In this paper recent developments of diffusion in three related areas will be reviewed: The first part is devoted to self- and solute diffusion in metals with particular emphasis on Al. Contrary to most other metallic solvents, diffusion of transition elements in Al is anomalous in several respects: diffusion is very slow, activation enthalpies, pre-exponential factors and activation volumes are unusually high. By contrast, non-transition elements in Al show more or less normal solute diffusion behaviour. The anomalous behaviour is attributed to a strong repulsive interaction between transition metal solutes and vacancies. Ab-initio calculations could help to understand this well-documented diffusion problem in detail.

In the second part very recent diffusion studies on single crystals of the Al-base quasicrystalline intermetallic compound Al-Pd-Mn will be discussed. Diffusion of Zn, Ge, Mn, Fe, Co, Pd and Au has been studied by various groups. At least in the high-temperature regime diffusion in the quasicrystal – despite some differences in detail – shows striking similarities to diffusion in Al, for which a vacancy-type mechanism is generally accepted. The activation volumes of +0.67 and +0.74 atomic volumes measured for Mn- and Zn-diffusion in Al-Pd-Mn strongly favour a vacancy mechanism as well. For the low temperature regime of Pd and Au diffusion the possibility of a phason-related mechanism is discussed.

The third part deals with recent investigations of iron-aluminides and iron-silicides for which Fe self-diffusion and diffusion of selected foreign elements (Ge in Fe–Si, In and Zn in Fe–Al) has been investigated. There is no doubt that vacancies mediate the diffusion process. Within this general mechanism a number of factors like the crystal structure, the state of order, the composition, and the type of bonding have strong influence on diffusion. Such factors are discussed also in connection with results from positron annihilation and M6ssbauer spectroscopy.

By means of statistical mechanics the relations between the effective formation energies, entropies and volumes of atomic defects in ordered compounds which may be obtained experimentally and the parameters characterizing the microscopic properties of the single defects are derived, and the microscopic parameters are determined by the ab-initio electron theory. In a second step, the migration energies for possible self-diffusion paths are calculated by the transition-state theory in combination with the ab-initio electron theory. Results are reported for B2-FeAl and for Fe3Al, Ni3Sb and Fe3Si with D03 structure, and the impact of the calculations on the interpretation of experimental data is discussed.

A single model is proposed to describe the cohesive energy and the vacancy jump frequencies as a function of the alloy configuration at the atomic level. The very same model therefore yields both equilibrium and kinetic properties, close and far away from equilibrium. The model is handled at two levels of approximation: Monte Carlo techniques and mean-field type approximations. The model yields equilibrium properties (including the transport coefficients and complex diffusion mechanisms in ordered compounds close to equilibrium) as well as the kinetic path for phase separation, with or without ordering. This allows to identify specific effects of the vacancy diffusion mechanism on the kinetic path for alloy decomposition. Here, we summarise the main results of the above approach.

Diffusion of self-interstitial atoms (SIAs) has been studied in bcc-Fe and fcc-Cu using molecular dynamics and interatomic potentials of different types. The Fe potentials describe SIA configurations of different stability. The temperature dependence of the SIA diffusion mechanisms is qualitatively similar for both potentials. At high temperature the diffusion is three-dimensional via the <110> dumbbell mechanism. The contribution of one-dimensional mechanism via the <111> crowdion increases when temperature decreases. At low temperature (<300K) the diffusion mechanism depends on the stable configuration of the SIA.

In fcc-Cu all the potentials reproduce the same stable configuration, namely the <100> dumbbell. The migration mechanism is mainly a three-dimensional random walk via this dumbbell with small contributions from the <110> crowdion at high temperature and a two-dimensional caging mechanism at low temperature.

Molecular dynamics (MD) simulation has been used to study the thermally activated mobility of clusters of self-interstitial atoms (SIAs) in Fe and Cu. Such clusters are formed in metals during irradiation with energetical particles and, according to the cascade production bias model, they play an important role in the microstructure evolution of metals under irradiation. An extensive simulation of clusters from 2 to 30 interstitials has been carried out for the temperature range ≍360-1200K using long-range interatomic pair potentials. The results show that clusters bigger than two SIAs are one-dimensionally mobile. Di-interstitials have two migration mechanisms depending on the temperature. At low temperature the mechanism is one-dimensional whereas at high temperature the probability of rotation and three-dimensional migration increases. It was found that in both metals the effective migration energy of clusters estimated via their jump frequency does not depend on the cluster size, although the cluster jump frequency decreases as the cluster size increases. The mechanism of cluster migration and problems of the treatment of one-dimensional mobility are discussed.

HRSEM analyses of copper/graphite interfaces are presented, showing a narrow solid solution zone. Atomistic simulations in the framework of the Generalized Simulated Annealing approach lead to very reasonable relaxed geometries around carbon interstitials and vacancy complexes of a Cu host, and for a Cu/graphite interface. Embedded Cluster Density Functional results indicate a charge transfer of ~1 e to carbon, mostly from the first neighbor shell, in all relaxed environments studied.

Using quasielastic neutron scattering, we have studied the dynamics of hydrogen and deuterium in crystalline Pd9Si2. For both isotopes, a localized motion was found which takes place between two energetically different sites. For the hydrogenated sample, the spatial and temporal parameters characterizing this motion are derived. The results are in agreement with neutron powder diffraction and neutron vibrational spectroscopic measurements.

Modification of materials by ion beams creates defects and defect formation processes. The implantation of nitrogen into titanium influences the hydrogen content in this metal. Hydrogen accumulation enhances hydrogenations in the implanted region. This effect may have important consequences, because excessive hydrogen accumulation generally leads to precipitating hydrids in the matrix lattice and the metal undergoes degradation of its mechanical properties. Many studies have shown that defects in metals trap light gas atoms like H or He which are solved or implanted in the sample. Therefore, the decoration of defects with these atoms is a method to trace defect concentrations and to study the trapping and detrapping mechanism. Mobile defects can be trapped at implanted atoms, at inhomogeneities or at inner surfaces like grain boundaries or interfaces of different phases. Using the slow positron beam technique the traps for hydrogen attributed to vacancy-type defects have been investigated in cp-Ti implanted with nitrogen or carbon.

The concentration of hydrogen has been detected by the 15N profiling technique (1H(15N,αγ)12C). The nitrogen and carbon content were measured by 15N(1H,αγ)12C and 13C(p,γ)14N reaction, respectively.

The interstitial carbides HoErFe15Ga2Cy (y=0,0.5,1.0,1.5,2.0) were synthesized by are melting technique and characterized by X-ray diffraction and magnetization measurements. The hexagonal Th2Ni17 type structure persisted in all compounds. Both the Curie temperature TC and unit cell volume v are found to increase monotonically with increasing carbon concentration. The unit cell volume increase of Ga substituted carbide HoErFe15Ga2C2.0 is around 6.1% compared to HoErFe17. The Curie temperature increase is mainly due to the strengthening of exchange interaction. The Ga substitution is found to not only help the formation of single phase but also enhance the uniaxial anisotropy.

A simulation model for intrinsic diffusion of multicomponent multiphase systems is presented. The model is not restricted onto a certain number of components or phases. For simplicity, Manning's random alloy model with vanishing vacancy wind effect is used. Then the cross terms of the diffusion flux can be neglected. The simulation routine uses equations for the fluxes, the equation of continuity and an equation for the change of the thickness of volume elements due to the vacancy flux. With this model diffusions paths, concentration profiles, fluxes of the components as well as marker positions can be calculated. The shift of interfaces and the growth of new phases can also be determined. The simulation results were compared with experimental data of the Cu-Fe-Ni system. Diffusion was studied in single-phase areas and across interfaces.

In classical treatments of diffusional mixing of multilayers it is usually supposed that i) the intrinsic diffiision coefficients, Di, are independent of concentration, and they are equal (the Kirkendall shift is zero) [1]; ii) the stress effects are discussed in the framework of the CahnHilliard--theory [1,2]; iii) the deviation from the continuum description can be analysed for a sinusoidal concentration distribution in the discrete Fick equations. These limitations are discussed here and numerical simulations are used to show the effects of the strong concentration dependence of Di. The role of stresses are discussed in the framework of the treatment given by Stephenson [3], which contains the effect of simultaneous stress relaxation (Kirkendall-shift) as well. For the correct description of the Kirkendall-effect a generalised analytical expression for the gradient energy term is also given. The consequences of above effects on the decay of the intensity of the first small angle Bragg peak, due to the concentration modulation, is illustrated.

We report study of recovery dynamics, followed by in-situ resistivity measurement, after 100 MeV oxygen ion irradiation in cold rolled Fe at 300K. Scaling behavior with microstructural density and temperature of sample has been used to establish stress induced defects formed during irradiation as a new type of sink. The dynamics after irradiation has been shown to be due to migration of defects to two types of sinks i.e. stress induced defect as variable sinks and internal surfaces as fixed sinks.

Theoretical investigation of interstitial atom diffusion in a binary alloy A-B with crystal lattice of CsCl type with atomic and magnetic (ferromagnetic or antiferromagnetic) order has been performed. The influence of external pressure on diffusion of hydrogen atoms has been defined. Calculations has been carried out by methods of statistical physics with application of thermodynamic functions.

For the understanding of the properties of the technically important intermetallic compounds as transition metal aluminides and silicides the understanding of atomic defect properties is pivotal. From recent positron lifetime studies high or low values for the effective vacancy formation enthalpy were found for close-packed or for more open-structured bcc type compounds, respectively, which can be well understood theoretically. In B2-FeAl the vacancy migration enthalpy could be additionally derived at high temperatures from vacancy equilibration processes. It is shown here by a study on B2-FeAl in comparison to the positron annihilation experiments that the thermal formation and migration of defects can be specifically investigated by time-dependent length-change experiments at high temperatures by the defect equilibration behavior after temperature changes. With the present data on vacancy formation and migration the wide variation of the transition-metal self-diffusivities in intermetallic compounds can be understood.

In this paper we provide an overview of the progress that has been made in the understanding of diffusion kinetics in intermetallic compounds. Both analytical theories and computer simulation are dealt with and the following ordered structures are covered: B2 (and B1), L12, A15 and DO3.

The elementary diffusion jump in crystalline solids can be determined by methods derived from nuclear physics. With these methods not only diffusion rate(s) but also diffusion vector(s), i.e. the complete diffusion mechanism can be deduced. We report on a new method for probing the elementary diffusion jumps in crystalline lattices on an atomistic scale and demonstrate its potential by a study of 57Fe diffusion in different intermetallic alloys. Compared to the results of conventional tracer (macroscopic) technique, the new method provides clear and doubtless statements concerning the direction and distance of elementary jumps. One can also determine (though less precisely than with tracer diffusion), iron diffusion coefficients.

In this paper we present a new formalism for impurity diffusion in A3B alloys taking the L12 structure. We analyse two limiting cases, where impurities remain entirely on the α sublattice and where the impurities are distributed between the two sublattices but the actual mobility is largely confined to the α sublattice. Application is made to In diffusion in Ni3Al and Al diffusion (which may itself act like an impurity on the α sublattice) in Ni3Al.

Using atomistic computer simulations, we calculate the diffusion parameters of an Ll2-ordered Ni3Al-alloy. A conjugate gradient algorithm under constant zero pressure and a semi-empirical N-body potential are applied to evaluate potential barrier heights and pre-exponential factors. We focus our investigation on those diffusion mechanisms that have been proposed to account for the experimentally observed but theoretically still disputed fast self-diffusion of Al in Ni3Al: antisite bridge mechanisms and correlated six-jump cycles. Our results demonstrate that the most competitive jumps or jump sequences involve AlNJ-antistructure atoms which are shown to play a key role in the diffusion process by either actively or passively lowering the activation energy of migration.

Diffusion of the Al-substituting elements Ga, Ge, Ti and Nb has been investigated in Ni3Al single crystals by the secondary ion mass spectrometry (SIMS). A model for the minority component diffusion by anti-structure defects has been suggested for the Ll2 structure. It involves both nearest neighbor jumps of the solute atoms on the Ni sublattice as anti-structure atoms and the formation of so-called anti-structure bridges which correspond to jumps between different sublattices. The model under consideration was shown to agree with the experimental data on the Al-substituting solute diffusion (X = Ga, Ge, Ti, Nb) in Ni3Al and it allows to explain also the observed ratio of the diffusivities DNi/DX, which may be higher and/or lower than unity in dependence on the solute and temperature.

The properties of intrinsic point defects and the self-diffusion behaviour of the constituent elements in Ni3Ga have been studied by positron annihilation, tracer diffusion and interdiffusion experiments. Thermal vacancies have been detected by positron lifetime measurements for specimens quenched from high temperatures. The vacancy formation energy is in the range between 1.7 and 1.8 eV, and is not dependent strongly on the composition. The tracer diffusion coefficients of Ni and Ga are of the same order of magnitude, and the interdiffusion coefficient is about 10 times larger than the diffusion coefficient of Ni. The diffusion in Ni3Ga has been found to satisfy the Darken-Manning equation, as expected from the model of the self-diffusion in this type of materials, where both the species of atoms are assumed to migrate primarily in the sub-lattice of the major element via the ordinary vacancy mechanism.