Exact Solution for Clustering Coefficient of Random Apollonian Networks

By means of the series method, we obtain the exact analytical solution of clustering coefficient in random Apollonian networks [Phys. Rev. E 71 （2005）046141]. Our exact analytical result is identical with the simulation, whereas in the original work, there is a deviation of about 4% between their approximate analytical result and the simulation.

Effects of Ca and Nd addition on plastic instability in extruded Mg-Mn alloy deformed under various conditions

Plastic instability, called Portevin-Le-Chatelier(PLC) effect, manifests itself as an unstable plastic flow during tensile tests of structural materials. This phenomenon has a strong influence on diverse properties, leading to unexpected vulnerabilities in the service environment.Among various magnesium-based alloys, PLC phenomenon is most prominently observed in the Mg-Mn-Nd alloy under elevated temperature and low strain rate conditions. An important aim of the study is to clarify and compare the significance of the RE and Ca addition, which are known to cause a formation of a largely weakened non-basal type texture, in the occurrence of plastic instability. Due to the PLC phenomenon, there is a risk of weakening texture and formability improvement by the addition of RE and Ca elements in Mg alloys. Based on the understanding of the role of Nd to the PLC phenomenon in Mg-Mn alloy identified in previous studies, the PLC characteristics according to alloying elements and deformation conditions were compared and analyzed. To identify the micromechanical mechanisms of the PLC phenomenon, varies in the microstructure and mechanical properties during deformation of Mg-Mn binary and Ca or Nd-containing Mg-Mn-based ternary alloys in various conditions were systemically analyzed. The addition of Ca did not show a marked PLC effect due to the formation of low number density Mn-Ca and Ca-Ca solute clusters and an unbalanced Mn:Ca ratio. In contrast, the addition of Nd leads to the formation of a higher number density of Nd-Nd and Mn-Nd solute clusters than that of Ca-Ca and Mn-Ca solute clusters of the Mg-Mn-Ca alloy, resulting in a stable solute-dislocation interaction atmosphere under specific ranges of deformation temperature and strain rate. The deformation in the regime of PLC phenomenon, results in a decrease in ductility and an increase in strength, despite deformation at elevated temperatures with maintaining the weakened texture.

Possibility and stabilizing effect of Mo clusters in the Ni-based single-crystal superalloy

Nickel-based single-crystal superalloys are crucial materials for the preparation of aero-engine turbine blades. Many solute elements are added to superalloys for strengthening. However, the relationship between the clustering behavior of solute atoms and the properties of nickel-based single-crystal superalloys is still unclear. Herein, we conduct first-principles calculations onγ phases with Mo-Mo and Mo-Mo-Ru clusters to reveal the possibility and stabilizing mechanism of solute clusters. Introducing Mo lowers the total energy, binding energy, and formation energy of the γ phase due to the replacement of weak Ni-Ni interaction with strong Mo-Ni bonding. Note that the γ phase containing the Mo-Mo cluster is more stable than that containing a Mo single atom, possibly owing to a wide affecting range. The Ru atom added to the γ phase can further boost system stability, and it tends to form a Mo-Mo-Ru cluster. The stabilizing impact of the Mo-Mo-Ru cluster is demonstrated to be the replacement of weak Ni-Mo interaction by the strong Ru-Mo interaction, which may be derived from the enhanced d-orbital hybridization.

Solute clusters-promoted strength-ductility synergy in Al-Sc alloy

Sc solute clusters with a high number density were produced in an Al-0.3 wt.%Sc alloy when aged at250℃,while fine Al_(3)Sc precipitates were predominantly formed in the same alloy aged at 300℃.The alloy strengthened by Sc solute clusters displayed higher yield strength and simultaneously greater ductility than its counterpart strengthened by Al_(3)Sc precipitates.This clearly demonstrates a superior strengthductility synergy promoted by the Sc solute clusters in Al-Sc alloys.The effects of Al_(3)Sc precipitates and Sc solute clusters on ductility were discussed in comparison by using a micromechanics fracture model.Since the Sc clusters were stabilized at 250℃,the Al-Sc alloys strengthened by Sc solute clusters should find extensive application fields within a wide temperature range,due to their high temperature resistance.

Influence of electric field on the quenched-in vacancy and solute clustering during early stage ageing of Al-Cu alloy

The effects of electric field on the evolution of excess quenched-in vacancy as well as solute clustering in Al-4wt%Cu alloy, and on the vacancy migration and formation enthalpy of pure aluminum were investigated, using positron annihilation lifetime spectroscopy, high-angle annular dark-field scanning transmission electron microscopy, transmission electron microscopy, hardness measurement and four-probe electrical resistivity measurement. The results showed that the electric field improved age hardening response obviously and postponed the decay of excess vacancies for 30rain during the early stage ageing of Al-4wt%Cu alloy. A large number of 2-4nm GP zones with dense distribution were observed after 1 min ageing with an electric field applied. The electric field-assisted-aged sample owned a lower coarsening rate of GP zone, which was about three fifths of that in the aged sample without an electric field, from 1 min to 120 rain ageing. The electric field contributed 8% increase of the vacancy migration enthalpy （0.663 ±0.021 eV） of pure Al, comparing with that （0.611 ±0.023 eV） of pure Al without an electric field. The increase of vacancy migration enthalpy, induced by the electric field, was responsible for the difference on evolution of quenched-in vacancy, rapid solute clustering and age hardening improvement during the early stage ageing of Al-4wt%Cu alloy.

Clustering and precipitation in Al-Mg-Si alloys during linear heating

Differential scanning calorimetry(DSC) is a technique extensively applied to analyse precipitation phenomena in Al-Mg-Si alloys, yet the processes occurring during non-isothermal DSC heating, in particular the formation of clusters in the early stage and their evolution at higher temperatures, remain obscure. Here, we carry out experiments not only to measure heat(via DSC) but also to measure hardness,positron lifetime, electrical resistivity and microstructure of an Al-Mg-Si alloy heated at 3 different rates.Electrical resistivity is measured in situ, the other properties after interrupting the heating process. It is demonstrated that the precipitation process during heating can be divided into various stages, with transition temperatures depending on the heating rate, but the relative behavior of the various measured quantities is connected in the same way. Quenched-in excess vacancies are found to play an important role in cluster formation at lower temperatures, which explains the seeming peculiarity that linear heating at lower temperatures can lead to stronger clustering than isothermal ageing at a higher temperature.These trends are well simulated using a recently developed precipitation model. New aspects about the evolution of these clusters at higher temperatures are revealed by correlating the different measured properties. The methodology applied here could also be extended to investigating more complex nonisothermal heat treatments.