Fan-type Structures Research Articles

The Mechanism of Grain Boundary Serration and Fan-Type Structure Formation in Ni-Based Superalloys

A model of discontinuous precipitation of γ′ phase at grain boundaries (GBs) in polycrystalline Ni-based superalloys during continuous cooling from supersolvus temperature was developed. The model calculates the size and γ′ phase fraction in GB precipitates as a function of cooling rate and GB mobility. The model is based on the classical mechanism of diffusion-controlled precipitation. It considers fast diffusion of γ′-forming elements along the GB and the motion of the GBs under driving force induced by alloy decomposition. The model predicts either discrete GB gamma-prime particles and GB serration or the growth of fan-type structures depending on the cooling rate and GB mobility. We conclude from the model predictions that the GB mobility is the key factor controlling the type and morphology of GB precipitates. High GB mobility results in formation of fan-type structures, while the lower GB mobility leads to GB serration. The predicted dependence of the size of GB precipitates on the cooling rate is in good agreement with the experimental observations.

Effect of Ti and Al on microstructure and partitioning behavior of alloying elements in Ni-based powder metallurgy superalloys

The microstructure and partitioning behaviors of alloying elements in the γ and γ′ phases in Ni-based powder metallurgy superalloys with different Ti and Al contents were investigated. The results showed that Ti and Al were mainly enriched in the γ′ phase, partially partitioned in the γ matrix, and slightly distributed in the carbides. Different Ti and Al contents in various alloys influenced the composition and amount of MC carbides but did not influence the MC carbides’ morphology. With increasing Ti and Al contents, γ + γ′ fan-type structures formed at the grain boundary, eventually resulting in a coarsened γ′ phase. In addition, the morphology of the secondary γ′ phase transformed from nearly spherical to cuboidal. The saturation degrees of Cr, Co, and Mo in the γ matrix were substantially improved with increasing Ti and Al contents.

Probing into the isomers and bonding natures of PuC6

Isomers, bonding characters and spectra of the PuC6 were investigated with DFT and ab initio calculations. A fan-type structure with septet spin multiplicity was found to have the lowest energy through extensive structure research. The energy orders of low-lying isomers were assessed with different DFT functionals and CCSD (T). The main ionic natures of Pu-C bonds derived from electrostatic interaction were revealed by QTAIM. Meanwhile, the quantum-exchange correlation from the directly orbital overlaps of Pu and C also play a significant role in stabilizing. IR and UV-vis spectra were simulated to provide spectra information for the structural identification of PuC6 in future experiments.

Influence of sub-solvus solution heat treatment on γ′ morphological instability in a new Ni–Cr–Co-based powder metallurgy superalloy

Abstract The influence of the sub-solvus solution heat treatment on the microstructure, especially the γ′ morphology (γ′ fan-type structure), and microhardness of a new Ni–Cr–Co-based powder metallurgy superalloy was studied by means of field emission scanning electron microscopy (FESEM) and microhardness testing. The results show that sub-solvus solution heat treatment changes the microstructure of an as-forged alloy. It makes large primary γ′ phases at grain boundaries smaller and the distribution of secondary γ′ phases in the interior of the grains more homogeneous. Moreover, the grain boundaries widen because of the supplementary precipitate. The sub-solvus solution heat treatment before the super-solvus solution heat treatment does not change nucleation sites of the γ′ fan-type structures which precipitate during the super-solvus solution heat treatment. However, it influences the morphology of γ′ fan-type structures. Length distribution of the secondary γ′ dendrites in fan-type structures changes from a bimodal to a unimodal distribution, which means the lengths of the secondary γ′ dendrites become more uniform. Applying a sub-solvus solution heat treatment after the super-solvus solution heat treatment causes the secondary γ′ dendrites to be broken off in the fan-type structures and a refinement of the γ′ phases, and this improves stability of the γ′ phases.

Formation mechanism and coarsening behavior of fan-type structures in a new Ni–Cr–Co-based powder metallurgy superalloy

The formation mechanism and coarsening behavior of fan-type structures in a new Ni–Cr–Co-based powder metallurgy superalloy were investigated by means of field scanning electron microscope, transmission electron microscope, electron backscattered diffraction, and differential scanning calorimetry. The results show that the fan-type structures consist of finger-shaped γ′ dendrites and γ matrix between them. They nucleate in the chemical segregation regions on grain boundaries and grow by diffusion. There are three types of solute atoms flow: (a) rapid diffusion along grain boundary; (b) the diffusion from supersaturated γ matrix to fan-type γ′ phases; and (c) short-distance diffusion from the previous formed γ′ phases at high temperature to γ′ phases formed at low temperature within the branches of fan-type structures. These γ′ dendrites are perpendicular to grain boundaries and grow asymmetrically, resulting in grain boundary serration. In addition, the fan-type structures coarsen within the γ′ depletion zone after the standard aging treatment.

Three-level control systems for ecological-economic objects with fan structure

Mathematical formalization of control systems for ecological-economic objects with fan-type organizational structure is suggested. These systems are considered using three-level model of superficial water quality control systems as the corresponding example. The methods of compulsion and impetus are involved as the ones of hierarchical control. A certain algorithm to evaluate the solution is developed; some natural examples are provided and the obtained results are analyzed.

Small iron doped carbon clusters: A comparison with early and late first-row transition metal doped clusters

A systematic study of the three lowest-lying structures, namely, linear, fan, and cyclic, of neutral FeC(n) (n = 1-8) clusters on the singlet, triplet, quintet, and septet potential energy surfaces has been carried out. Predictions for their electronic energies, rotational constants, dipole moments, and vibrational frequencies have been made using the B3LYP method in conjunction with the 6-311+G(d) basis set. Triplet or quintet states are found as the lowest-lying ones for FeC(n) clusters, and the septet states are found more stable than the singlet ones. The incremental binding energies show an even-odd parity effect, with n-even clusters being more stable than the n-odd ones in the linear and fan clusters, whereas a decrease with n is found for cyclic ones. The most stable isomers for FeC(n) clusters correspond to a fan-type structure for n < or = 4, whereas for n > or = 6 cyclic structures are the most stable. Only in the case of n = 5 the most stable isomer is the linear structure. Comparing the results of FeC(n) clusters with the previously studied TMC(n) (TM = Sc, Ti, V, Co, and Zn) systems, we can see that, as it should be expected, iron doped carbon clusters present an intermediate behavior between early and late first-row transition metal doped clusters.

On the formation of serrated grain boundaries and fan type structures in an advanced polycrystalline nickel-base superalloy

The formation of serrated grain boundaries and fan-type structures in an advanced polycrystalline nickel-base superalloy has been extensively studied and linked to the thermal history. The development of grain boundary serrations has been quantitatively linked to the cooling rate from the solution heat treatment temperature. Slower cooling rates were found to result in more convoluted grain boundaries formed as a result of impingement of growing secondary γ′. Subtle differences were also noted in the γ′ distributions in the vicinities of the grain boundaries, in particular they exhibit differences in size, morphology and chemistry as a function of location within the grain, all of which are reported in the paper. Fan-type structures were found to form in the alloy, irrespective of the cooling rate employed, although their size and volume fraction increased with a decrease in cooling rate. The presence of these structures is shown to impact upon the total length of grain boundary and the degree of serration. The fan-type structures exhibit a typical dendritic morphology and were found to nucleate on minor phases present within the alloy.

Molecular structure and thermodynamic properties of the gaseous ThC 2 and ThC 4 species

The geometry and vibrations of the ThC 2 and ThC 4 molecules have been derived from quantum chemical calculations. The results indicate an asymmetric L-type structure for ThC 2 and a planar fan-type structure for ThC 4, in contrast to the linear structures assumed earlier. The entropies of ThC 2 and ThC 4 calculated from the results are compared to ‘experimental’ values derived from existing vaporisation studies.

Small Carbon Clusters Doped with Vanadium Metal: A Density Functional Study of VCn (n = 1-8).

A theoretical study of the different isomers of neutral VCn (n = 1-8) clusters has been carried out. Predictions for their electronic energies, rotational constants, dipole moments, and vibrational frequencies have been made using the B3LYP method with different basis sets. For linear and cyclic VCn clusters, the lowest-lying states correspond to quartet states, with the only exception being VC, which has a (2)Δ ground state. In the fan-type structures, the electronic ground state is found to be a quartet state for even n values, whereas for odd n values, the ground state is a doublet for VC3 and VC5 and a quartet for VC7. From the incremental binding energies, we can deduce an even-odd parity effect, with n-even clusters being more stable than n-odd ones in the linear and fan clusters. It was also found that neutral VCn clusters with n ≤ 6 prefer fan structures over linear and cyclic isomers, whereas cyclic ground states are predicted for the clusters with n > 6.

Molecular Dynamics Simulations of Formation of Metal-Containing Fullerene.

The growth process of metal-containing fullerene was studied using the molecular dynamics method. As for metalcontaining fullerene, only the metal atoms such as La, Y or Sc are experimentally assigned to be contained inside the carbon cage. In this paper, the difference of growth process and structures of metal-attached carbon clusters were examined using lanthanum and nickel as the additional metal atoms to clarify the effect of the metal atoms. In order to model the potential function between carbon and metal atoms appropriate for the classical MD simulation, the binding energy and charge state of various forms of small clusters MCn (M: La,Ni; n =1-3) were calculated with the density functional theory. A multi-body potential function was constructed as a function of coordinate number of a scandium atom. Here, the Coulomb term and the Morse-type term were separately described considering the large charge transfer from a lanthanum atom to carbon atoms. By using the potential function, the clustering process starting from 500 isolated carbon atoms and 5 metal atoms in a 342 A cubic cell was simulated under the controlled temperature condition at Tc = 3000 K, and the growth history of metal-attached clusters was studied in detail. Figure A-1 shows the growth process of La attached clusters obtained in the simulation. The fan-type structure and mono-cyclic or bi-cyclic rings were reproduced around the metal atom for LaCn (n<20). An open cap structure surrounding the La atom was formed for LaCn (20<n<50) due to the strong Coulomb interaction, and that resulted in the lanthanum-containing caged cluster. When Ni atoms were applied as shown in Figure A-2, the structures of small clusters up to NiC n (n<20) were similar to LaCn (n<20), while tangled-poly-cyclic structures and random cage were dominant for NiCn (20<n<50). The nickel atom attached on one face of the caged structure, and could not stay stably inside the carbon cage structure.

Bifurcation phenomena in second-order digital filter with saturation-type adder overflow characteristic

An analysis of the dynamic behavior of a second-order digital filter operating outside the region of absolute stability in the case of saturation nonlinearity of the accumulator is presented. Bifurcation phenomena associated with changes of one of the parameters of the filter's linear part are investigated. On the basis of a numerical study, it is conjectured that systems trajectories become chaotic for some parameter ranges. Several interesting bifurcation patterns have been revealed-including devil's staircase and self-similar, fan-type structures. >