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«STRUCTURE AND PROPERTIES OF ELECTRODEPOSITED NANOCRYSTALLINE NI AND NI-FE ALLOY CONTINUOUS FOILS by Jason Derek Giallonardo A thesis submitted in ...»

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A schematic representation of load versus indenter displacement data. Pmax is the peak indentation load; hmax is the indenter displacement at peak load; h f is the final depth of contact impression after unloading; and S is the initial unloading stiffness [Oliver and Pharr (1992)].

–  –  –

section of an indentation that identifies the parameters used in the analysis and Fig. 3.3 shows a schematic of a load versus indenter displacement data. According to Oliver and Pharr (1992), the relationship used to describe the unloading data for the stiffness measurement is,

–  –  –

where, P is the load and h is the contact height provided by the depth-load data, and P0, m, and h f are all constants determined by a least squares fitting procedure. At peak load, the load and displacement are Pmax and hmax. Given Pmax, hmax can be calculated using Eq. 3-19.

The measured stiffness, S, at hmax may be calculated as follows,

–  –  –

Finally, the contact area, A( hc )  24.5hc2, is calculated and values for the hardness, H, and reduced Young’s modulus, Er, are determined,

–  –  –

Where,  is the Poisson’s ratio of the specimen and Ei and  i are the Young’s modulus and Poisson’s ratio for the indenter.

In this study, the hardness and Young’s modulus were determined using a SHIMADZU Dynamic Ultra-Micro Hardness Tester with a Berkovich (three sided pyramid) nanoindenter. Measurements were made by using cyclic loading (four cycles per load) in order for the last unloading curve to be almost purely elastic, allowing for a reliable Young’s modulus determination. At the beginning of each set of measurements, the mechanical drift of the equipment was minimized by a stabilization process whereby loading was carried out at 100 mN for approximately 1.3 hrs. To assure reliability, the equipment was regularly calibrated using a series of standard relatively isotropic samples, including fused quartz, W, and Al, representing a wide range of Young’s modulus values. The samples were prepared by mounting on their cross-section, mechanically grinding and polishing to a mirror finish.

Each sample was measured under five different loads (150, 130, 110, 90 and 70 mN) with four trials per load. The loading rate was 13.3 mN/s for all loads. The last elastic unloading curves were analyzed to determine hardness and Young’s modulus using the procedure outlined by Oliver and Pharr (1992).

3.7. Macrostress The effects of strain on diffraction lines are described as either uniform or nonuniform [Cullity and Stock (2001)]. If the grain is under uniform tension, the d-spacing is larger than d 0, and the corresponding diffraction line shifts to lower angles as shown in Fig.

3.4 for the normal (N) direction.

–  –  –

Figure 3.4.

Schematic of the strain measurement based on the Bragg law. N is the plane normal direction and when there is a strain the d-spacing is not in equilibrium and thus there is a strain,  n, in the plane normal direction [He (2009)].

In the case where the grain is under uniform compression the d-spacing is smaller and diffraction line shift is to the left. This line shift is the basis of the X-ray method for the determination of macrostress [James and Cohen (1980)]. There are two main XRD methods for determining internal stress: conventional and two-dimensional (2D). In both cases, the Bragg law is the basis of the stress analysis and is used to detect changes in the d-spacing of a variety of grains in different orientations along the sample plane.

The conventional method is carried out with an X-ray diffractometer equipped with a point detector. In the case of a 2D X-ray diffractometer, an area detector is used. When using an area detector parts of the diffracted rings become visible as opposed to simply lines on the diffractometer plane in the conventional method. 2D X-ray diffraction has the advantage of including a larger number of crystallites which provides better accuracy and

–  –  –

sampling statistics (see Fig. 3.5). This method to determine macrostress has been well developed by He (2009). In 2D X-ray diffraction, an unstressed sample will produce a regular cone having the same 2θ at all  angles. In a stressed sample, the cone is not regular but distorted and thus the 2θ value becomes a function of γ and the sample orientation (,,  ). The strain may then be related to the degree of cone distortion via the Bragg law.

Referring to Fig. 3.6, consider a point on a given {hkl} diffraction ring, P, such that the corresponding diffraction vector points to P'. The strain can then be measured based on the true strain definition [He (2009)],

–  –  –

where, pij are stress coefficients that include the Young’s modulus, Poisson’s ratio, and Xray elastic constants for the material being analyzed. A complete derivation of this equation can be found in He (2009). In most stress determinations, and especially in the case of electrodeposited metals, the thickness of the material is relatively low and thus, the average stress in the normal direction is taken to be zero. Furthermore, when the stress is biaxial,  33 =  13 =  23 = 0. In order to accommodate for the fact that a precise d 0 value is not

–  –  –





Figure 3.7.

(a) Stress components on a volume element [He (2009)], and (b) the stress tensor.

available, a directionless “faulty stress” is introduced into the equation and is termed a “pseudo-hydrostatic stress” [He (2009)], however, it does not have a physical meaning.

Accounting for the biaxial stress and introducing the “pseudo-hydrostatic stress”, Eq. 3-26 is reduced to,

–  –  –

where, p ph and  ph are the “pseudo-hydrostatic” stress coefficient and the “pseudohydrostatic” stress, respectively. It should also be noted that in the analysis it is recommended to take into account the anisotropic nature of these materials, i.e., considering the fact that stresses determined from diffracting crystallographic planes may have different As such, a radiocrystallographic anisotropy factor, ARX, is introduced into the values.

analysis and used to calculate the X-ray elastic constants for the plane on which the

–  –  –

(2009)].

In this study, macrostress determinations were carried out using an XRD system configuration consisting of a Bruker SMART 6000 CCD detector, a Bruker D8 3-circle fixed-χ (or ψ) goniometer, a Rigaku Ru200 rotating anode Cu-K (λ = 0.1542 nm) X-ray generator, and a Goebel cross-coupled parallel-focusing mirror. The diffractometer was operated at 45kV/30mA to generate the Cu-K radiation with a monochromator. Each sample was measured at a fixed ω and ψ angle of 165.0o and 35.2o, respectively. The ϕ angle range was 135 to 240o and the step size was 15o. The 2θ values were integrated along a γ range of 63.3 to 117.2o with a step size of 0.01o. The software used in the analysis was provided by Bruker Advanced X-Ray Solutions (1999) for their General Area Detector Diffraction System (GADDS) V.4.1.29. For the analysis, the (311) ring occurring in the 2θ range of 90.5 to 95.5o was chosen in order to maximize spatial resolution.

–  –  –

3.8. References Andricacos, P.C., C. Arana, J. Tabib, J. Dukovic and L.T. Romankiw, J. Electrochem. Soc.

136 (1989) 1336.

Balzar, D., in “Defect and Microstructure Analysis from Diffraction”, Ed. R.L. Snyder, H.J.

Bunge, and J. Fiala, International Union of Crystallography, Monographs on Crystallography No. 10, Oxford University Press, New York, 1999.

Brenner, A., “Electrodeposition of Alloys – Principles and Practice, Volume II”, Academic Press, New York, 1963.

Bruker Advanced X-Ray Solutions, “General Area Detector Diffraction System (GADDS) User Manual”, Bruker AXS Inc., Madison, WI, 1999.

Cohen, J.B. and C.N.J. Wagner, J. Appl. Phys., 33 (1962) 2073.

Cullity, B.D. and S.R. Stock, “Elements of X-Ray Diffraction, Third Edition”, Prentice Hall, New Jersey, 2001.

Dahms, H. and I.M. Croll, Journal of the Electrochemical Society, 112 (1965) 771.

Dini, J.W., H.R. Johnson and H.J. Saxton, J. Vac. Sci. Technol. 12 (1975) 766.

Doerner, M.F. and W.D. Nix, J. Mater. Res. 1 (1986) 601.

El-Sherik, A.M. and U. Erb, J. Mater. Sci., 30 (1995) 5743.

Erb, U. and A.M. El-Sherik, U.S. Patent 5,352, 266, 1994.

Erb, U., A.M. El-Sherik, C.K.S. Cheung and M.J. Aus, United States Patent No. 5,433,797, 1995.

Fischer-Cripps, A.C., “Nanoindentation”, Springer, New York, 2002.

He, B.B., “Two-Dimensional X-Ray Diffraction”, John Wiley & Sons, Hoboken, New Jersey, 2009.

Hessami, S. and C.W. Tobias, J. Electrochem. Soc. 136 (1989) 3611.

James, M.R. and J.B. Cohen, “The Measurement of Residual Stresses by X-Ray Diffraction Techniques”, in: “Treatise on Materials Science and Technology”, Ed.: H. Herman, Academic Press, New York, 1980, 1-62.

Klinger, L. and E. Rabkin, Scripta Mater. 48 (2003) 1475.

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Marcus, P. and H. Talah, Corr. Sci. 29 (1989) 455.

Matlosz, M., J. Electochemc. Soc. 140 (1993) 2272.

Matulis, J. and R. Slizys, Electrochimica Acta, 9 (1964) 1177.

Nakano, H., M. Matsuno, S. Oue, M. Yano, S. Kobayashi and H. Fukushima, Materials Transactions, 45 (2004) 3130.

Nichol, M.J. and H.I. Philip, J. Electroanal. Chem. Interfacial Electrochem. 70 (1976) 233.

Oliver, W.C., R. Hutchings and J.B. Pethica, in ASTM STP 889, Ed. P.J. Blau and B.R.

Lawn, American Society for Testing and Materials, Philadelphia, PA, 1986.

Oliver, W.C. and G.M. Pharr, J. Mater. Res., 7 (1992) 1564.

Oliver, W.C. and G.M. Pharr, J. Mater. Res., 19 (2004) 3.

Palumbo, G., I. Brooks, J. McCrea, G.D. Hibbard, F. Gonzalez, K. Tomantschger and U. Erb, United States Patent Application No. US 2005/0205425 A1, 2005.

Pethica, J.B., R. Hutchings and W.C. Oliver, Phil. Mag. A 48 (1983) 593.

Piatti, R.C.V., A.J. Arvia and J.J. Podesta, Electrochimica Acta, 14 (1969) 541.

Romankiw, L.T., in: Proceedings of the Symposium on Electrodeposition Technology – Theory and Practice, ed. L.T. Romankiw, The Electrochemical Softbound Series, PV87-17, Pennington, NJ, 1987.

Willson, K.S. and J.A. Rogers, Tech. Proc. American Electroplaters Soc. 51 (1964) 92.

Wilson, A.J.C., X-Ray Optics, London, Methuen, 1962.

Yin, K.-M., J.-H. Wei and J.-R. Fu, J. Appl. Electrochem. 25 (1995) 543.

Yin, K.-M., J. Electrochem. Soc. 144 (1997) 1560.

CHAPTER 4 Materials Synthesis and Characterization

4.1. Introduction Ni naturally occurs in the γ (fcc) phase. When alloyed with Fe, it can either occur in the  (fcc) phase or the  (bcc) phase. There are many interesting properties associated with Ni-Fe alloys. For example, at approximately 20wt.%Fe in the γ (fcc) phase an alloy commonly known as permalloy is a material with unique soft magnetic properties, including a high magnetic permeability. At approximately 64wt.%Fe also in the γ (fcc) phase a commercial alloy commonly known as Invar has a uniquely low coefficient of thermal expansion. Given the importance of these materials in commercial applications, the Ni-Fe family of alloys has been a subject of interest for many years.

–  –  –

One of the first proposals for the Ni-Fe phase diagram was made as early as 1904 [Osmond and Cartaud (1904)]. The most recent version can now be found in handbooks, e.g., Scott (1992). Fig. 4.1 presents the equilibrium phase diagram for Ni-Fe. When produced using conventional metallurgical processing methods, the resulting alloys will normally have structures that agree with the phase diagram. Electrodeposited alloys, on the other hand, do not entirely follow the conventional phase diagram partly because of the relatively low temperatures at which the materials are synthesized. Fig. 4.2 shows the phases commonly seen in electrodeposited Ni-Fe alloys as a function of Fe concentration [Fukumuro et al.

(2004)].

  

–  –  –

Figure 4.2.

The phases found in electrodeposited Ni-Fe alloys [Fukumuro et al. (2004)].

For example, according to the Ni-Fe equilibrium phase diagram (Fig. 4.1), compositions in the neighbourhood of Ni-(10-28)wt.%Fe show the presence of the ordered FeNi3 structure in the  (fcc) phase. The phase diagram holds true for this particular subset of Ni-Fe alloys when produced using conventional metallurgical processing methods.

However, electrodeposited Ni-Fe alloys in the same compositional range may not entirely exhibit the ordered FeNi3 structure which, again, could be due to the relatively low temperatures at which the synthesis process is operated at. As a result, the Ni-Fe alloys produced by electrochemical synthesis techniques typically have non-equilibrium structures.

–  –  –

The determination of the crystal structure of Ni-Fe alloys by, for example, X-ray diffraction, is somewhat ineffective since the respective atomic scattering factors of Ni and Fe are similar. That is, the structure factor values for superlattice reflections in the unit cell with an ordered FeNi3 structure are so small that any scattering of X-rays are practically undetectable. Electron diffraction is also ineffective, since the scattering characteristics of the electrons by Ni and Fe are also very similar. Other methods, such as Mössbauer spectroscopy, can be used to study the short range order; however, the interpretation of the data is often challenging and is likely to lead to significant uncertainties [Cranshaw (1987)].

The existence of an ordered structure in electrodeposited Ni-Fe alloys has been suggested indirectly in the study of the thermal properties of nanocrystalline Ni-Fe alloys by Turi (1997). Turi (1997) noted significantly increased total enthalpy releases upon grain growth when compared to nanocrystalline Ni samples with similar grain sizes. The additional release of energy was owed to the formation of the ordered FeNi3 structure from the initial disordered structured obtained from the electrodeposition synthesis technique.



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