«STRUCTURE AND PROPERTIES OF ELECTRODEPOSITED NANOCRYSTALLINE NI AND NI-FE ALLOY CONTINUOUS FOILS by Jason Derek Giallonardo A thesis submitted in ...»
Thus, it appears to be obvious that grain size as such must have some effect on internal stresses. Kushner (1958) also studied in some detail the effect of hydrogen and determined that it cannot be the main cause of internal stresses and that microstructural features, such as grain size, may play a more influential role. Other studies have also considered the effect of grain boundaries as an origin of internal stresses. Feigenbaum and Weil (1979) studied structure-internal stress relationships in the early stages of Ni electrodeposition and found that as the thickness increases, the “coalescence” internal stress decreases. They also identified the influence of sulfur-containing organic additives as affecting “coalescence” by influencing the size and shape of the joining crystallites and the surface energies, which are the driving forces for the process.
Coalescence mechanisms based on the effect of grain boundaries are the most developed [e.g. Doljack and Hoffman (1972), Hoffman (1976), and Nix and Clemens (1999)] Coalescence mechanisms have been used to explain the origins of internal stresses in electrodeposited metals [e.g., Feigenbaum and Weil (1979), Czerwinski (1996a), Lin et al.
(2005)]. The coalescence mechanism has also been applied to metals produced by other means, such as sputtering [Mitra et al. (2001), Shamsutdinov et al. (2007)]. Realizing that there has been no success in making quantitative predictions, Doljack and Hoffman (1972) made one of the first attempts to relate the observed internal stresses with the grain size in vapor-deposited polycrystalline Ni thin films on polished silicon substrates. In their study, they considered the final grain size, the surface free energy, the average grain boundary energy and the elastic constants to calculate an internal stress value. A model was proposed whereby a grain separation potential is introduced and a value for the grain boundary relaxation distance is computed from this potential for each grain diameter, d. The internal stress, , is obtained by inserting the values of ∆ and d in the expression,
into consideration, Kushner (1973) in his experiments with electrodeposited Ni, described the magnitude of the stress as being dependent on the grain size. That is, the smaller the grain size, the higher the number of grains per unit area and thus, the higher the measured internal stress.
Hoffman (1976) in a later publication emphasized the importance of grain boundaries and their contribution to internal stresses. A grain boundary model was developed which considered the decrease in energy when a grain boundary is formed from two growing isolated surfaces. Using this concept a grain boundary potential model was introduced for Ni,
constraint due to the adhesion with the substrate, the surface free energy decrease becomes a strain energy increase in the adjoining crystals.
This mechanism was further explored and it was generally agreed upon that internal stresses are associated with the formation of grain boundaries [Abermann and Koch (1985), Nix and Clemens (1999), Sheldon et al. (2001), Freund and Chason (2001)]. Fig. 2.15 describes the before and after effect of crystal coalescence. The process of crystal coalescence leads to an internal stress. The concepts presented by Nix and Clemens (1999) were further refined by Freund and Chason (2001) which resulted in a model that is based on
the theory of contact of elastic solids with cohesion. The model was developed based on one-dimensional, two-dimensional, and three-dimensional states of deformation of coalescing islands. The latter case was found to provide estimates of film stress generally consistent with observations.
2.2.4. Internal Stress Measurements in Nanocrystalline Materials Various measurements of internal stresses in a number of different nanocrystalline materials have been made, for example, nanocyrstalline metals [Sanders et al. (1995), Mitra et al. (2001), El-Sherik et al. (2005), Shamsutdinov et al. (2007), Chung et al. (2011)] and nanocrystalline metal alloys [Czerwinski (1996a,b), Czerwinski (1998), Li and Ebrahimi (2003), Lin et al. (2005), Lee et al. (2005), Auerswald and Fecht (2010), Pathak et al. (2011)].
However, there are only a few which provide some insight into a structure-stress relationship.
For example, in a structure-stress investigation of electrodeposited nanocrystalline Ni-Fe, Czerwinski (1996a) established a relationship between grain size and internal stress in Fe-Ni alloy deposits (15wt.%Ni): a decrease in grain size is accompanied by a rise in internal stresses. In this study, internal stresses were measured using the curvature or “bent strip” method and grain sizes determined by imaging thin foils with a TEM. The results showed that the coalescence theory was applicable for grains with sizes less than 100 nm and a deposit thickness less than 500 nm. However, for thicker deposits the coalescence contribution diminished. Given this observation, it was suggested that for thicker layers, other factors might have an influence on the stress generation. Hydrogen was considered, but ruled out since post-deposition stress evolution was small (approximately 4.5%). Czerwinski (1996a) specifically emphasized that to date there is no clear explanation of the stress
changes during electrodeposition and that all hypotheses should be related to the deposit microstructure. In a more recent example of a structure-internal stress relationship study, Shamsutdinov et al. (2007) produced magnetron sputtered nanocrystalline Fe thin films of varying grain size on Si wafers and measured the curvature to determine the internal stress.
The internal stress was also found to increase with decreasing grain size.
In many of these studies, the internal stress in electrodeposited materials has been measured using the curvature or “bent strip” method which often leads to conflicting results.
On the other hand, XRD methods are rarely used since the method is not as cost effective and practical as the curvature or “bent strip” method. However, XRD methods have the advantage of isolating the intrinsic stresses in the material rather than combining both intrinsic and extrinsic stresses as is in the case of the curvature or “bent strip” method.
Furthermore, the ability to isolate the intrinsic stresses can allow for a better correlation to the structure of the material. For example, El-Sherik et al. (2005) used an XRD method to measure the internal stresses in nanocrystalline Ni electrodeposits (10 nm) and microcrystalline Ni electrodeposits (5000 nm). It was found that nanocrystalline Ni electrodeposits had about six times the compressive internal stress of microcrystalline Ni.
This study further supports the effect of grain size on internal stress values and the need for obtaining an advanced understanding of this phenomenon.
2.2.5. Microstrain in Nanocrystalline Materials Microstrain in conventional polycrystalline metals and alloys is normally caused by high dislocation densities resulting from deformation processes. However, the microstrain in
nanocrystalline materials has generally been reported to increase with decreasing grain size, e.g., Eckert et al. (1992), Weissmuller et al. (1995), Eastman et al. (1995), Sanders et al.
(1995), Sun et al. (1996), Malow and Koch (1997), Zhao et al. (2001), Li and Ebrahimi (2003), Mishra et al. (2004), Derlet et al. (2005), Qin and Szpunar (2005), and Biju et al.
(2008), even when no external loads have been applied. In as-prepared nanocrystalline inert gas condensed [Weissmuller et al. (1995)] and electrodeposited [Mehta et al. (1995)] materials, dislocation densities are typically very low and thus, are not considered to be a major contributor to the observed microstrain. Nanocrystalline materials typically have a high volume fraction of intercrystal defects (grain boundaries and triple junctions) which can become quite significant at the smallest grain sizes [Palumbo et al. (1990)]. For example, at a grain size of 10 nm, about 24% of the volume consists of grain boundaries and 3% of triple junctions (Eq. 2-1, 2-2, 2-3). Local strains in nanocrystalline materials have often been reported to appear near grain boundaries. Using high-resolution transmission electron microscopy (HR-TEM) inert gas condensed nanocrystalline Pd with grain sizes less than 10 nm exhibited distorted lattice planes near grain boundaries [Wunderlich et al. (1990)].
Similar observations were made for materials synthesized by other means, e.g., crystallization of amorphous precursors, mechanical alloying, and severe plastic deformation [Ping et al. (1995), Li et al. (2000), Valiev et al. (2000)].
The use of X-ray line profile analysis for the characterization of nanocrystalline materials has been shown to be a powerful tool, especially when combined with transmission electron microscopy [Ungar (2007)]. Considering the earlier HR-TEM observations of distorted lattice planes near grain boundaries [Wunderlich et al. (1990), Ping et al. (1995), Li
et al. (2000), Valiev et al. (2000)], Qin and Szpunar (2005) developed a quantitative model to describe the dependence of microstrain induced XRD line broadening on grain size. The model is based on the assumption that excess volume in the grain boundaries produces a stress field that causes the lattice strain. Stukowski et al. (2009), employed molecular dynamics simulations to investigate the atomistic origin of microstrain in nanocrystalline materials. In their study, it was concluded that microstrain induced XRD line broadening is generated by long range displacement fields that spread throughout the grains. In general, the presence of a significant volume fraction of intercrystal defects associated with relatively small grain sizes in nanocrystalline materials is considered to be the dominant factor in controlling the microstrain and thus, the basis upon which most theoretical models are constructed. Often, there is good agreement between theoretical and experimental values;
however, there are also noticeable variations that could be related to other possible sources which can also contribute to microstrain induced XRD line broadening in nanocrystalline materials [Li and Ebrahimi (2003), Qin and Szpunar (2005), Qin et al. (2008)].
Wagner (1957) established that both twin and deformation stacking faults can be detected from the XRD patterns of fcc metals and alloys. On the (111) planes of fcc metals and alloys, twin stacking faults (ABCACBA, also referred to as growth stacking faults [Wagner (1957)]) cause an asymmetric line broadening and a negligible peak shift [Paterson (1952)], whereas deformation stacking faults (ABCACABC, also referred to as intrinsic stacking faults [Wagner (1957)]) cause a symmetric line broadening and a small peak shift [Paterson (1952)]. An illustration of these types of stacking faults is given in Fig. 2.16. As in the case of dislocations, deformation stacking faults in nanomaterials are considered to be
present in negligible quantities when prepared by non-mechanical methods and have not experienced any deformation thereafter. However, twin stacking faults have been shown to be present in conventional electrodeposited fcc metals and alloys, e.g., Ag, Cu, Ni and Ni-Fe [Hinton et al. (1963), Hofer et al. (1965), Suoninen (1967), Nakahara (1981), Anderson et al.
(1973)], even when no deformation has taken place. In particular, electrodeposited Ni has been shown to possess twin stacking faults of the growth type and not of the deformation induced type [Nakahara (1981)]. From this point onward, we refer to such twin stacking faults of the growth type as “growth faults”. The presence of these growth faults and their contribution to microstrain induced XRD line broadening in these materials produced using electrodeposition processes should be considered.
2.3. References Abermann, R. and R. Koch, Thin Solid Films 129 (1985) 71.
Anderson, R.L., A. Gangulee and L.T. Romankiw, J. Electron. Mater. 2 (1973) 161.
Armyanov, S. and G. Sotirova, Surf. Coat. Tech. 34 (1988) 441.
Armyanov, S. and G. Sotirova-Chakarova, Metal Finish., March (1993) 42.
Armyanov, S. and G. Sotirova-Chakarova, Metal Finish., April (1993) 59.
Auerswald, J. and H.-J. Fecht, J. Electrochem. Soc. 157 (2010) D199.
Aust, K.T., G.D. Hibbard, G. Palumbo and U. Erb, Z. Metallk. 94 (2003) 10.
Aust, K.T., G.D. Hibbard and G. Palumbo, in: Encyclopedia of Nanoscience and Nanotechnology (H.S. Nalwa, ed.), p.627, American Scientific Publications, 2004.
Biju, V., N. Sugathan, V. Vrinda, and S.L. Salini, J. Mater. Sci. 43 (2008) 1175.
Buckel, W., J. Vac. Sci. Technol. 6 (1970) 606.
Cao, H.S., J.J. Hunsinger and O. Elkedim, Scripta Mater. 46 (2002) 55.
Cheung, C.K.S., F. Djuanda, U. Erb and G. Palumbo, Nanostruct. Mat., 5 (1995) 513.
Cho, H.S., K.J. Hemker, H. Lian, J. Goettert and G. Dirras, Sens. Actuators A 103 (2003) 59.
Chung, C.K., W.T. Chang, C.F. Chen and M.W. Liao, Mater. Lett. 65 (2011) 416.
Clarebrough, L.M., M.E. Hargreaves and G.W. West, Proc. Roy. Soc. London, 232A (1955) 252.
Cullity, B.D. and S.R. Stock, “Elements of X-Ray Diffraction, Third Edition”, Prentice Hall, New Jersey, 2001.
Czerwinski, F., J. Electrochem. Soc. 143 (1996) 3327.
Czerwinski, F., Thin Solid Films, 280 (1996) 199.
Czerwinski, F., Electrochim. Acta 44 (1998) 667.
D’Heurle, F.M. and J.M.E. Harper, Thin Solid Films 171 (1989) 81.
Derlet, P.M., S. Van Petegem and H. Van Swygenhoven, Phys. Rev. B 71 (2005) 024114.
Dini, J.W., Electrodeposition: The Materials Science of Coatings and Substrates, Noyes Publications, New York, 1993.
Doljack, F.A. and R.W. Hoffman, Thin Solid Films, 12 (1972) 71.
Eastman, J.A., M.A. Beno, G.S. Knapp and L.J. Thompson, Nantostruct. Mater. 6 (1995) 543.
Eckert, J., J.C. Holzer, C.E. Krill, III and W.L. Johnson, J. Mater. Res. 7 (1992) 1751.
El-Sherik, A.M., U. Erb, G. Palumbo and K.T. Aust, Scripta Metall. Mater., 27 (1992) 1185.
El-Sherik, A.M. and U. Erb, J. Mater. Sci., 30 (1995) 5743.
El-Sherik, A.M., J. Shirokoff and U. Erb, J. All. Comp. 389 (2005) 140.