Contributions of atom probe tomography to the understanding of nickel-based superalloys

Atom probe tomography enables atomic level microstructural characterization to be performed on complex engineering materials such as superalloys. The technique provides information on the size, morphology and compositions of coexisting phases, the solute partitioning of the elements between the phases, and solute segregation to interfaces and grain boundaries. This information leads to a more complete understanding of nickel-based superalloys. The types of atomic level information that may be obtained with atom probe tomography are illustrated with examples of the formation of fine γ precipitates within the central region of the γ′ phase in PW 1480, the evolution of the dual γ′/γ″ nature of secondary precipitates in alloy 718, the interphase precipitation of the γ′ phase at the primary γ″–γ interface in alloy 718, and the quantification of the level and spatial extent of the boron segregation at grain boundaries in a nickel–molybdenum superalloy.     

Spin and spin-orbit coupling effects in nickel-based superalloys: A first-principles study on Ni3Al doped with Ta/W/Re

Heavy elements(X=Ta/W/Re)play an important role in the performance of superalloys,which enhance the strength,anti-oxidation,creep resistance,and anti-corrosiveness of alloy materials in a high-temperature environment.In the present research,the heavy element doping effects in FCC-Ni(γ)and Ni₃Al(γ')systems are investigated in terms of their thermodynamic and mechanical properties,as well as electronic structures.The lattice constant,bulk modulus,elastic constant,and dopant formation energy in non-spin,spin polarized,and spin-orbit coupling(SOC)calculations are compared.The results show that the SOC effects are important in accurate electronic structure calculations for alloys with heavy elements.We find that including spin for bothγandγ'phases is necessary and sufficient for most cases,but the dopant formation energy is sensitive to different spin effects,for instance,in the absence of SOC,even spin-polarized calculations give 1%to 9%variance in the dopant formation energy in our model.Electronic structures calculations indicate that spin polarization causes a split in the metal d states,and SOC introduces a variance in the spin-up and spin-down states of the d states of heavy metals and reduces the magnetic moment of the system.     

Elastic stability and electronic structure of tantalum boride investigated via first-principles density functional calculations

The elastic properties, electronic structure and thermodynamic behavior of the TaB have been investigated for the first time in this work. Using first-principles plane-wave ultrasoft-pseudopotential density functional theory (DFT), the ground state properties and equation of state of TaB have been obtained. The average zero-pressure bulk modulus of TaB is 302 GPa. By analyzing the elastically anisotropic behavior and the relative structure parameters of TaB, we found that the crystal cell along the b-axis was more compressible than along the a and c axes. The calculated ratio of bulk modulus and shear modulus (B/G) for TaB is 1.58, demonstrating that TaB is rather brittle. From the elastic stiffness constants, we found that TaB in the Cmcm phase is mechanically stable. The calculated hardness of TaB is 28.6 GPa which is close to the previous data. Moreover, using the Gibbs 2 model, the thermodynamic properties such as the thermal expansion and Debye temperature of TaB have been obtained firstly. At the ambient temperature, the Debye temperatures of TaB are 792 K and 845 K from GGA calculation and LDA calculation, respectively.     

A model for oxidation-driven surface segregation and transport on Pt-alloys studied by atom probe tomography

Using a purpose-built 3D atom probe, we have previously shown that exposure to oxidising gases (NO, N₂O, O₂) induces Rh surface segregation in Pt–Rh alloys, the extent of which is strongly dependent on treatment temperature, crystallographic plane and the presence of ternary alloy additions. In this paper, the segregation trends identified on three different crystallographic surfaces of Pt–Rh are analysed using thermodynamic and kinetic arguments. The segregation model we present is generic for diffusion on alloy surfaces in the presence of active gases. From it we obtain activation energies and diffusion coefficients for the processes of metal-oxide species diffusion both perpendicular to and laterally across the surface. Using these we propose a simple model for the interaction of chemically active gases with the surfaces of such alloys. Applying this understanding to sequential oxidation/reduction treatments would in principle allow improved control of the surface composition of alloy catalysts. Related applications of this model include optimisation of core–shell catalyst nanoparticles.     

Statistical model of an atom in electron scattering calculations

The parameters describing scattering of electrons by atoms, which usually involve multiple integration of the atomic potentials, may be severely affected by the accuracy of these potentials. In the present work an iterative procedure is proposed providing a sequence of solutions of the Thomas-Fermi equation with increasing accuracy. Such a sequence makes it possible to establish the sensitivity of a given parameter to the accuracy of the atomic potential, and consequently to determine the accurate value of this parameter. Based on the present solutions, the differential scattering cross-sections for the Thomas-Fermi atom are calculated, and are found to deviate from the literature data.     

Electric field gradients at 181Ta probe in ZrNi: Results from perturbed angular correlation and first-principles calculations

Results of temperature dependent perturbed angular correlation (PAC) measurements in the equiatomic ZrNi alloy have been reported for the first time using ¹⁸¹Hf probe. At room temperature, values of quadrupole frequency and asymmetry parameter for the major component (~80%) are found to be ω_Q=26.8(4) Mrad/s, and η=0.413(7). The resulting electric field gradient comes out to be V_zz=2.99 ×10¹⁷ V/cm² and this corresponds to the probe nuclei occupying the regular substitutional Zr sites. In ZrNi system, no magnetic interaction is observed down to 77 K indicating absence of any magnetism in this material. X-ray diffraction (XRD) and X-ray photoelectron spectroscopy (XPS) studies on an inactive but similarly prepared sample confirm the dominant presence of the orthorhombic ZrNi phase in the sample. A complementary density functional theory (DFT) calculation results in V_zz=−2.35×10¹⁷ V/cm², η=0.46 at the ¹⁸¹Ta probe impurity site and zero magnetic moment on each atomic site, in close agreement with the experimental results. Furthermore, it is found that electric field gradient for the regular component follows a T^3/2 temperature dependence between 77 and 353 K, beyond which it varies linearly with temperature.     

Phase decomposition and ordering in Ni-11.3 at.% Ti studied with atom probe tomography

The decomposition behavior of Ni-rich Ni–Ti was reassessed using Tomographic Atom Probe (TAP) and Laser Assisted Wide Angle Tomographic Atom Probe. Single crystalline specimens of Ni-11.3 at.% Ti were investigated, the states selected from the decomposition path were the metastable γ″ and γ′ states introduced on the basis of small-angle neutron scattering (SANS) and the two-phase model for evaluation. The composition values of the precipitates in these states could not be confirmed by APT data as the interface of the ordered precipitates may not be neglected. The present results rather suggest to apply a three-phase model for the interpretation of SANS measurements, in which the width of the interface remains nearly unchanged and the L1₂ structure close to 3:1 stoichiometry is maintained in the core of the precipitates from the γ″ to the γ′ state.     

Direct observation of Cu interphase precipitation in continuous cooling transformation by atom probe tomography

Atom probe tomography (APT) combined with electron back scatter diffraction and transmission electronic microscopy (TEM) is utilized to characterize the nature of copper precipitation during austenite–ferrite transformation in a continuous cooling high-strength low-alloy steel. The copper precipitation manners in association with the austenite decomposition kinetics are studied. The prevailing microstructure of the continuous cooling steel consists of acicular ferrite (AF), which is formed at an intermediate cooling rate of 10?°C/s. Besides, a limited volume of polygonal ferrite (PF) because of fast cooling rate and a trace of retained austenite are detected. Numerous copper-rich phase is found by TEM observation both in highly dislocated AF and dislocation-free PF. Generally, the copper-rich precipitates have comparatively large sizes and are considered to be formed by interphase precipitation during austenite–ferrite transformation. A high number density of nanometre sized copper-rich clusters that are lack of diffraction contrast in conventional TEM observation are detected by APT. These smaller copper-rich clusters, which are usually located between the linear-arranged copper-rich precipitates, are considered to be formed from supersaturated solid solution after the cessation of austenite–ferrite transformation. That means an ageing reaction for Cu precipitation occurs during continuous cooling transformation. The copper-rich precipitates and clusters are both rich in nickel, manganese and iron.     

Self-diffusion rates in Al from combined first-principles and model-potential calculations

Monovacancy diffusion alone dominates over diffusion due to divacancies and interstitials in Al for all temperatures up to the melting point. Deviations from a single Arrhenius dependence are due to anharmonicity. The conclusion is based on a combination of theoretical methods, from density functional theory to thermodynamic integration, without fitting to experimental data. The calculated diffusion rate agrees with experimental data over 11 orders of magnitude.     

Fine-structure effects in relativistic calculations of the static polarizability of the helium atom

We use the relativistic configuration-interaction method and the model potential method to calculate the scalar and tensor components of the dipole polarizabilities for the excited states 1s3p ³ P ₀ and 1s3p ³ P ₂ of the helium atom. The calculations of the reduced matrix elements for the resonant terms in the spectral expansion of the polarizabilities are derived using two-electron basis functions of the relativistic Hamiltonian of the atom, a Hamiltonian that incorporates the Coulomb and Breit electron-electron interactions. We formulate a new approach to determining the parameters of the Fuss model potential. Finally, we show that the polarizability values are sensitive to the choice of the wave functions used in the calculations. Zh. éksp. Teor. Fiz. 115, 494–504 (February 1999)     

A study of threshold switching of NbO2 using atom probe tomography and transmission electron microscopy

Threshold switching is a phenomenon where the resistivity of an insulating material changes and the insulator exhibits metallic behavior. This could be explained by phase transformation in oxide materials; however, this behavior is also seen in amorphous insulators. In this study, through an ex-situ experiment using transmission electron microscopy (TEM), we proved that threshold switching of amorphous NbO₂ accompanies local crystallization. The change in I–V characteristics after electroforming was examined by evaluating the concentration profile. Atom probe tomography (APT) combined with in-situ TEM probing technique was performed to understand the threshold switching in amorphous NbO₂. The local crystallization in amorphous NbO₂ was validated by the observed difference in time-of-flight (ToF) between amorphous and crystalline NbO₂. We concluded that the slower ToF of amorphous NbO₂ (a-NbO₂) compared with crystalline NbO₂ (c-NbO₂) is due to the resistivity difference and trap-assisted recombination.     

硼原子掺杂对碳纳米管吸附Ne原子影响的第一性原理计算

采用基于第一性原理的密度泛函理论(DFT)和局域密度近似(LDA)方法,优化计算得到碳纳米管(CNT),硼原子取代碳原子及其吸附氖原子前后系统的几何结构,能量,电子能带和态密度.结果显示,碳纳米管的能带结构与石墨的层状几何结构相似,能量的变化只在kz=0和kz=0.5平面之间沿着c轴方向出现.B原子取代C原子使价带和导带分别分裂为两个和三个能带.对Ne原子的吸附使价带能量沿着c轴方向升高并导致Fermi面附近的态密度下降.Ne原子的吸附在谷位H最稳定,顶位A其次.C-C间σ键的弯曲使Ne原子吸附在桥位b1比桥位b2处更为稳定.Ne原子在管外的吸附均为放热过程,而管内则为吸热过程.结构分析表明Ne原子对C原子有排斥作用,对B原子却具有吸引作用.B原子取代C原子的位置略凸出于CNT的管壁之外,使Ne原子的吸附能增加.     

硼原子掺杂对碳纳米管吸附Ne原子影响的第一性原理计算

采用基于第一性原理的密度泛函理论（DFT）和局域密度近似（LDA）方法,优化计算得到碳纳米管（CNT）,硼原子取代碳原子及其吸附氖原子前后系统的几何结构,能量,电子能带和态密度。结果显示,碳纳米管的能带结构与石墨的层状几何结构相似,能量的变化只在kz=0和kz=0.5平面之间沿着c轴方向出现。B原子取代C原子使价带和导带分别分裂为两个和三个能带。对Ne原子的吸附使价带能量沿着c轴方向升高并导致Fermi面附近的态密度下降。Ne原子的吸附在谷位H最稳定,顶位A其次。C-C间σ键的弯曲使Ne原子吸附在桥位b1比桥位b2处更为稳定。Ne原子在管外的吸附均为放热过程,而管内则为吸热过程。结构分析表明Ne原子对C原子有排斥作用,对B原子却具有吸引作用。B原子取代C原子的位置略凸出于CNT的管壁之外,使Ne原子的吸附能增加。     

Alloying effects and site occupancies of Re in the C14 Cr-based Laves phases: a first-principles study

First-principles calculations based upon the density functional theory have been carried out to investigate the alloying effects and site occupancies of Re in the C14 XCr₂ (X?=?Nb, Ta, Ti, Zr, Hf) Laves phases. The calculated results indicate that Re tends to facilitate and participate in the formation of the Laves phases, generating X₈Cr₁₅Re accordingly. The partial density of states and charge density di?erence were analysed to re?ect the bonding characteristics. For X₈Cr₁₅Re, the bonding between the doped Re and its nearest neighbour Cr atoms all show covalent characteristics, which contribute to the phase stability. The substitution of Re on X sites is energetically unfavourable due to the weak bonding between Re and its nearest neighbour X atoms.     

Prediction of novel ultra-incompressibility compounds TM2B (TM=Mo,W, Re and Os) by first-principles calculations

Abstract

Several novel ultra-incompressibility compounds TM₂B (TM = Mo, W, Re and Os) have been predicted by means of the first-principles calculations. Those novel compounds were assumed to have a ReB₂-type structure [P6₃/mmc space group (No.194, Z = 2), atomic sites: TM 4f (2/3, 1/3, z), B 2c (1/3, 2/3, 1/4)]. We calculated the mechanical properties of the TM₂B, and the results reveal that they exhibit brittle behaviour and mechanically stable. The hardness values are 23.8 GPa, 23.3 GPa, 26.6 GPa and 26.3 GPa for Mo₂B, W₂B, Re₂B and Os₂B, respectively, which suggests that they are hard materials. Additionally, we found that the anisotropy of Re₂B is weaker than the others. Finally, the Mo₂B has the highest Debye temperature (905.8 K), while Os₂B has the lowest Debye temperature (615.5 K). We hoped that our results can help to offer a theoretical data for future experimental work and application of TM₂B.     

Electronic and magnetic properties of beryllium oxide with 3d impurities from first-principles calculations

The ab initio VASP–PAW method with the generalized gradient approximation (GGA) has been applied to predict the electronic and magnetic properties of wurtzite-like beryllium oxide (BeO) doped with all 3d metals. Adding of 3d metal ions into BeO transforms the initial non-magnetic insulator BeO into series of magnetic and non-magnetic materials with various functional properties.     

Elastic and thermodynamic properties in CdO at high pressures from first-principles calculations

In this study, we report first-principles calculations of the elastic and thermodynamic properties for CdO in both the B1 (rocksalt) phase and B2 (cesium chloride) phase. The calculations are performed within the framework of density functional theory, using the pseudopotential plane-wave method. From the theoretical results, we find that the high pressure structural phase transition of CdO from B1 structure to B2 structure is 90.31 GPa. The calculated values are, generally speaking, in good agreement with experiments and with similar theoretical calculations. According to the quasi-harmonic Debye model, we investigate the sound velocity and Debye temperature of CdO under pressures in the range of 0<P<150 GPa.