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Power difference ( P ), increment in electrical resistivity (  ), and hardness (VHN) for specimens of polycrystalline Ni deformed in torsion and heated at 6o/min [Clarebrough et al. (1955)].

When nanocrystalline Ni is anisothermally annealed it exhibits heat releases that are not necessarily due to the same types of heat release events when compared to cold worked conventional polycrystalline Ni. A typical nanocrystalline Ni anisothermal anneal curve is

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shown in Fig. 2.12 [Klement et al. (1995a)]. The maximum heat release in the anisothermal anneal curve is referred to as the peak temperature, Tp, and can be used as a relative measure of the thermal stability.

Figure 2.12.

Anisothermal anneal curve (DSC) of a 10 nm electrodeposited Ni sample at a heating rate of 10 oC/min [Klement et al. (1995a)].

The H (area under the curve) can be used to determine the interfacial enthalpy if the grain sizes and shapes of the initial nanostructure and the final structure after grain growth are known. The H for the total heat release in Fig. 2.12 was found to be about 18 J/g which is in good agreement with measurements of other materials such as nanocrystalline Pd where a 16 J/g heat release was found [Rupp and Birringer (1987)]. Klement et al.

(1995a) and Klement et al. (1995b) described the three distinct exothermic reactions shown

in Fig. 2.12 in the following manner:

(1) “nucleation” and abnormal grain growth induced by sub-grain coalescence (80

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(2) normal grain growth process (289-370oC) (3) growth towards equilibrium (370-500oC) In the first stage, the formation of the first grown grains may be explained by a combination of a relaxation and the subgrain coalescence model known from primary recrystallization [Hu (1963), Li (1962)]. Further to this, Rupp and Birringer (1987) suggested that a relaxation of the nanocrystalline microstructure takes place at a sufficiently high temperature. This relaxation leads to positions of “lower energy” for the grain boundaries creating the first grown grains “accidentally” by removing low angle grain boundaries. These three events are considered to be the major contributors to the observed heat releases, however there may be other factors involved such as the influence of impurities. In particular, S and C tend to be present in significant quantities in electrodeposited Ni. Klement et al. (1995a) investigated the influence of S and concluded that there is likely a significant enrichment of S in the grain boundaries which may hinder the formation of larger grains with boundaries in equilibrium positions and diminishes the third exothermic stage of the anisothermal anneal curve.

Unfortunately, they were not able to determine the influence of C which is also present in nanocrystalline Ni. Similar DSC curves for annealed nanocrystalline Ni were later presented by Wang et al. (1997) and Hibbard et al. (2002).

2.2. Internal Stress 2.2.1. Overview In conventional metals, internal stresses may be introduced by various means. These stresses are normally present when regions of the material are inhomogeneously elastically or plastically deformed in a permanent manner such that strain incompatibilities occur. Internal

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stresses are self-equilibrating, so the resultant force produced must be zero. Macherauch and Kloos (1987) classify these stresses into three categories using the term “homogeneous” to

describe the condition “constant in magnitude and direction”:

I. Nearly homogeneous across large areas (several grains) of a material and are equilibrated within the whole body.

II. Nearly homogeneous across microscopic areas (one grain or parts of a grain) of a material and are equilibrated across a sufficient number of grains.

III. Inhomogeneous across submicroscopic areas of a material (several atomic distances within a grain) and are equilibrated across small parts of a grain.

Type I stresses are called “macrostresses” but are commonly known as either “residual” or simply “internal” stresses. On the other hand, Type II and III stresses are commonly referred to as “microstresses”. Note that in the case of Type III stresses, the corresponding strain values are typically reported which are referred to as “microstrain”.

There are many processes which generate internal stresses including mechanical, thermal, and chemical treatments or any combination of these. Table 2.1 lists the main sources and sub-sources of Type I stresses. In all cases, the resulting internal stress depends heavily on the geometrical conditions and on the parameters of the treatments and processes applied. Type I stresses are usually observed after the material has been exposed to elasticplastic loading resulting in a homogeneous lattice strain. Type I stress varies over large

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distances and causes shifting of the characteristic XRD lines [Macherauch and Kloos (1987)].

On the other hand, Type II stresses vary over the grain scale and can also cause XRD line shifts. These Type II stresses may also be referred to intergranular stresses which are always present in polycrystalline materials and are a result of the varying elastic and thermal properties between differently oriented grains which form grain boundaries [Withers and Bhadeshia (2001)]. Finally, Type III stresses result from a number of imperfections in the materials on an atomic scale, for example, dislocations, vacancies, grain boundaries, voids, inclusions, etc, resulting in an inhomogeneous lattice strain [Macherauch and Kloos (1987)].

Fig. 2.13 schematically displays typical examples based on a simple cubic grain structure.

Each of the types of stresses mentioned can affect XRD lines. A homogeneous stress typically results in a uniform strain while an inhomogeneous stress results in a non-uniform strain. When the material is uniformly strained the interplanar spacing changes from their stress-free value to some new value. This uniform strain effectively causes a shift of the diffraction lines to new 2 positions (see Fig. 2.14b). On the other hand, the non-uniform strain varies from one grain to another or from one part of a grain to another part on a microscopic scale. In this case, the lattice planes usually become distorted in such a way that the spacing of any particular (hkl) set varies from one grain to another. This non-uniform microstrain causes a broadening of the diffraction lines (see Fig. 2.14c). Usually, both uniform and non-uniform strains are superimposed [Cullity and Stock (2001)].

There are a variety of methods available for measuring the internal stresses in materials that are deposited (e.g., vapour deposited, electrodeposited, etc.) using various

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Figure 2.14.

Effect of uniform and non-uniform strains (left side of the figure) on diffraction peak position and width (right side of the figure). (a) Shows the unstrained sample, (b) shows uniform strain, and (c) shows non-uniform strain within the volume samples by the Xray beam [Cullity and Stock (2001)].

synthesis techniques, e.g., the curvature or “bent strip” method and X-ray diffraction. A comparison of these two stress measurement methods for thin films has often led to significant differences [Noyan et al. (1995)]. The X-ray diffraction method involves determining the strain in the material via a change in lattice parameter whereas the curvature technique measures the deflection of a substrate having a deposit resulting from the distribution of forces of the deposit and substrate around the neutral plane. The nature of this interaction with the substrate may be classified as being either extrinsic or intrinsic. Extrinsic stresses are often related to thermal stresses that result from the incompatibility of the two materials coefficient of thermal expansion [D’Heurle and Harper (1989)]. Extrinsic stresses may also arise from the lattice mismatch at the interface between the two materials [Buckel

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(1970)]. On the other hand, intrinsic stresses result from the growth process of the depositing material on the substrate [Klokholm and Berry (1968), D’Heurle and Harper (1989)].

2.2.2. Electrodeposited Metals and Alloys Internal stresses in electrodeposited metals can also be referred to as “intrinsic stresses” since they are not directly caused by applied loads. Internal stresses cause long range bending of metal strips which are electroplated on one side and therefore may be quite uniform over large distance. These stresses are the type which most electroplaters understand as “internal stress” [Schlesinger and Paunovic (2000)]. The first investigation on this subject was recorded by Gore (1858) and almost 20 years later, Mills (1877) and others made the first attempt to measure the stresses in electrodeposits. Internal stresses can cause distortions, cracking of the deposit, loss of adhesion to the substrate, increased corrosion, etc [Schlesinger and Paunovic (2000)]. High internal stresses can also deteriorate fatigue properties of, for example, Ni deposited onto steel. High internal stresses in electrodeposited permalloy cause increased coercivity values when compared to thermally prepared permalloy [Safranek (1986)]. In general, there is considerable practical and commercial importance of understanding internal stresses in electrodeposited metals.

It is a well-known fact that certain sulfur-containing organic compounds cause a reduction in internal stress when present in the plating solution in rather small amounts [Kushner (1958), Weil (1971a), Safranek (1986), Armyanov and Sotirova-Chakarova (1993a), Dini (1993)]. Armyanov and Sotirova-Chakarova [1993a] indicated that the deposition of Ni in the presence of saccharin (C7H5NO3S) may cause structural changes

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which are considered to be due to the adsorption and inclusion of S in the crystal lattice of Ni and along the grain boundaries. It is generally accepted that saccharin decreases grain size owing to the restriction of lateral crystal growth during the deposition process. El-Sherik and Erb (1995) observed a decrease in grain size as a function of saccharin concentration in the production of nanocrystalline Ni. Armyanov and Sotirova-Chakarova [1993a] also noted that plating in the presence of saccharin impedes hydrogenation while other additives, for example, 1,4-butynediol can promote hydrogenation of the coatings [Armyanov and Sotirova (1988)]. In fact, it was found that the addition of saccharin to the bath decreases by one-fifth the content of hydrogen occluded in the Ni deposit [Mukasa and Maeda (1980)].

There is general agreement that increasing Fe concentration in Ni electrodeposits results in an increased internal stresses and therefore, Fe acts as a “stress-intensifier” [Kushner (1958), Weil (1971a), Nakamura et al. (1985), Safranek (1986), SotirovaChakarova and Armyanov (1990), Armyanov and Sotirova-Chakarova (1993b), Dini (1993), Grimmett et al. (1993), Hadian and Gabe (1999)]. To manage the increase in stress for applications requiring a significant amount of Fe, saccharin has also been widely used as a “stress-reducer” in Ni-Fe alloy deposits [Safranek (1986), Toledo (1970), Uehara (1963), Wolf (1963), Maeda and Mukasa (1967)]. In a study by Perakh [1975] using a constant concentration of saccharin, there was an observed increasing internal stress with increasing Fe content. Similarly, Sotirova-Chakarova and Armyanov [1990] used a constant concentration of saccharin and found that when the amount of Fe increased from 0 to 28 wt.%, the tensile internal stresses increased. They also noted a decrease in grain size with

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increasing Fe and suggested that this may be the reason for the observed increase in internal stresses.

2.2.3. Theories on the Origins of Internal Stresses There are numerous experimental results on the effects of such factors as current density, acidity, temperature, and bath composition on internal stresses. For example, Kushner (1958), Weil (1971a) and Safranek (1986) described the effect of these variables on Ni electrodeposits. Most reports in the literature indicate that there is a rise in the internal stress with increasing current density. A sharp rise in internal stress in the range of pH values 4 to 6 is also observed. Increasing temperature decreases the internal stress.

Increasing Fe concentration in the Ni deposit is generally known to increase the internal stress while it is also a well known fact that the addition of certain sulfur-containing organic substances to the electrolyte causes an internal stress reduction [Weil (1971a)]. In the past, the effects of processing variables have often been used to explain the observed internal stresses. However, this traditional approach does not provide a fundamental understanding of internal stresses by taking into consideration the effect of processing variables on the microstructure of the electrodeposited material.

Since the time studies on internal stresses appeared in the open literature, there have been a number of theories presented to explain experimental results. Buckel (1970) pointed

out that aside from thermal stresses, there may be up to six other mechanisms including:

incorporation of atoms (e.g. residual gases or chemical reactants), lattice mismatch between the substrate and the deposit, variation of the interatomic spacing with crystal size,

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recrystallization processes, voids and dislocations, and phase transformations. Weil (1971b), in his review article for electrodeposited materials provided an overview of the major theories which were broken down into five categories: hydrogen effects, changes in foreign substances, lattice defects, crystallite-joining (or coalescence), and excess energy.

While no grain size measurements were made, Kushner (1958) introduced the concept that grain boundaries are essentially high energy regions or active centers where initially depositing metal atoms likely gains its first foothold with the parent metal lattice.

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