Wolfgang Püschl

Long-range ordering in B2 FeAl: a resistometric study

Abstract Changes in the degree of order have been studied by residual electrical resistivity measurement (REST) in B2 long-range ordered Fe–44.8 at.% Al during isochronal and isothermal step-annealing temperature treatment. Restricted atomic mobility starts already below about 500 K. Assuming the vacancy concentration to remain constant over an extended temperature range, as known from the literature, the complicated variations of resistivity with temperature can be explained by two regimes of ordering: a fast local ordering due to the restricted motion of the vacancies at low temperatures and a very slow global adjustment of long-range order (LRO) within the total sample volume. Kinetic parameters are determined from the detailed process analysis of the ordering kinetics during isothermal small-step annealing. Using these parameters, the results of isochronal annealing treatment can be calculated with a very good correspondence to experiment.

Energetics of point defect formation in Ni3Al

Abstract Vacancy and anti-site defect formation energies in L1 2 -ordered Ni 3 Al are calculated by ab initio approaches. Based on a statistical-thermodynamic model the thermodynamic activities of both components are derived as a function of temperature and composition. Comparison with measured activities demonstrates the high reliability of the ab initio approach to defect formation.

Changes of microstructure during post-deformation annealing in α-CuAl

It is well investigated that concentrated {alpha}-CuAl shows effects of short-range order (SRO) which for thermodynamical reasons are a function of temperature. In most cases, however, it was tried rather to carefully avoid complications by a defect structure than to study SRO-effects in the presence of a heavily defected microstructure after plastic deformation. Depending on the temperature ranges of recovery and recrystallization, defect annihilation of a cold-worked alloy may occur simultaneously with changes in the degree of SRO during an annealing treatment. In previous works on {alpha}-AgZn it has been shown that these processes of defect recovery and SRO could be separated. For the technical application of a material, but also as a basis for the separation of SRO-effects from effects of defect annealing it is of great interest to investigate the microstructural changes during post-deformation annealing. In a preliminary study on the interaction between SRO and post-deformation annealing certain stages of defect annealing could be detected. In the present work the authors concentrate on the interpretation of the microstructure of these stages as studied by TEM.

Homo or hetero? How vacancy motion brings discreteness into phase transformations

Abstract In the study of phase transformations experimental results are often interpreted in terms of the concept of homogeneous transformation, that is, the phase change involves a continuous amplification of short wavelength (ordering) or long wavelength (clustering) fluctuations in an appropriate order parameter. This quasi-continuum approach suggests that the system is not partitioned into transformed and untransformed regions but the order parameter proceeds towards equilibrium uniformly in all microvolumes of the system. However, defect-mediated diffusion (vacancy mechanism) involving local atomic jump processes during the early stages of transformation kinetics can produce discrete regions within which the order parameter has changed significantly embedded in an unperturbed matrix. An estimate of this ‘graininess’ is calculated in terms of vacancy diffusion parameters which allows us to distinguish between heterogeneous and homogeneous regimes of transformation processes in the alloy.

Changes in the Degree of LRO in B2-Ordered Intermetallic FeAl

Changes in the degree of long-range order (LRO) have been investigated in B2-ordered intermetallicFe-44.8at%Al by electrical resistivity measurement (resistometry). Order variations were observed during isochronal annealing for different states of initial thermal treatment. A complicated behaviour of resistivity changes with temperature is observed when starting with a small degree of disorder. Very slight re-ordering is found already at about 470K and is surprisingly followed by a slight disordering above 530K. Only for very long annealing times the expected ordering tendency is observed in this temperature range. Above 710K re-ordering is continued and reversible equilibrium changes of order with temperature are observed above 830K.

Looking into details of atom kinetics in intermetallics

Information on the atom jump processes during the establishment and destruction of long-range order can be gained from measurement of residual electrical resistivity (REST). By its nature this very sensitive method yields an integral signal, so theoretical efforts are mandatory to properly understand how the single atom jumps work together in generating it. As a valuable approach we report on Monte Carlo simulations of atom kinetics which process the individual jumps into macroscopic configurational changes. In order to create a more reliable quantitative basis for individual jump frequencies we propose ab initio calculations of defect energies and migration profiles, a method which has become increasingly accessible in recent years. When experimental investigation is enlightened by combining these two theoretical methods, we expect deep insight into the hierarchy of atomic movement during changes of the ordered state. First steps towards such an ideal program are discussed. An outlook is given how the theoretical methods described offer structural and kinetic information on various scales and in different systems.

Point Defect Energies in L12-Ordered Ni3Al

Experimental investigation of order-order relaxations in Ni3Al by residual resistometry yielded a very high ordering activation energy of about 4.6eV being in correspondence with tracer experiments, where the tracer atom substitutes the Al-atom. Qualitatively, this might be interpreted by breaking of bonds to the 12 surrounding Ni nearest neighbour atoms of the ordered Ll2-lattice. For the purpose of a more fundamental understanding the properties of vacancies and antisites in Ni3Al were studied by means of ab-initio calculations for supercells. Formation energies for Ni- and Al-vacancies were derived using a grandcanonical ensemble. Further, vacancy migration energies were determined successively displacing atoms from their equilibrium position to a vacant nearest neighbour position. Correlated jumps during a jump cycle were also taken into account.

Competition Between SRO and LRO in CuAu 3

Ordering in CuAu{sub 3}, was investigated by residual resistivity and X-ray scattering. L1{sub 2} long-range ordering (LRO) in this alloy is quite sluggish, therefore for low quenching temperatures and sufficiently short annealing times only effects of short-range order (SRO) are observed. With increasing quenching temperature and/or increasing annealing time evolution of LRO was observed by both residual resistometry and X-ray scattering. From the resistivity measurements information can be gained on the boundaries of the order-disorder two-phase field. An analysis of SRO-relaxation yields an ordering activation energy of 2.1 {+-} 0.1 eV.

Saddle Point Energies from Ab Initio Jump Profiles in MC Simulation of Order Kinetics in Intermetallics.

Kinetic Monte Carlo (KMC) simulation is a valuable tool to investigate configu-ration changes in intermetallic compounds. The elementary process is the jump of an atomfrom a lattice site to a neighboring vacancy. In classical transition state theory the jump ratecontains the energy difference between the original equilibrium state and the saddle point (=transition) state. In traditional KMC the saddle point has mostly received rather careless treat-ment, setting it constant or relating it to the type of jumping atom. In the present work, saddlepoint heights were considered explicitly. Taking L12 ordered Ni3Al as an example, jump energyprofiles for various atom environments were calculated ab initio in relaxed configurations ofa 3x3x3 supercell, employing the Nudged Elastic Band method where necessary. From theseresults, effective ’pure’ saddle point heights were extracted. To show the effect on kinetics,simulations of order-order transitions were done with jump probabilities based on these results.When compared to the old assumption of constant saddle point heights, both overall kineticsand detailed jump statistics result considerably changed.

Short-range order kinetics during post-deformation annealing in different binary alloys☆

Abstract Alloys of Cu–15at.% Al, Ag–21at.% Zn and Au–14at.% Fe are compared with respect to short-range ordering in the recrystallized state and after high deformation by cold-rolling, respectively. Additional information on the defect annealing behaviour is gained from an investigation of microhardness and by microscopy.