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spring 1998 logo1998 MRS Spring Meeting & Exhibit

April 13 - 17, 1998 | San Francisco
Meeting Chairs: John A. Emerson, Ronald Gibala, Caroline A. Ross, Leo J. Schowalter

Symposium Z—Diffusion Mechanisms in Crystalline Materials


C.R.A. Catlow 
Royal Inst of Great Britain 

Nick Cowern
Philips Research Laboratories
Bldg WL-01

Diana Farkas 
Dept of MS&E 
Virginia Polytechnic Inst 
213 Holden Hall 
Blacksburg, VA 24061-0237 

Yuri Mishin
Dept of MS&E
Virginia Polytechnic Inst
213 Holden Hall
Blacksburg, VA 24061-0237

Gero Vogl 
Inst fur Materialphysik 
Univ of Vienna 
Wien, A-1090 AUSTRIA 

Symposium Support 
*Technology Modeling Associates, Inc. 
*Virginia Polytechnic Institute 

Proceedings published as Volume 527 
of the Materials Research Society 
Symposium Proceedings Series.

* Invited paper

Chairs: Yuri Mishin and Gero Vogl 
Monday Morning, April 13, 1998 
Golden Gate C1
8:30 AM *Z1.1 DIFFUSION IN METALS AND INTERMETALLIC COMPOUNDS. Helmut Mehrer, Institut für Metallforschung, Universität Münster, Münster, GERMANY. 

Diffusion processes are fundamental and ubiquitous in the art and science dealing with solid materials at elevated temperatures. A knowledge of diffusion is therefore of interest for the production of materials and for their use in technological applications. In the present paper diffusion results from our laboratory in three related areas will be discussed: The first part is devoted to solute diffusion in Al and dilute Al-SiGe alloys. 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 contrasst, non-transition elements in Al and Ge diffusion in Al-SiGe alloys show more or less normal solute diffusion behaviour. The solution seems to lie in a strong repulsive interaction between transition metals solutes and vacancies. The second part deals with intermetallic compounds. Particular attention will be devoted to recent investigations of Fe-Al and Fe-Si systems. Relevant factors for self-diffusion like the crystal structure, the state of order, the temperature and composition dependence are discussed also in connection with results from positron annihilation and Möbauer spectroscopy. Diffusion of selected foreign elements will be considered as well. An atomistic understanding of diffusion in intermetallics in terms of defect structure and diffusion mechanisms is obviously more complex than for metallic elements. There is, however, strong evidence that the defects which mediate diffusion are of vacancy type. In the final part diffusion studies on the quasicrystalline intermetallic compound Al-Pd-Mn will be presented. Diffusion of Mn, Fe and Zn has been studied in our laboratory as functions of temperature and hydrostatic pressure. In the temperature ranges investigated the quasicrystal diffusion is not significantly different from diffusion in related crystalline Al-base materials, for which a vacancy-type mechanism is generally accepted. Doc #20301 

9:00 AM Z1.2 
MOBILITY OF SELF-INTERSTITIALS IN FCC AND BCC METALS. Yuri Osetsky, Liverpool Univ, Dept. Mater. Sci. and Eng., UNITED KINGDOM; Anna Serra and Vicenc Priego, Univ. Politecnica de Catalunya, Dept. Matematica Aplicada III, Barcelona, SPAIN. 

Diffusion of self-interstitial atoms has been studied by molecular dynamics using interatomic potentials of different types. In Fe, different potentials describe different stable configurations of the self-interstitial atom. Nevertheless, the temperature dependence of the diffusion mechanism was found to be qualitatively similar for all the potentials. At low temperatures, self-interstitials migrate one-dimensionally via <111> crowdion while at high temperatures a three-dimensional mechanism via <110> dumb-bell has been observed. In Cu all the potentials reproduce the same stable configuration which is <100> dumb-bell. The migration mechanism was found to be three-dimensional random walk via <100> dumb-bell for the long ranged pair potential. In the case of the short ranged many-body potential at low temperature, a significant contribution from a two-dimensional <100> dumb-bell has been observed. At high temperature another contribution from <110> crowdion was found. The methods to simulate and to treat results for the diffusion study have been discussed. The phenomenon of the interstitial interaction with the periodic boundaries was found. The method to avoid this interaction in the study of diffusion by molecular dynamics is suggested. 

9:15 AM Z1.3 
DIFFUSION OF BORON IN COPPER BY DIRECT-EXCHANGE MECHANISM. B. Ittermann, H. Ackermann, H.-J. Stöckmann, K.-H. Ergezinger, M. Heemeier, F. Kroll, F. Mai, K. Marbach, D. Peters, G. Sulzer, Fachbereich Physik der Universität Marburg, Marburg, GERMANY. 

Using -radiation detected nuclear magnetic resonance and cross-relaxation (CR) spectroscopy we studied lattice sites and diffusion behavior of implanted 12B impurities in single-crystalline Cu. Up to about 400 K we exclusively observe interstitial B (Bi) at octahedral sites migrating via a simple interstitial mechanism. Starting at 400 K part of the diffusing Bi encounter Cu vacancies from the own implantation damage and form substitutional B (Bs). At temperatures above 600 K also the Bs becomes mobile. From combined NMR and CR informations we conclude that no other lattice defect is involved in this Bs migration. This leaves only the spontaneous direct-site exchange between Bs and neighboring Cu atoms as the underlying diffusion mechanism. Bs in Cu is, to our knowledge, the first diffusion system where the long postulated direct exchange has ever been established experimentally. 

9:30 AM Z1.4 
LOCALIZED DIFFUSIONAL MOTION OF HYDROGEN AND DEUTERIUM IN CRYSTALLINE Pd9Si2C. Karmonik1, T.J. Udovic1, Q. Huang1, J.J. Rush1, Y. Andersson2, T.B. Flanagan31 NIST Center for Neutron Research, National Institute of Standards and Technology (NIST), Gaithersburg, MD; 2 University of Uppsala, SWEDEN; 3University of Vermont, Burlington, VT. 

Using a variety of neutron scattering techniques, we have investigated the dynamics of hydrogen and deuterium in solid solution with crystalline Pd9Si2. In powder diffraction experiments, we have identified two/three different interstitial sites for D/H absorption. The sites common for hydrogen and deuterium exhibit a temperature-dependent occupancy. The corresponding vibrational modes found in inelastic measurements suggest a different dynamic behaviour for D/H in these sites. Quasielastic scattering experiments have revealed that hydrogen and deuterium undergo a localized motion between two of the sites. Results are consistent with the presence of a temperature dependent, asymmetric double-well potential. The present study is an excellent example of the complementary nature of different neutron scattering techniques for elucidating hydrogen dynamics in solid-state materials. Further experiments with higher H/D concentrations are underway to explore the nature of these sites in more detail. 

10:15 AM *Z1.5 
DIFFUSION IN METALS AND INTERMETALLIC COMPOUNDS: THE IMPACT OF AB INITIO CALCULATIONS. Manfred Fähnle, Bernd Meyer, Jens Mayer, Juan S. Oehrens, Gabriel Bester, Max-Planck-Institut für Metallforschung, Stuttgart, GERMANY. 

In ordered intermetallic compounds the mechanisms of self-diffusion are more complex than in monoatomic crystals: First, to maintain the homogeneity of the sample always various types of atomic defects must be generated simultaneously, and second, the diffusion processes must preserve the atomic order. Because experiments often yield only macroscopic information (concentrations, diffusion constants) on the collective behavior of all defects or limited microscopic information (e.g., on diffusion jump vectors rather than on diffusion paths), theory is required to determine the microscopic properties of the defects and thus to provide a basis for materials design. By a generalized grandcanonical statistical approach it is shown that the experimentally obtained effective defect formation parameters (formation energy, entropy and volume) depend in a generally complicated manner on suitably defined microscopic defect formation parameters of all possible atomic defects, and that this must be taken into account in order to avoid serious misinterpretations of experimental data. Ab initio electron theory is used to determine these microscopic parameters and to elucidate the electronic reasons for the different behavior of various materials. In a second step, possible diffusion paths are considered within the transition state theory by calculating the saddle point energies ab initio. The reliability of the ab initio electron theory is demonstrated for the elementary metals Li, Na, K, Al and Mo. Then the results on the formation and migration properties of atomic defects in B2-FeAl and in compounds with D03 structure (Fe3Al, Fe3Si, Ni3Sb) are presented and discussed from the viewpoint of the electronic structure, and the impact on the interpretation of experimental data is outlined. 

10:45 AM Z1.6 

The origin of the anomalous behaviour of the self-diffusion coefficient in BCC transition metals is investigated by performing systematic electronic-structure calculations of the vacancy parameters. The qualitative trends predicted from tight-binding models for the vacancy formation and migration energies as function of d-band filling are confirmed by quantitative Density Functional Theory studies along the 5d-series (-Hf, Ta and W). These two approaches also underline the effect of finite electron-temperature, in particular in group-VI elements (Cr, Mo, W), and of structural relaxations, which are most important in group-IV elements (-Ti, -Zr, and -Hf). The comparison with experiments support the mono-vacancy mechanism at low temperatures, with parameters having a strong dependence both on d-band filling and on temperature. 

11:00 AM *Z1.7 
FROM DIFFUSION MECHANISM TO CONFIGURATIONAL KINETICS. G. Martin, F. Soisson, M. Athenes, CEREM, Section de Recherches de Metallurgie Physique, CEA-Saclay, Gif sur Yvette, FRANCE; C. Desgranges, Framatome, Nuclear Fuel, Lyon, FRANCE. 

Configurational evolutions in alloys, resulting from thermally activated vacancy jumps, are modelled by a Monte Carlo technique using a residence time algorithm with improved efficiency. Special attention is paid to the effect of the diffusion mechanism on the kinetic path of the configuration: interesting results are found in the early stages of unmixing as well as of phase separation coupled to ordering, in the BCC structure. The effect of the non conservation of vacancies is addressed in the simplest meanfield approximation of the above model: the formation and elimination of vacancies at discrete sinks distorts the interdiffusion profiles in a way which can be rationalised with simple arguments. 

11:30 AM Z1.8 
A NEW MICROSCOPIC KINETIC APPROACH TO CALCULATION OF THE PHENOMENOLOGICAL (ONSAGER) COEFFICIENTS IN ALLOYS. Maylise Nastar1, Vladimir Yu. Dobretsov2, Georges Martin1,1CEA,Gif-sur-Yvette, FRANCE; 2Russian Research Center, Kurchatov Institute, RUSSIA. 

A new microscopic kinetic approach to calculation of the phenomenological coefficients for matter transport (sometimes called Onsager's coefficients) in alloys has been developed. This approach is based on the master equation which describes time evolution of the distribution function of a system. At equilibrium the distribution function is defined by the configurational Hamiltonian depending on physical interactions between atoms. To describe non-equilibrium states we use the same distribution function but with an effective Hamiltonian including time-dependent effective interactions completely determined from kinetic equations. The 0th-order approximation consists in taking into account only pairwise effective interactions. In this approximation the kinetic equations have been written and solved for a steady state closed to equilibrium. We give the microscopic analytical expressions of the diagonal and cross phenomenological coefficients for a homogeneous binary alloy where matter transport is controlled by the vacancy-mediated diffusion mechanism. These expressions only depend on the physical interactions, the alloy composition and the geometric correlation factor which reflects the crystallographic structure. Our approach allowed us to calculate this factor exactly. Comparison with values obtained from Monte Carlo simulations using Allnatt's time-correlation method shows quite good agreement: the relative difference is within the range 1 - 10 % both for positive and negative mixing energy except for the cross coefficients in a low concentrated alloy where it is about 20 %. To compare with the known phenomenological models we calculated within our approach the tracer diffusion coefficients and using, as an example, Manning's relations obtained new expressions for the phenomenological coefficients which turned to be different from our microscopic ones but quantitatively very closed (within 1%). 

11:45 AM Z1.9 
SIMULATION OF INTRINSIC DIFFUSION IN MULTICOMPONENT MULTIPHASE SYSTEMS. Martin Hunkel, Dietrich Bergner, TU BA Freiberg, Inst. of Physical Metallurgy, Freiberg, GERMANY. 

The simulation of diffusion in multicomponent multiphase systems is of interest for many systems which are used in industrial applications. The use of intrinsic diffusion is a practicable way for the simulation of multicomponent multiphase systems. Especially if one can use Manning's random alloy model, intrinsic diffusion is an easy way to simulate diffusion effects. A simulation model for intrinsic diffusion is presented for multicomponent multiphase systems. The model is not restricted on a certain number of components or phases. For simplicity, Manning's random alloy model with vanishing vacancy wind effect is used for the model. Then the cross terms can be neglected. The simulation routine uses equations for the fluxes, the equation of continuity and an equation for the change of volume elements due to the vacancy flux. With this model diffusion paths, concentration profiles, fluxes of the components, vancancy fluxes 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 an interface. The agreement between the simulated and the measured concentration profiles is good. The measured Kirkendall shift can be reproduced.

Chair: Diana Farkas 
Monday Afternoon, April 13, 1998 
Golden Gate C1
1:30 PM *Z2.1 
ADDRESSING ATOMISTIC MECHANISMS WITH HYDROSTATIC AND NONHYDROSTATIC STRESS. Michael J. Aziz, Division of Engineering and Applied Sciences, Harvard University, Cambridge, MA. 

Measurements of the dependence of the diffusivity on hydrostatic pressure and nonhydrostatic stress provide direct information that cannot be obtained by other measurements about the operative atomistic mechanisms. A thermodynamic formalism has been developed for illuminating the predominant point defect mechanism of self and impurity diffusion and is used to provide a rigorous basis for point defect-based interpretation of diffusion experiments in biaxially strained epitaxial thin films in the Si-Ge system. Thermodynamics connect the effects of hydrostatic pressure and biaxial stress on diffusion with point defect-related dimension changes occurring on the atomistic scale. These dimension changes can now be predicted with molecular statics or dynamics simulations and compared directly with the measured stress effects. A combination of the hydrostatic and biaxial stress dependences of the diffusivity is either +1 or -1 times the atomic volume, depending upon whether the predominant mechanism involves vacancies or interstitials. Key experiments and simulation procedures for continued progress in elucidating point defect mechanisms will be reviewed and proposed. 

2:00 PM Z2.2 
THEORY OF DIFFUSION UNDER PRESSURE. Andrei V. Nazarov, E.A. Ivanova, Dept of Materials Science, Moscow State Engineering Physics Institute, Moscow, RUSSIA; Alexandr A. Mikheev, Dept. of Metal Physics, I.P.Bardin Central Res. Institute of Ferrous Metallurgy, Moscow, RUSSIA. 

A new approach is suggested to resolve this problem. The influence of elastic stress on jump rate for atomic diffusion via the vacancy mechanism in crystals is evaluated by using statistical mechanics as was done by Glyde. As the stress fields can alter the surrounding atom configuration the height of the activation barrier is altered. The change of activation barrier is obtained to depend on the displacement field, symmetry of crystal, atom structure near the point defects and pair potential. Knowing this change it is possible to calculate the jump rate. The expression for the vacancies flow is obtained with the help of the hole gas method, by using jump rate [1]. Flow equations for binary system and interstitial solutes are obtained in a similar way. The diffusion processes under pressure are analyzed by using obtained equations. We consider some particular cases. In case of pure metals and binary alloys the expressions for migration and formation volumes are obtained and the calculation for some BCC and FCC metals is made at various temperatures. The activation volume of the interstitial solute diffusion is also calculated. 

2:15 PM Z2.3 
STRESS EFFECTS AND NON-LINEARITIES IN DIFFUSIONAL MIXING OF MULTILAYERS. Dezso Laszlo Beke, Peter Nemes, Zoltan Erdelyi, Istvan Andras Szabo, Gabor Langer, Department of Solid State Physics, L. Kossuth University, Debrecen, HUNGARY. 

In the classical treatment of diffusional mixing of binary multilayers it is usually supposed that i) the intrinsic diffusion coefficients, Di, are independent of concentration (linear description) or have only a slight concentration dependence, and they are equal (the Kirkendall shift is zero) [1] ii) the stress effects are discussed in the continuum description can be analysed for a sinusoidal concentration distribution in the discrete Fick equations. In our lecture all of these limitations will be discussed. Numerical simulations are used to show the effects of the strong concentration dependence of Di. The effect of stresses are discussed in the framework of the treatment given by Stephenson [3], which contains the effect of simultaneous stress relaxation and contains the 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 deviation from the continuum description is treated for the more realistic rectangular initial profile. The consequences of the above effects on the ln I/Io versus t profile (I is the intensity of the first small angle Bragg peak due to the concentration modulation) will be illustrated and changes in the critical wavelength - as compared to the linear treatment - will be also shown. 

2:30 PM Z2.4 
DISTRIBUTION FUNCTION FOR THE ACTIVATION VOLUME OF THE DISCONTINUOUS ORDERING REACTION IN THE Fe - 50 at. %Co ALLOY. D. Kolesnikov, M. Zenotchkin, J. Jun, W. Lojkowski, High Pressure Research Center, Warsaw, POLAND; V. Semenov, Institute of Solid State Physics, Chernogolovka, RUSSIA; E. Rabkin, TECHNION-Israel Institute of Technology, Haifa, ISRAEL; W. Gust, Institut für Metallkunde, University of Stuttgart, GERMANY. 

We have investigated the effect of pressure on the kinetics of the discontinuous ordering (DO) reaction in the Fe -50 at.% Co alloy. During the DO reaction, the disordered matrix is replaced by an ordered structure and the ordering takes place by rearrangement of atoms in the migrating interface. The annealing temperature was 670 K. Annealing was carried out under gas pressures up to 1.2 GPa. For each pressure the distribution function for the rate of the DO reaction as a function of the grain boundary was determined. Based on the distribution functions for the reaction rate at each pressure, we determined the distribution function for the activation volume. It was found that the activation volume is in the range 0 - 0.25 of the average atomic volume of the alloy. It can be concluded that the DO reaction takes place at the grain boundary by a non-vacancy mechanism. 

2:45 PM Z2.5 
DIFFUSION OF STRAIN INDUCED DEFECTS AFTER HEAVY ION IRRADIATION. G. Aggarwal, P. Sen, School of Physical Sciences, Jawaharlal Nehru University, New Delhi, INDIA. 

Ion irradiation is one of the many techniques employed for creating non-equilibrium concentration of defects. Diffusion of these defects control properties like energy of migration and greatly influence mechanical properties in a host metal. In polycrystalline metals, individual grains can be thought of as single crystals with dislocation lines providing natural interfaces. We have shown that ion irradiation causes strain across such interfaces [1]. Under high energy heavy ion irradiation defects other than point defects i.e. strain induced defects (SID) have been identified using scaling behaviour with temperature in Fe and Ni metal foils. Allowing non-equilibrium concentration of defects achieved during irradiation to come to equilibrium simulates annealing. In this process interaction of SIDs with dislocations have been established to follow  law in these metals. Evidence of sessile ring formation due to defect migration has been established and residual resistivity is observed only in F.C.C. metals. The present understanding of the processes involved will be presented in some details. 

Chair: Yuri Mishin 
Monday Afternoon, April 13, 1998 
Golden Gate C1
3:30 PM *Z3.1 
THEORY AND SIMULATION OF DIFFUSION KINETICS IN ORDERED ALLOYS AND INTERMETALLIC COMPOUNDS . Graeme E. Murch and Irina V. Belova, Department of Mechanical Engineering, the University of Newcastle, Callaghan, NSW, AUSTRALIA. 

In this paper we review recent theoretical (simulation and analytical) advances made in understanding some of the complexities of self, impurity and chemical diffusion in ordered alloys and intermetallic compounds. The review is restricted to the B2, L12A15 and DO3 structures. Within the framework of a generalized vacancy mechanism some emphasis will be put on the means to assess the limits of usefulness of specialized mechanisms such as the six jump cycle, antistructural bridge and rotational antistructural bridge mechanisms. 

4:00 PM Z3.2 

We use a semi-empirical N-body potential to calculate potential barrier heights and pre-exponential factors in an ordered Ni3 Al alloy. These quantities enter the atomic jump frequencies which characterize the mass transport in the alloys. The crystal lattice is statically relaxed by applying a conjugate-gradient algorithm under constant pressure. The normal mode analysis is actually restricted to the calculation of the determinants of the force-constants matrices in the stable and saddle positions together with the search for the minimum eigen value at the saddle position. We focused on those few relevant mechanisms which are proposed to account for the experimental findings, namely the individual vacancy jump and the jump cycles. These quantities are evaluated in a perfectly ordered system as wall as in an alloy containing a nearby antisite defect. The tendency for the latter to lower the migration enthalpy of the vacancy gives some substance to a recent interpretation of the mass transport in terms of vacancy-antisite defect pairs. 

4:15 PM Z3.3 
ROLE OF A VACANCY-ATOM INTERACTION IN MONTE-CARLO SIMULATIONS OF LONG-RANGE ORDER KINETICS. Cristian Mocuta, Emmanuel Kentzinger, Véronique Pierron-Bohnes, and Marie-Claire Cadeville, IPCMS-GEMM, Strasbourg, FRANCE. 

Monte-Carlo simulations of order-order kinetics in the ordered B2 structure of AB alloys have been performed in the frame of a Glauber formalism applied to a vacancy jump mechanism. Pair interaction energies including first and second nearest neighbours are taken into account, but we have restricted this study to the cases with: VAA=VBB=-VAB. A saddle point energy can be added depending on the jumping atom. A constant vacancy concentration of 0.015% which is temperature independent is used in the simulations. Thus our model yields the migration part of the activation energy. An effective migration energy is deduced from the Arrhenius plots of the relaxation times of the order-order kinetics. When changing the ratio V2/V1, this effective energy is found to vary linearly with the B2-A2 transition temperature which is deduced from the temperature variation of the long-range order parameter. Here the effect of an attractive interaction between the vacancies and the A atoms has been studied. We find that the predominant effect, mainly visible at low temperatures, is a preferential occupation of the B sites by the vacancies. The migration energy is slightly increased (5 to 10 percents). The B2-A2 transition temperatures are changed proportionnally to the mean interaction, averaged over all the pairs of sites in the sample. This study shows that the presence of such interaction could be partially at the origin of the asymmetries observed in some B2 aluminides: shape of the phase diagram around the stoichoimetry, different vacancy concentrations on both sublattices [1], and disymmetric variation of the activation energy for the interdiffusion with the concentration [2]. 

4:30 PM Z3.4 
MECHANISMS OF Al SELF- AND Al-SUBSTITUTING SOLUTE DIFFUSION IN Ni3Al. Sergiy Divinski*, Stefan Frank, Christian Herzig, Institut für Metallforschung, Westfalische-Wilhelms Universität, Münster, GERMANY. *Permanent address: Institute for Metal Physics, National Academy of Sciences of Ukraine, Kyiv, UKRAINE. 

Experimental investigations of Al self-diffusion in Ni3Al are to some extent restricted by a lack of relevant tracers. The temperature dependencies of the Al substituting solute diffusion of Ge, Ga, Nb, and Ti in Ni3Al (75.9 at.% Ni singe crystals) were therefore measured in our group. A theoretical approach is derived to explain the features of both Al self-diffusion and Al-substituting solute diffusion in Ni3Al. The model relies on the diffusion of Al anti-structure atoms by so-called anti-structure bridges. The approach incorporates not only the nearest-neighboring (nn) jumps of Al anti-structure atoms via the Ni sublattice, but also the two-step jumps at positions of 2nd, 3rd and 4th coordination shells. This drastically increases the Al diffusivity in comparison with only nn jumps. Although diffusion of Al and Ni atoms invokes the same vacancies on the Ni sublattice, Al atoms can diffuse even faster than Ni atoms at high temperatures. The contribution of the anti-structure bridge mechanism is shown to be different for self- and impurity diffusion and depends crucially on the anti-structure defect formation energy. The model allows to explain the observed diffusion behaviour of the Al-substituting solutes. 

4:45 PM Z3.5