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Internal interfaces in metals
Materials Science and Engineering, 83 (1986) 205-211
205
CHAPTER 4 INTERNAL INTERFACES IN METALS W° A. T. CLARK
Department of Metallurgical Engineering, The Ohio State University, 116 West 19th Avenue, Columbus, OH 43210-1179 (U.S.A.) C. J. McMAHON, JR.
Department of Materials Science and Engineering, School of Engineering and Applied Science, University of Pennsylvania, Philadelphia, PA 19104 (U.S.A.) R. H. WAGONER
Department of Metallurgical Engineering, The Ohio State University, 116 West 19th Avenue, Columbus, OH 43210-1179 (U.S.A.) R. P. WEI
Department of Mechanical Engineering and Mechanics, Lehigh University, Bethlehem, PA 18015 (U.S.A.)
1. INTRODUCTION
Internal interfaces in metals control many of their most important thermomechanical properties, such as ductility, high temperature creep behavior and susceptibility to intergranular fracture resulting from the segregation of impurities. An example of the latter is found in high strength alloys (temper embrittlement) and in the presence of hydrogen (hydrogen embrittlement) and is an important technological problem. Relatively little is known about the influence of the atomic structure of interfaces on these properties, although considerable progress has been made in several areas in recent years in understanding the crystallography of interfacial structure (see for example ref. 1). Experimental techniques for observing and determining interfacial structure and chemistry have also improved significantly during the last 10 years, to the point where atomic level imaging in the transmission electron microscope can reveal the presence of both line defects and solute atoms in interfaces [ 2], and surface chemical techniques such as Auger electron spectroscopy (AES) can detect submonolayer surface coatings [ 3 ]. In parallel with these developments, there has also been considerable progress in improv-
ing the speed and sophistication of first-principles computer calculations of the atomistic and electronic structure of interfaces [4]. These advances have in some cases only been made possible by the availability of computers capable of carrying o u t with reasonable speed the large numerical calculations necessary to model even very small and simple clusters of atoms. Even so, considerable controversy still exists as to the relevance of such computations to actual materials, and also a b o u t the choice of c o m p u t a t i o n a l model used. None of these calculations of the theoretical strength of bicrystals has been systematically correlated with experimental measurements, but the rapid developments in computing capacity and experimental techniques which have occurred over the last few years offer some hope that such essential comparisons m a y become feasible, although not in the immediate future. Just as in atomistic calculations of boundary structure, descriptions of the continuum behavior at interfaces during intergranular fracture are also increasing in sophistication and can more readily be coupled with experimental results obtained under carefully controlled experimental conditions. As an example, the calculated thermodynamic strength of interfaces [ 5] can be compared with measured b o u n d a r y adhesion, although these calcula© Elsevier Sequoia/Printed in The Netherlands
206 tions, again, take no account of the defect structure and unique character of each individual interface. Such research carried out on intergranular fracture of polycrystals has yielded a wealth of information on the types of material and conditions in which it occurs. These generally involve the presence of some impurity or segregated solute which weakens the interface, although recent studies employing AES [6] have indicated, however, that some polycrystals m a y have inherently weak grain boundaries. It therefore appears certain that, with or without embrittling impurities, intergranular strength is closely related to grain boundary structure. Although fracture studies on polycrystals remain useful for elucidating the various factors that contribute to interfacial fracture, t h e y are not suitable for quantifying the effects of the structure of individual interfaces, since that differs significantly from boundary to boundary, even within the same polycrystal. The properties considered above all depend on the detailed atomistic nature of the structure of individual interfaces. This is dictated in part by the crystallography of the boundary and the nature of the atomic bonding across it, but it is also strongly affected by the presence of impurities which segregate preferentially to the interface. These impurities m a y actually enhance the strength of the boundary (boron in steels is an example) but more c o m m o n l y have a deleterious effect on adhesion; in some cases, this adverse effect is catastrophic, causing severe embrittlement and premature failure. Hydrogen is a particularly virulent embrittling agent, causing cracking along m a n y interfaces, principally by the rupture of m e t a l - h y d r o g e n - m e t a l bonds [7, 8]. It is now widely accepted as the mechanism of cracking in stress corrosion and corrosion fatigue and thus argues for greater attention. Considerations of impurity segregation can be divided into three parts: (i) the processes that supply solute to the internal interfaces in the material, (ii) the interaction of the solute with the structure of the interface, and its partition amongst the various microstructural elements, and (iii) the embrittlement process itself. These processes, occurring consecutively or concurrently, govern the rate of crack growth and its response to changes in environmental, metallurgical and loading con-
ditions. Useful understanding of the first two parts has been and is being developed through the improved understanding of the crystallography and atomic structure of interfaces, through the types of approach referred to above, and through interactions between researchers in fracture mechanics and surface chemistry (see for example refs. 9-16). A more complete understanding of intergranular fracture and hydrogen embrittlement has been hampered, however, by the paucity of information on the nature of metal-metal and m e t a l - h y d r o g e n - m e t a l bonds, particularly at internal interfaces. There is a need in this area for improved computer modeling, and the development of a broader understanding will require close interactions between investigators in metallurgy, materials science, solid state physics and fracture mechanics, together with surface chemists and others. Recent advances in all the fields described above hold the promise of significant advances in quantitative understanding of the role that interfaces play in the adhesion and decohesion of polycrystalline materials. In the following sections an outline of the potential and problems in each of these areas is given, some of the key issues to be addressed are identified and suggestions made as to the facilities necessary to accomplish these aims.
2. BACKGROUND
2.1. Characterization of interfacial structure It has been demonstrated clearly that certain grain boundaries, with misorientations close to certain special coincidence site lattice (CSL) [ 17] values, exhibit regular arrays of linear defects identifiable as grain boundary dislocations. These grain boundary dislocations have been described as necessary to conserve the low energy of the CSL orientation, in a manner analogous to small-angle tilt and twist boundaries in single crystals. In some cases, transmission electron microscopy (TEM) experiments have verified this hypothesis and found that the dislocations have Burgers vectors derived from the DSC lattice [18] and are different from one CSL to another. In general, grain boundary dislocations are distinct from crystal lattice dislocations found in the crystal interior in that t h e y have, in
207 addition to their Burgers vector, a geometrically necessary step associated with their core. This step can be used to describe mechanisms of coupled grain b o u n d r y sliding and migration which involve the motion of grain boundary dislocations across an interface [ 19]. An example of this is the growth of an annealing twin boundary in f.c.c, metals by the passage of (a/6)(112) Shockley partials across alternate {111} twin planes. This twin boundary can also be described as a E = 3 CSL boundary, and the (a/6)(112> Shockley partial is one of the DSC vectors for this system. It is the displacement of the twin plane by ½(111), the step at the core of the Shockley partial when it is in the twin boundary, which causes the twin to grow. However, partly because of the difficulty of the experimental work involved, and partly because of the wide variety of CSLs and crystal systems involved, only limited systematic attempts have been made to determine the generality of this process to all CSLs. Experimental observations which extend this concept to the wider field of interphase boundaries are even rarer, although even this limited evidence suggests that it has wide applicability (see for example ref. 20). There are many other processes occurring at grain boundaries in which grain boundary dislocations can be expected, and in some cases have already been observed, to play an important role. These include solute absorption, grain boundary diffusion, diffusioninduced boundary migration, precipitation of second phases and propagation of crystalline strain through boundaries by dislocations (see ref. 1 for reviews on some of these phenomena). Almost no experimental information is available on the relationship between grain boundary structure and these p h e n o m e n a on the atomic scale, despite the fact that macroscopic bicrystal experiments carried o u t several years ago indicated that near-CSL boundaries did have, for example, different diffusion coefficients and migration rates when compared with boundaries far from a low E CSL orientation [21]. These earlier experiments were n o t able, however, to examine the boundary structure, nor could they investigate the variation in these parameters as a function of an orientation close to an exact CSL (i.e. to a precision of +0.1 °). This order of precision is almost essential if the influence of grain boundary structure on any one property is to
be measured quantitatively as a function of orientation.
2.2. Continuum and atomic contributions to macroscopic adhesion at crystalline interfaces Macroscopic adhesion at crystalline interfaces depends intimately on the propagation and nucleation of cracks at or near the interface. Much progress has been made in deriving elastic-plastic solutions for cracks and other crystal defects. These continuum-based solutions may be quasi-analytic in form or m a y involve detailed numerical solutions based on finite element modeling and m a y include continuum descriptions of crystalline defects, such as dislocations. Although these models are capable of arriving at the proper solution forms, they all suffer from a lack of fundamental knowledge of the atomic mechanisms which determine the critical propagation events. Examples of these fundamental events include bond rupture, incremental crack advance, dislocation nucleation and incremental dislocation motion. Activation and dissipation energies for these events, crucial for quantitative macroscopic predictions, can only be obtained b y reference to atomic bonding models. Until recently, the only viable m e t h o d for estimating defect core structures and energies was based on the use of atomic pair potentials [4] and central-force models. The accuracy of such models is the subject of great current controversy, particularly for problems involving large local density changes from the bulk crystal, as near a defect core. The choice of potential is largely arbitrary, b u t widely differing structures and energies are obtained [ 5] depending on the exact form. In general, no reliable m e t h o d for obtaining t o t a l energies based on these methods is available, although arguments on the validity of relative energies have been proposed. For these reasons, pair potential calculations, at least in their present state, offer little promise of providing the activation energy information needed for the fundamental crystal mechanisms. Quantum mechanical calculations of metal electronic structures at planar surfaces and interfaces have begun to appear, including total energy and adhesion (microscopically reversible) calculations [ 2 2 - 2 4 ] . The model is based on self-consistent solutions of SchrSdinger's equation and can provide first-prin-
208 ciples answers to energies, atomic structures etc. The major impediment to widespread use of the method lies in the extensive computer times required for even "small" problems. Periodic boundary conditions are generally employed and at the present only 50-100 atoms can be considered in the repeat "cell". Nonetheless, the addition of these ab initio calculations to the existing arsenal holds the most promise for advancing the fundamental continuum and crystalline descriptions of fracture, decohesion and defect motion. Because of computer time and storage limitations, a hybrid approach will be required to undertake many problems of practical importance. Specifically, various spatial regions of a crystal may need to be described elastically, plastically and by discrete defects while minimizing the region described quantum mechanically. It is hoped that this approach will allow treatment of a broad range of problems inaccessible by any single approach. Even with these improve: ments, many larger-scale problems will require order-of-magnitude improvements in computational efficiency.
2.3. Intergranular fracture Decades of research on intergranular fracture of polycrystals have yielded a wealth of information on the types of material and the conditions in which it occurs. It generally involves the presence of some impurity or segregated solute which weakens the interface (see for example ref. 3), but recent studies employing AES have indicated that some polycrystals may have inherently weak grain boundaries. With or without embrittling impurities, it appears certain that intergranular strength is closely related to grain boundary structure. Although studies on polycrystals remain extremely useful for the study of various factors which contribute to interfacial fracture, they are inherently unable to deal with the effect of structure, since that is rarely constant even over one intergranular facet. In order to obtain a complete fundamental understanding of interfacial adhesion, it will be necessary to carry out fracture studies on bicrystals of very carefully controlled and characterized structure and composition. Such studies will require the commitment of much time and special facilities for specimen preparation and will therefore have to be limited to carefully selected materials which
have already been thoroughly investigated in polycrystalline form. They should also be amenable to a wide variety of experimental and theoretical approaches and should be sufficiently strong, with regard to plasticity, that stresses high enough to cause brittle fracture can be attained. There is a class of brittle interfacial fracture in which the embrittling species must diffuse to the site of decohesion. This results in a large temperature dependence and, in many cases, quasi-static crack growth. Perhaps the best-known example of this is hydrogeninduced cracking of steel. However, it has recently been established that other embrittling species besides hydrogen can produce diffusion-controlled brittle fracture. The specific case studied so far involved embrittling impurities (mainly sulfur) which segregated to the surface of cavities or cracks in steel and were driven into adjacent grain boundaries by an applied tensile stress across the boundary. If the stress is sufficiently high, the grain boundary diffusion zone is short and the impurity concentration is high, so that decohesion can occur. This process is similar to that of diffusive creep cavity growth, except that in the latter process (which is the reverse of sintering) it is matrix atoms which diffuse into the grain boundary and decohesion does not enter the picture. In principle, this diffusion~ontrolled brittle fracture should be possible in any case of adsorption of an embrittling element near the top of a flaw, regardless of whether the element is supplied by a solid in contact with the flaw surface (e.g. a sulfide in steel or a lead particle in copper) or by a surrounding vapor or liquid. Therefore, it appears that it would be fruitful to ask whether or not there actually exists a generic class of interfacial fracture of this type. The ultimate question, which requires a combined experimental and theoretical approach, is how a particular solute or impurity element acts to raise or lower the strength of a particular interface. This must include considerations of both bond breaking under a tensile stress and inelastic shearing under the accompanying shear stresses at a crack tip.
2.4. Hydrogen embrittlement Embrittlement of high strength alloys by hydrogen involves the rupture of metal-
209 hydrogen-metal bonds (often at internal interfaces, such as grain boundaries) and is now widely accepted as the mechanism of cracking in stress corrosion and corrosion fatigue [ 7, 8]. Considerations of hydrogen embrittlement can be divided into three parts: (i) the processes that supply hydrogen to the material, (ii) the distribution or partition of hydrogen amongst the various microstructural elements and (iii) the embrittlement process itself. These processes, occurring sequentially or in parallel, govern the rate of crack growth and its response to changes in environmental, metallurgical and loading conditions. Useful understanding of the first two parts has been and is being developed through interactions between researchers in fracture mechanics and surface chemistry (see for example refs. 9-16). For highly reactive systems, crack growth is controlled by external transport of the deleterious environment to the crack tip or by the internal diffusion of hydrogen to the embrittlement site [7, 8, 12]. When the surface reaction is slow, crack growth is then controlled by the rates of these reactions [ 712]. The overall response is governed in part by the partitioning of hydrogen among the various microstructural sites and by the rates of bond rupture along these paths [14-16]. A more complete understanding of hydrogen embrittlement, however, is hampered by the paucity of information on the strength of metal-metal and metal-hydrogen-metal bonds, particularly at internal interfaces [ 7, 8]. The improved understanding will require close interactions between investigators in fracture mechanics, materials science and solid state physics, analogous to that of fracture mechanics workers and surface chemists. 3. KEY ISSUES AND RESEARCH OPPORTUNITIES
3.1. Characterization of interracial structure The influence of grain boundary dislocations on these properties and ultimately on the strength of polycrystalline materials is not well understood; it still needs to be clearly determined by a combined experimental and theoretical approach. It is therefore proposed to investigate the following problems. 3.1.1. Short-term programs (3-6 years) (a) Further detailed TEM analyses of interfacial structure in pure metals, using bicrystals
of predetermined misorientations grown to high (+0.1 ° ) precision, need to be carried out. These TEM techniques will involve diffraction contrast and high resolution lattice imaging, to determine grain boundary dislocation Burgers vectors and step heights. (b) Repeated analyses of the same interfaces need to be made after the introduction of impurities, to determine the changes in interfacial structure which these bring about. Dopants known to be both beneficial and detrimental to boundary strength will be used. (c) Results from the experiments above should be correlated with fracture measurements made on sections of the same bicrystals.
3.1.2. Longer-term programs (3-10 years) (a) Modeling of the observed interfacial structures with atomistic calculations, with and without impurities in the boundaries, should be done. Atomistic calculations will provide theoretical boundary structures used to simulate high resolution TEM images of the interfaces, for example. (b) The investigations of interfacial structure in bicrystals of pure metals should be extended to bicrystals of dissimilar metals (phase boundaries) and to metal-non-metal systems (e.g. metal-ceramic or metal-semiconductor). 3.2. Continuum and atomistic modeling Here again the problems to be studied are divided into those which can be addressed immediately and those which require further developments in modeling or experimental methods to be tractable. 3.2.1. Static planar problems (1-4 years) (a) The adhesion energy and force of uncontaminated grain boundaries should be calculated. (b) The adhesion energy and force of crystal planes doped with periodic arrays of interstitials should be calculated. (c) The adhesion energy and force of doped grain boundaries should be calculated. (d) The calculated total energies of various grain boundaries based on structures obtained from central-force models should be systematically compared. (e) Improved pair potentials suitable for defect calculations should be derived and verified.
210
(f) Dislocation core energies in assumed structures should be calculated.
3.2.2. Longer-term problems (3-10 years) (These involve the calculation of relaxed structures with small periodicities.) (a) The motion of dislocations through periodic arrays of lattice sites should be investigated. (b) The nucleation of dislocations at free surfaces should be studied. (c) The relaxed core structures of surfaces, dislocations and grain boundaries (minimum energy configuration) should be determined. (d) The modeling of atomically flat planar cracks should be undertaken.
3.3. Intergranular fracture To develop further an Understanding of this process, model systems should be examined. In general, a mechanistic understanding of the cracking process will require determination of the rates of surface and grain boundary diffusion and of the stress dependence of the power law creep rate ahead of the flaw in the solid. These proposed research topics win address intergranular fracture in materials affected by the introduction of impurities and the process of hydrogen embrittlement.
3.3.1. Short-term problems (1-5 years) (a) The dependence of grain boundary strength on structure in materials which appear to have inherently weak grain boundaries should be investigated. (b) The suitability of other spectroscopic techniques than AES for revealing low levels of impurity contamination at interfaces should be investigated. (c) Suitable fracture experiments which will measure interfacial strength, and their interpretation on the microstructural and atomistic levels, should be developed. The feasibility of separating the criteria for fracture initiation and propagation will be investigated.
3.3.2. Longer-term problems (1-10 years) (d) The relative importance of various contaminants on strength, and the dependence of impurity behavior on the grain boundary structure, should be determined in terms of atomic arrangement, maximum concentration and embrittling effect.
(e) The relationship between the behavior of impurities in grain boundaries and studies of free surfaces of appropriate orientations, including those resulting from a freshly produced fracture and those allowed to relax to equilibrium, should be investigated.
4. RECOMMENDATIONS In the opinion of this Working Group, those research issues which are outlined above will be more productively investigated using a multidisciplinary approach. In particular, the need for joint studies of carefully prepared simple crystal systems has been stressed by each individual. These studies will involve TEM, atomistic calculations and measurements of the strength of the same boundaries. We believe that this is the only way to attempt to achieve an understanding of the basic atomistic processes which affect adhesion and bonding at interfaces. To achieve this purpose, it will be necessary to have access to a supply of bicrystals grown, with high precision, to predetermined orientations. There is currently no laboratory in the U.S.A. which makes such bicrystals on request, and the absence of this kind of facility means that it is not possible to implement the type of systematic interdisciplinary research effort which we all agree is necessary. We therefore propose that the U.S. Department of Energy consider the following course of action. (1) It should support the establishment of a National Crystal Growth Facility in the U.S.A., which will be accessible to researchers from universities, government laboratories and industrial laboratories involved in joint research. The location of this facility should be such as to make travel to and from it as economical as possible, but it could, for example, be patterned along the lines of the National Electron Microscope Facility at Berkeley. (2) The U.S. Department of Energy should give financial support to the establishment of interdisciplinary research groups which employ a variety of experimental and computational methods to address the types of problem outlined above. The basis of the experimental work would be the bicrystals provided by the National Crystal Growth Facility, while the
211 c o m p u t a t i o n s w o u l d be p e r f o r m e d o n t h e largest a n d m o s t s o p h i s t i c a t e d c o m p u t e r s curr e n t l y available. One especially i m p o r t a n t asp e c t o f these n e w research t e a m s is t h a t t h e y n e e d n o t be based in a single i n s t i t u t i o n b u t s h o u l d include w o r k e r s f r o m several d i f f e r e n t laboratories, so as t o capitalize o n t h e strengths t h a t each possesses. I n h e r e n t in this s c h e m e w o u l d be a s y s t e m o f regular m e e t i n g s (say o n c e a y e a r ) o f all t h e researchers involved in t h e p r o j e c t at o n e m u t u a l l y agreed site. This c o u l d t a k e t h e f o r m o f a lecture a n d / o r discussion a n d p r o v i d e a m e a n s o f r e p o r t i n g , discussing and directing t h e research effort. While this t y p e o f o r g a n i z a t i o n represents a fairly radical d e p a r t u r e f r o m t h e p a t t e r n s o f research f u n d i n g c u r r e n t l y in use, we feel t h a t it offers t h e m o s t realistic m e a n s o f a c c o m p l i s h ing t h e objective o f u n d e r s t a n d i n g t h e f u n d a m e n t a l s o f a d h e s i o n and b o n d i n g at interfaces a n d m a k e s t h e best use o f the d i f f e r e n t areas o f expertise t h a t d i f f e r e n t researchers bring t o this p r o b l e m .
REFERENCES FOR CHAPTER 4 1 R. W. Balluffi (ed.), Grain Boundary Structure and Kinetics, American Society for Metals, Metals Park, OH, 1980. 2 J. C. H. Spence, High Resolution Electron Microscopy Oxford University Press, Oxford, 1983. 3 W. Johnson (ed.), Interfacial Segregation, American Society for Metals, Metals Park, OH, 1978. 4 J. K. Lee (ed.), Interatornic Potentials and Crystalline Defects, Metallurgical Society of AIME, Warrendale, PA, 1981. 5 D. Wolf, Acta MetaU., 32 (1984) 245, 735. 6 C. J. McMahon, personal communication, 1985. 7 R. P. Wei, K. Klier, G. W. Simmons and Y. T. Chou, Fracture mechanics and surface chemistry investigations of environment assisted crack growth, in R. Gibala and R. F. Hehemann (eds.),
Hydrogen Embrittlement and Stress Corrosion Cracking A ~riano Festschrift, American Society for Metals, Metals Park, OH, 1984, pp. 103133. 8 R. P. Wei and M. Gao, Chemistry, microstructure and crack growth response, in R. A. Oriani, J. P. Hirth and M. Smialowski (eds.), Hydrogen Degradation o f Ferrous Alloys, Noyes Publications, Park Ridge, NY, to be published. 9 N. H. Chan, K. Klier and R. P. Wei, Scr. Metall., 12 (1978) 1043. 10 N. H. Chan, K. Klier and R. P. Wei, Hydrogen isotope exchange reactions over the AISI 4340 steel, Proc. 2nd JIM Int. Syrup. on Hydrogen in Metals, Minakami, 1979, in Trans. Jpn. Inst. Met., Suppl., 21 (1980) 305. 11 M. Lu, P. S. Pao, N. H. Chan, K. Klier and R. P. Wei, Hydrogen assisted crack growth in AIS14340 steel, Proc. 2nd JIM Int. Syrup. on Hydrogen in Metals, Minakami, 1979, in Trans. Jpn. Inst. Met., Suppl., 21 (1980) 449. 12 M. Lu, P. S. Pan, T. W. Weir, G. W. Simmons and R. P. Wei, Metull. Trans. A, 12 (1981) 805. 13 G. W. Simmons, P. S. Pao and R. P. Wei, MetaU. Trans. A, 9 (1978) 1158. 14 M. Gao, M. Lu and R. P. Wei, Metall. Trans. A, 15 (1984) 735. 15 M. Gao and R. P. Wei, Acta Metall., 32 (1984) 2115. 16 M. Gao and R. P. Wei, Metall. Trans. A, 16 (1985) 2039. 17 T.W. Schober and R. W. Balluffi, Philos. Mag., 20 (1969) 511. 18 W. Bollmann, Crystal Defects and Crystalline Interfaces, Springer, Berlin, 1970. 19 D. A. Smith and A. H. King, Philos. Mag. A, 44 (1981) 333. 20 A. G. Guha, W. A. T. Clark and H. I. Aaronson, Metall. Trans. A, 15 (1984) 1623. 21 K.T. Aust and J. W. Rutter, Trans. AIME, 215 (1959) 119. 22 J.G. Gay, J. R. Smith, R. Richter, F. J. Arlinghaus and R. H. Wagoner, J. Vac. Sci. Technol. A, 2 (1984) 931. 23 J. G. Gay, J. R. Smith and F. J. Arlinghaus, Phys. Rev. B, 25 (1982) 643. 24 J. R. Smith, J. G. Gay and F. J. Arlinghaus, Phys. Rev. B, 21 (1980) 2201. -
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205
CHAPTER 4 INTERNAL INTERFACES IN METALS W° A. T. CLARK
Department of Metallurgical Engineering, The Ohio State University, 116 West 19th Avenue, Columbus, OH 43210-1179 (U.S.A.) C. J. McMAHON, JR.
Department of Materials Science and Engineering, School of Engineering and Applied Science, University of Pennsylvania, Philadelphia, PA 19104 (U.S.A.) R. H. WAGONER
Department of Metallurgical Engineering, The Ohio State University, 116 West 19th Avenue, Columbus, OH 43210-1179 (U.S.A.) R. P. WEI
Department of Mechanical Engineering and Mechanics, Lehigh University, Bethlehem, PA 18015 (U.S.A.)
1. INTRODUCTION
Internal interfaces in metals control many of their most important thermomechanical properties, such as ductility, high temperature creep behavior and susceptibility to intergranular fracture resulting from the segregation of impurities. An example of the latter is found in high strength alloys (temper embrittlement) and in the presence of hydrogen (hydrogen embrittlement) and is an important technological problem. Relatively little is known about the influence of the atomic structure of interfaces on these properties, although considerable progress has been made in several areas in recent years in understanding the crystallography of interfacial structure (see for example ref. 1). Experimental techniques for observing and determining interfacial structure and chemistry have also improved significantly during the last 10 years, to the point where atomic level imaging in the transmission electron microscope can reveal the presence of both line defects and solute atoms in interfaces [ 2], and surface chemical techniques such as Auger electron spectroscopy (AES) can detect submonolayer surface coatings [ 3 ]. In parallel with these developments, there has also been considerable progress in improv-
ing the speed and sophistication of first-principles computer calculations of the atomistic and electronic structure of interfaces [4]. These advances have in some cases only been made possible by the availability of computers capable of carrying o u t with reasonable speed the large numerical calculations necessary to model even very small and simple clusters of atoms. Even so, considerable controversy still exists as to the relevance of such computations to actual materials, and also a b o u t the choice of c o m p u t a t i o n a l model used. None of these calculations of the theoretical strength of bicrystals has been systematically correlated with experimental measurements, but the rapid developments in computing capacity and experimental techniques which have occurred over the last few years offer some hope that such essential comparisons m a y become feasible, although not in the immediate future. Just as in atomistic calculations of boundary structure, descriptions of the continuum behavior at interfaces during intergranular fracture are also increasing in sophistication and can more readily be coupled with experimental results obtained under carefully controlled experimental conditions. As an example, the calculated thermodynamic strength of interfaces [ 5] can be compared with measured b o u n d a r y adhesion, although these calcula© Elsevier Sequoia/Printed in The Netherlands
206 tions, again, take no account of the defect structure and unique character of each individual interface. Such research carried out on intergranular fracture of polycrystals has yielded a wealth of information on the types of material and conditions in which it occurs. These generally involve the presence of some impurity or segregated solute which weakens the interface, although recent studies employing AES [6] have indicated, however, that some polycrystals m a y have inherently weak grain boundaries. It therefore appears certain that, with or without embrittling impurities, intergranular strength is closely related to grain boundary structure. Although fracture studies on polycrystals remain useful for elucidating the various factors that contribute to interfacial fracture, t h e y are not suitable for quantifying the effects of the structure of individual interfaces, since that differs significantly from boundary to boundary, even within the same polycrystal. The properties considered above all depend on the detailed atomistic nature of the structure of individual interfaces. This is dictated in part by the crystallography of the boundary and the nature of the atomic bonding across it, but it is also strongly affected by the presence of impurities which segregate preferentially to the interface. These impurities m a y actually enhance the strength of the boundary (boron in steels is an example) but more c o m m o n l y have a deleterious effect on adhesion; in some cases, this adverse effect is catastrophic, causing severe embrittlement and premature failure. Hydrogen is a particularly virulent embrittling agent, causing cracking along m a n y interfaces, principally by the rupture of m e t a l - h y d r o g e n - m e t a l bonds [7, 8]. It is now widely accepted as the mechanism of cracking in stress corrosion and corrosion fatigue and thus argues for greater attention. Considerations of impurity segregation can be divided into three parts: (i) the processes that supply solute to the internal interfaces in the material, (ii) the interaction of the solute with the structure of the interface, and its partition amongst the various microstructural elements, and (iii) the embrittlement process itself. These processes, occurring consecutively or concurrently, govern the rate of crack growth and its response to changes in environmental, metallurgical and loading con-
ditions. Useful understanding of the first two parts has been and is being developed through the improved understanding of the crystallography and atomic structure of interfaces, through the types of approach referred to above, and through interactions between researchers in fracture mechanics and surface chemistry (see for example refs. 9-16). A more complete understanding of intergranular fracture and hydrogen embrittlement has been hampered, however, by the paucity of information on the nature of metal-metal and m e t a l - h y d r o g e n - m e t a l bonds, particularly at internal interfaces. There is a need in this area for improved computer modeling, and the development of a broader understanding will require close interactions between investigators in metallurgy, materials science, solid state physics and fracture mechanics, together with surface chemists and others. Recent advances in all the fields described above hold the promise of significant advances in quantitative understanding of the role that interfaces play in the adhesion and decohesion of polycrystalline materials. In the following sections an outline of the potential and problems in each of these areas is given, some of the key issues to be addressed are identified and suggestions made as to the facilities necessary to accomplish these aims.
2. BACKGROUND
2.1. Characterization of interfacial structure It has been demonstrated clearly that certain grain boundaries, with misorientations close to certain special coincidence site lattice (CSL) [ 17] values, exhibit regular arrays of linear defects identifiable as grain boundary dislocations. These grain boundary dislocations have been described as necessary to conserve the low energy of the CSL orientation, in a manner analogous to small-angle tilt and twist boundaries in single crystals. In some cases, transmission electron microscopy (TEM) experiments have verified this hypothesis and found that the dislocations have Burgers vectors derived from the DSC lattice [18] and are different from one CSL to another. In general, grain boundary dislocations are distinct from crystal lattice dislocations found in the crystal interior in that t h e y have, in
207 addition to their Burgers vector, a geometrically necessary step associated with their core. This step can be used to describe mechanisms of coupled grain b o u n d r y sliding and migration which involve the motion of grain boundary dislocations across an interface [ 19]. An example of this is the growth of an annealing twin boundary in f.c.c, metals by the passage of (a/6)(112) Shockley partials across alternate {111} twin planes. This twin boundary can also be described as a E = 3 CSL boundary, and the (a/6)(112> Shockley partial is one of the DSC vectors for this system. It is the displacement of the twin plane by ½(111), the step at the core of the Shockley partial when it is in the twin boundary, which causes the twin to grow. However, partly because of the difficulty of the experimental work involved, and partly because of the wide variety of CSLs and crystal systems involved, only limited systematic attempts have been made to determine the generality of this process to all CSLs. Experimental observations which extend this concept to the wider field of interphase boundaries are even rarer, although even this limited evidence suggests that it has wide applicability (see for example ref. 20). There are many other processes occurring at grain boundaries in which grain boundary dislocations can be expected, and in some cases have already been observed, to play an important role. These include solute absorption, grain boundary diffusion, diffusioninduced boundary migration, precipitation of second phases and propagation of crystalline strain through boundaries by dislocations (see ref. 1 for reviews on some of these phenomena). Almost no experimental information is available on the relationship between grain boundary structure and these p h e n o m e n a on the atomic scale, despite the fact that macroscopic bicrystal experiments carried o u t several years ago indicated that near-CSL boundaries did have, for example, different diffusion coefficients and migration rates when compared with boundaries far from a low E CSL orientation [21]. These earlier experiments were n o t able, however, to examine the boundary structure, nor could they investigate the variation in these parameters as a function of an orientation close to an exact CSL (i.e. to a precision of +0.1 °). This order of precision is almost essential if the influence of grain boundary structure on any one property is to
be measured quantitatively as a function of orientation.
2.2. Continuum and atomic contributions to macroscopic adhesion at crystalline interfaces Macroscopic adhesion at crystalline interfaces depends intimately on the propagation and nucleation of cracks at or near the interface. Much progress has been made in deriving elastic-plastic solutions for cracks and other crystal defects. These continuum-based solutions may be quasi-analytic in form or m a y involve detailed numerical solutions based on finite element modeling and m a y include continuum descriptions of crystalline defects, such as dislocations. Although these models are capable of arriving at the proper solution forms, they all suffer from a lack of fundamental knowledge of the atomic mechanisms which determine the critical propagation events. Examples of these fundamental events include bond rupture, incremental crack advance, dislocation nucleation and incremental dislocation motion. Activation and dissipation energies for these events, crucial for quantitative macroscopic predictions, can only be obtained b y reference to atomic bonding models. Until recently, the only viable m e t h o d for estimating defect core structures and energies was based on the use of atomic pair potentials [4] and central-force models. The accuracy of such models is the subject of great current controversy, particularly for problems involving large local density changes from the bulk crystal, as near a defect core. The choice of potential is largely arbitrary, b u t widely differing structures and energies are obtained [ 5] depending on the exact form. In general, no reliable m e t h o d for obtaining t o t a l energies based on these methods is available, although arguments on the validity of relative energies have been proposed. For these reasons, pair potential calculations, at least in their present state, offer little promise of providing the activation energy information needed for the fundamental crystal mechanisms. Quantum mechanical calculations of metal electronic structures at planar surfaces and interfaces have begun to appear, including total energy and adhesion (microscopically reversible) calculations [ 2 2 - 2 4 ] . The model is based on self-consistent solutions of SchrSdinger's equation and can provide first-prin-
208 ciples answers to energies, atomic structures etc. The major impediment to widespread use of the method lies in the extensive computer times required for even "small" problems. Periodic boundary conditions are generally employed and at the present only 50-100 atoms can be considered in the repeat "cell". Nonetheless, the addition of these ab initio calculations to the existing arsenal holds the most promise for advancing the fundamental continuum and crystalline descriptions of fracture, decohesion and defect motion. Because of computer time and storage limitations, a hybrid approach will be required to undertake many problems of practical importance. Specifically, various spatial regions of a crystal may need to be described elastically, plastically and by discrete defects while minimizing the region described quantum mechanically. It is hoped that this approach will allow treatment of a broad range of problems inaccessible by any single approach. Even with these improve: ments, many larger-scale problems will require order-of-magnitude improvements in computational efficiency.
2.3. Intergranular fracture Decades of research on intergranular fracture of polycrystals have yielded a wealth of information on the types of material and the conditions in which it occurs. It generally involves the presence of some impurity or segregated solute which weakens the interface (see for example ref. 3), but recent studies employing AES have indicated that some polycrystals may have inherently weak grain boundaries. With or without embrittling impurities, it appears certain that intergranular strength is closely related to grain boundary structure. Although studies on polycrystals remain extremely useful for the study of various factors which contribute to interfacial fracture, they are inherently unable to deal with the effect of structure, since that is rarely constant even over one intergranular facet. In order to obtain a complete fundamental understanding of interfacial adhesion, it will be necessary to carry out fracture studies on bicrystals of very carefully controlled and characterized structure and composition. Such studies will require the commitment of much time and special facilities for specimen preparation and will therefore have to be limited to carefully selected materials which
have already been thoroughly investigated in polycrystalline form. They should also be amenable to a wide variety of experimental and theoretical approaches and should be sufficiently strong, with regard to plasticity, that stresses high enough to cause brittle fracture can be attained. There is a class of brittle interfacial fracture in which the embrittling species must diffuse to the site of decohesion. This results in a large temperature dependence and, in many cases, quasi-static crack growth. Perhaps the best-known example of this is hydrogeninduced cracking of steel. However, it has recently been established that other embrittling species besides hydrogen can produce diffusion-controlled brittle fracture. The specific case studied so far involved embrittling impurities (mainly sulfur) which segregated to the surface of cavities or cracks in steel and were driven into adjacent grain boundaries by an applied tensile stress across the boundary. If the stress is sufficiently high, the grain boundary diffusion zone is short and the impurity concentration is high, so that decohesion can occur. This process is similar to that of diffusive creep cavity growth, except that in the latter process (which is the reverse of sintering) it is matrix atoms which diffuse into the grain boundary and decohesion does not enter the picture. In principle, this diffusion~ontrolled brittle fracture should be possible in any case of adsorption of an embrittling element near the top of a flaw, regardless of whether the element is supplied by a solid in contact with the flaw surface (e.g. a sulfide in steel or a lead particle in copper) or by a surrounding vapor or liquid. Therefore, it appears that it would be fruitful to ask whether or not there actually exists a generic class of interfacial fracture of this type. The ultimate question, which requires a combined experimental and theoretical approach, is how a particular solute or impurity element acts to raise or lower the strength of a particular interface. This must include considerations of both bond breaking under a tensile stress and inelastic shearing under the accompanying shear stresses at a crack tip.
2.4. Hydrogen embrittlement Embrittlement of high strength alloys by hydrogen involves the rupture of metal-
209 hydrogen-metal bonds (often at internal interfaces, such as grain boundaries) and is now widely accepted as the mechanism of cracking in stress corrosion and corrosion fatigue [ 7, 8]. Considerations of hydrogen embrittlement can be divided into three parts: (i) the processes that supply hydrogen to the material, (ii) the distribution or partition of hydrogen amongst the various microstructural elements and (iii) the embrittlement process itself. These processes, occurring sequentially or in parallel, govern the rate of crack growth and its response to changes in environmental, metallurgical and loading conditions. Useful understanding of the first two parts has been and is being developed through interactions between researchers in fracture mechanics and surface chemistry (see for example refs. 9-16). For highly reactive systems, crack growth is controlled by external transport of the deleterious environment to the crack tip or by the internal diffusion of hydrogen to the embrittlement site [7, 8, 12]. When the surface reaction is slow, crack growth is then controlled by the rates of these reactions [ 712]. The overall response is governed in part by the partitioning of hydrogen among the various microstructural sites and by the rates of bond rupture along these paths [14-16]. A more complete understanding of hydrogen embrittlement, however, is hampered by the paucity of information on the strength of metal-metal and metal-hydrogen-metal bonds, particularly at internal interfaces [ 7, 8]. The improved understanding will require close interactions between investigators in fracture mechanics, materials science and solid state physics, analogous to that of fracture mechanics workers and surface chemists. 3. KEY ISSUES AND RESEARCH OPPORTUNITIES
3.1. Characterization of interracial structure The influence of grain boundary dislocations on these properties and ultimately on the strength of polycrystalline materials is not well understood; it still needs to be clearly determined by a combined experimental and theoretical approach. It is therefore proposed to investigate the following problems. 3.1.1. Short-term programs (3-6 years) (a) Further detailed TEM analyses of interfacial structure in pure metals, using bicrystals
of predetermined misorientations grown to high (+0.1 ° ) precision, need to be carried out. These TEM techniques will involve diffraction contrast and high resolution lattice imaging, to determine grain boundary dislocation Burgers vectors and step heights. (b) Repeated analyses of the same interfaces need to be made after the introduction of impurities, to determine the changes in interfacial structure which these bring about. Dopants known to be both beneficial and detrimental to boundary strength will be used. (c) Results from the experiments above should be correlated with fracture measurements made on sections of the same bicrystals.
3.1.2. Longer-term programs (3-10 years) (a) Modeling of the observed interfacial structures with atomistic calculations, with and without impurities in the boundaries, should be done. Atomistic calculations will provide theoretical boundary structures used to simulate high resolution TEM images of the interfaces, for example. (b) The investigations of interfacial structure in bicrystals of pure metals should be extended to bicrystals of dissimilar metals (phase boundaries) and to metal-non-metal systems (e.g. metal-ceramic or metal-semiconductor). 3.2. Continuum and atomistic modeling Here again the problems to be studied are divided into those which can be addressed immediately and those which require further developments in modeling or experimental methods to be tractable. 3.2.1. Static planar problems (1-4 years) (a) The adhesion energy and force of uncontaminated grain boundaries should be calculated. (b) The adhesion energy and force of crystal planes doped with periodic arrays of interstitials should be calculated. (c) The adhesion energy and force of doped grain boundaries should be calculated. (d) The calculated total energies of various grain boundaries based on structures obtained from central-force models should be systematically compared. (e) Improved pair potentials suitable for defect calculations should be derived and verified.
210
(f) Dislocation core energies in assumed structures should be calculated.
3.2.2. Longer-term problems (3-10 years) (These involve the calculation of relaxed structures with small periodicities.) (a) The motion of dislocations through periodic arrays of lattice sites should be investigated. (b) The nucleation of dislocations at free surfaces should be studied. (c) The relaxed core structures of surfaces, dislocations and grain boundaries (minimum energy configuration) should be determined. (d) The modeling of atomically flat planar cracks should be undertaken.
3.3. Intergranular fracture To develop further an Understanding of this process, model systems should be examined. In general, a mechanistic understanding of the cracking process will require determination of the rates of surface and grain boundary diffusion and of the stress dependence of the power law creep rate ahead of the flaw in the solid. These proposed research topics win address intergranular fracture in materials affected by the introduction of impurities and the process of hydrogen embrittlement.
3.3.1. Short-term problems (1-5 years) (a) The dependence of grain boundary strength on structure in materials which appear to have inherently weak grain boundaries should be investigated. (b) The suitability of other spectroscopic techniques than AES for revealing low levels of impurity contamination at interfaces should be investigated. (c) Suitable fracture experiments which will measure interfacial strength, and their interpretation on the microstructural and atomistic levels, should be developed. The feasibility of separating the criteria for fracture initiation and propagation will be investigated.
3.3.2. Longer-term problems (1-10 years) (d) The relative importance of various contaminants on strength, and the dependence of impurity behavior on the grain boundary structure, should be determined in terms of atomic arrangement, maximum concentration and embrittling effect.
(e) The relationship between the behavior of impurities in grain boundaries and studies of free surfaces of appropriate orientations, including those resulting from a freshly produced fracture and those allowed to relax to equilibrium, should be investigated.
4. RECOMMENDATIONS In the opinion of this Working Group, those research issues which are outlined above will be more productively investigated using a multidisciplinary approach. In particular, the need for joint studies of carefully prepared simple crystal systems has been stressed by each individual. These studies will involve TEM, atomistic calculations and measurements of the strength of the same boundaries. We believe that this is the only way to attempt to achieve an understanding of the basic atomistic processes which affect adhesion and bonding at interfaces. To achieve this purpose, it will be necessary to have access to a supply of bicrystals grown, with high precision, to predetermined orientations. There is currently no laboratory in the U.S.A. which makes such bicrystals on request, and the absence of this kind of facility means that it is not possible to implement the type of systematic interdisciplinary research effort which we all agree is necessary. We therefore propose that the U.S. Department of Energy consider the following course of action. (1) It should support the establishment of a National Crystal Growth Facility in the U.S.A., which will be accessible to researchers from universities, government laboratories and industrial laboratories involved in joint research. The location of this facility should be such as to make travel to and from it as economical as possible, but it could, for example, be patterned along the lines of the National Electron Microscope Facility at Berkeley. (2) The U.S. Department of Energy should give financial support to the establishment of interdisciplinary research groups which employ a variety of experimental and computational methods to address the types of problem outlined above. The basis of the experimental work would be the bicrystals provided by the National Crystal Growth Facility, while the
211 c o m p u t a t i o n s w o u l d be p e r f o r m e d o n t h e largest a n d m o s t s o p h i s t i c a t e d c o m p u t e r s curr e n t l y available. One especially i m p o r t a n t asp e c t o f these n e w research t e a m s is t h a t t h e y n e e d n o t be based in a single i n s t i t u t i o n b u t s h o u l d include w o r k e r s f r o m several d i f f e r e n t laboratories, so as t o capitalize o n t h e strengths t h a t each possesses. I n h e r e n t in this s c h e m e w o u l d be a s y s t e m o f regular m e e t i n g s (say o n c e a y e a r ) o f all t h e researchers involved in t h e p r o j e c t at o n e m u t u a l l y agreed site. This c o u l d t a k e t h e f o r m o f a lecture a n d / o r discussion a n d p r o v i d e a m e a n s o f r e p o r t i n g , discussing and directing t h e research effort. While this t y p e o f o r g a n i z a t i o n represents a fairly radical d e p a r t u r e f r o m t h e p a t t e r n s o f research f u n d i n g c u r r e n t l y in use, we feel t h a t it offers t h e m o s t realistic m e a n s o f a c c o m p l i s h ing t h e objective o f u n d e r s t a n d i n g t h e f u n d a m e n t a l s o f a d h e s i o n and b o n d i n g at interfaces a n d m a k e s t h e best use o f the d i f f e r e n t areas o f expertise t h a t d i f f e r e n t researchers bring t o this p r o b l e m .
REFERENCES FOR CHAPTER 4 1 R. W. Balluffi (ed.), Grain Boundary Structure and Kinetics, American Society for Metals, Metals Park, OH, 1980. 2 J. C. H. Spence, High Resolution Electron Microscopy Oxford University Press, Oxford, 1983. 3 W. Johnson (ed.), Interfacial Segregation, American Society for Metals, Metals Park, OH, 1978. 4 J. K. Lee (ed.), Interatornic Potentials and Crystalline Defects, Metallurgical Society of AIME, Warrendale, PA, 1981. 5 D. Wolf, Acta MetaU., 32 (1984) 245, 735. 6 C. J. McMahon, personal communication, 1985. 7 R. P. Wei, K. Klier, G. W. Simmons and Y. T. Chou, Fracture mechanics and surface chemistry investigations of environment assisted crack growth, in R. Gibala and R. F. Hehemann (eds.),
Hydrogen Embrittlement and Stress Corrosion Cracking A ~riano Festschrift, American Society for Metals, Metals Park, OH, 1984, pp. 103133. 8 R. P. Wei and M. Gao, Chemistry, microstructure and crack growth response, in R. A. Oriani, J. P. Hirth and M. Smialowski (eds.), Hydrogen Degradation o f Ferrous Alloys, Noyes Publications, Park Ridge, NY, to be published. 9 N. H. Chan, K. Klier and R. P. Wei, Scr. Metall., 12 (1978) 1043. 10 N. H. Chan, K. Klier and R. P. Wei, Hydrogen isotope exchange reactions over the AISI 4340 steel, Proc. 2nd JIM Int. Syrup. on Hydrogen in Metals, Minakami, 1979, in Trans. Jpn. Inst. Met., Suppl., 21 (1980) 305. 11 M. Lu, P. S. Pao, N. H. Chan, K. Klier and R. P. Wei, Hydrogen assisted crack growth in AIS14340 steel, Proc. 2nd JIM Int. Syrup. on Hydrogen in Metals, Minakami, 1979, in Trans. Jpn. Inst. Met., Suppl., 21 (1980) 449. 12 M. Lu, P. S. Pan, T. W. Weir, G. W. Simmons and R. P. Wei, Metull. Trans. A, 12 (1981) 805. 13 G. W. Simmons, P. S. Pao and R. P. Wei, MetaU. Trans. A, 9 (1978) 1158. 14 M. Gao, M. Lu and R. P. Wei, Metall. Trans. A, 15 (1984) 735. 15 M. Gao and R. P. Wei, Acta Metall., 32 (1984) 2115. 16 M. Gao and R. P. Wei, Metall. Trans. A, 16 (1985) 2039. 17 T.W. Schober and R. W. Balluffi, Philos. Mag., 20 (1969) 511. 18 W. Bollmann, Crystal Defects and Crystalline Interfaces, Springer, Berlin, 1970. 19 D. A. Smith and A. H. King, Philos. Mag. A, 44 (1981) 333. 20 A. G. Guha, W. A. T. Clark and H. I. Aaronson, Metall. Trans. A, 15 (1984) 1623. 21 K.T. Aust and J. W. Rutter, Trans. AIME, 215 (1959) 119. 22 J.G. Gay, J. R. Smith, R. Richter, F. J. Arlinghaus and R. H. Wagoner, J. Vac. Sci. Technol. A, 2 (1984) 931. 23 J. G. Gay, J. R. Smith and F. J. Arlinghaus, Phys. Rev. B, 25 (1982) 643. 24 J. R. Smith, J. G. Gay and F. J. Arlinghaus, Phys. Rev. B, 21 (1980) 2201. -
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