) crystal lattice. Beginning with a certain threshold value of the thermostat temperature, the number of fcc/bcc clusters decreases sharply with increasing temperature, which is an important signature of the beginning of the melting of the plasma crystal.     

Ab initio theory of the scattering-independent anomalous Hall effect

We report on first-principles calculations of the side-jump contribution to the anomalous Hall conductivity (AHC) directly from the electronic structure of a perfect crystal. We implemented our approach for a short-range scattering disorder model within the density functional theory and computed the full scattering-independent AHC in elemental bcc Fe, hcp Co, fcc Ni, and L1(0) FePd and FePt alloys. The full AHC thus calculated agrees systematically with experiment to a degree unattainable so far, correctly capturing the previously missing elements of side-jump contributions, hence paving the way to a truly predictive theory of the anomalous Hall effect and turning it from a characterization tool to a probing tool of multiband complex electronic band structures.     

Ti-Mo合金氢化物微观缺陷的小角X射线散射研究

采用小角X射线散射(SAXS)方法对Ti-Mo合金氢化物的微观缺陷进行了研究.结果表明,氢化物样品中Mo含量为5at％时,所测定的SAXS强度在高散射角区明显低于其他样品的SAXS强度.氢化物中的晶粒及其内部的亚结构是引起SAXS现象的散射体,而这些亚结构是由合金氢化时引入的大量位错所产生.Mo 含量为5at％合金主要为hcp结构而其他合金为bcc结构,但两种合金氢化后都成为fcc结构的氢化物.据此,认为hcp结构与bcc结构Ti-Mo合金在氢化时氢化物结构相同但引入的位错缺陷特征不同. 关键词： Ti-Mo合金氢化物 小角X射线散射 微观缺陷     

Stability of Ferromagnetism in Fe, Co, and Ni Metals under High Pressure with GGA and GGA+U

The stability of the ferromagnetic state in Fe, Co, and Ni metals under high pressure is investigated using generalized gradient approximation (GGA) and GGA+U within the density functional theory (DFT). It is found that the ferromagnetic state under pressure is very different for Fe, Co, and Ni metals, and is closely associated with the crystal structure. In the case of Fe, a ferromagnetic bcc ground state is obtained at ambient pressure and a nonmagnetic hcp ground state is found at pressure around 12 and 115 GPa for GGA and GGA+U, respectively. For Co, the phase transition from a ferromagnetic hcp to a nonmagnetic fcc is found around 107 GPa for GGA. In contrast to Fe and Co, a ferromagnetic fcc state in Ni is maintained even at 200 GPa. The calculated results suggest that the suppression of ferromagnetism in Fe, Co, and Ni is due to pressure-induced decrease of the density of state at the Fermi level.     

On the energetics of transversal and longitudinal fluctuations of atomic magnetic moments

By constrained spin-density functional calculations we estimate the relative role of the longitudinal and transversal fluctuations of the magnetic moments in the series of 3d metals (bcc Fe, hcp and fcc Co, and fcc Ni) for weak excitations from the ferromagnetic ground state. It is shown that the importance of longitudinal fluctuations strongly varies from relatively small in bcc Fe to large in fcc Ni. This means that a consistent adiabatic treatment of the low-energy spin fluctuations should include independent longitudinal fluctuations.     

Point-defect properties in HCP rare earth metals with analytic modified embedded atom potentials

The analytic embedded atom method (EAM) type many-body potentials of hcp rare earth metals (Dy, Er, Gd, Ho, Nd, Pr, and Tb) have been constructed. The hcp lattice is shown to be energetically most stable when compared with the fcc and bcc structure, and the hcp lattice with ideal c/a. The mechanical stability of the corresponding hcp lattice with respect to large change of density and c/a ratio is examined. The phonon spectra, stacking fault and surface energy are calculated. The activation energy for vacancy diffusion in these metals has been calculated and the most possible diffusion paths are predicted. Finally, the self-interstitial atom (SIA) formation energy and volume have been evaluated for eight possible sites. This calculation suggests that the crowdion and basal split are the most stable configurations. The SIA formation energy increases linearly with the increase of the melting temperature.Received: 26 March 2003, Published online: 9 September 2003PACS: 34.20.Cf Interatomic potentials and forces - 66.30.Fq Self-diffusion in metals, semimetals, and alloys - 61.72.Ji Point defects (vacancies, interstitials, color centers, etc.) and defect clusters - 61.72.Bb Theories and models of crystal defects     

Dislocation modeling in bcc lithium: A comparison between continuum and atomistic predictions in the modified embedded atoms method

In this study, the modified embedded-atom method (MEAM) was applied to compare the predictions of dislocation core properties obtained by molecular statics with the continuum predictions obtained in the framework of the simplified 1D-Peierls–Nabarro model. To this end, a set of four fictive Li potentials in the MEAM framework was proposed with the condition that all four potentials reproduce the same elastic constants, the same transition energies between bcc and fcc crystal structures, and between bcc and hcp crystal structures, while the unstable stacking fault energy on the plane {110} in the direction <111> was varied around the value predicted by first-principles. Within these potentials, direct atomistic calculations were performed to evaluate dislocation core properties such as dislocation half width and Peierls stress and the results were compared with continuum predictions. We found that the trends predicted by the Peierls–Nabarro model, i.e. (i) a decrease of the dislocation half width with increasing unstable stacking fault energy, and (ii) an increase of the Peierls stress with increasing the magnitude of the unstable stacking fault energy, were recovered using atomic calculations in the MEAM framework. Moreover, the magnitude of the dislocation half width and the Peierls stress calculated in the MEAM framework are in good agreement with the Peierls–Nabarro predictions when the dislocation half width is determined using a generic strategy. Specifically, the dislocation half width is defined as the distance for which the disregistery is included between b/4 and 3b/4. It was, therefore, demonstrated herein that the set of fictive potentials could be parameterized in the MEAM framework to validate or to disprove the continuum theory using atomistic methods.     

First-principles study of the elastic and thermodynamic properties of thorium hydrides at high pressure

The high pressure behaviors of Th_4H_(15) and ThH_2 are investigated by using the first-principles calculations based on the density functional theory(DFT). From the energy–volume relations, the bct phase of ThH_2 is more stable than the fcc phase at ambient conditions. At high pressure, the bct ThH_2 and bcc Th_4H(15) phases are more brittle than they are at ambient pressure from the calculated elastic constants and the Poisson ratio. The thermodynamic stability of the bct phase ThH_2 is determined from the calculated phonon dispersion. In the pressure domain of interest, the phonon dispersions of bcc Th_4H(15) and bct ThH_2 are positive, indicating the dynamical stability of these two phases, while the fcc ThH_2 is unstable. The thermodynamic properties including the lattice vibration energy, entropy, and specific heat are predicted for these stable phases. The vibrational free energy decreases with the increase of the temperature, and the entropy and the heat capacity are proportional to the temperature and inversely proportional to the pressure. As the pressure increases, the resistance to the external pressure is strengthened for Th_4H_(15) and ThH_2.     

First-principles study of He point-defects in HCP rare-earth metals

He defect properties in Sc, Y, Gd, Tb, Dy, Ho, Er and Lu were studied using first-principles calculations based on density functional theory. The results indicate that the formation energy of an interstitial He atom is smaller than that of a substitutional He atom in all hcp rare-earth metals considered. Furthermore, the tetrahedral interstitial position is more favorable than an octahedral position for He defects. The results are compared with those from bcc and fcc metals.