Thermal conductivity of bulk electrodeposited nanocrystalline nickel

Thermal conductivity of bulk electrodeposited nanocrystalline nickel

International Journal of Heat and Mass Transfer 100 (2016) 490–496 Contents lists available at ScienceDirect International Journal of Heat and Mass ...

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International Journal of Heat and Mass Transfer 100 (2016) 490–496

Contents lists available at ScienceDirect

International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt

Thermal conductivity of bulk electrodeposited nanocrystalline nickel H.J. Cho a, S. Wang a, Y. Zhou a,⇑, G. Palumbo b, U. Erb a a b

Department of Materials Science and Engineering, University of Toronto, 184 College Street, Suite 177, Toronto, ON M5S 3E4, Canada Integran Technologies Inc, 6300 Northam Drive, Mississauga, ON L4V 1H7, Canada

a r t i c l e

i n f o

Article history: Received 19 November 2015 Received in revised form 8 April 2016 Accepted 21 April 2016 Available online 12 May 2016 Keywords: Thermo-electrical transport Wiedemann–Franz law Lorenz number Nanocrystalline Ni Impurity effects

a b s t r a c t Room temperature thermoelectrical transport was investigated on a series of thick (300 lm), fully-dense electrodeposited nanocrystalline Ni materials with grain sizes below 50 nm. Strong grain size effects were observed on both electrical resistivity and thermal conductivity. As grain size decreased from 47 to 28 nm, the nanocrystalline Ni exhibited an increase in electrical resistivity from 9.42 to 10.2 lX cm, and a reduction of thermal conductivity from 74.7 to 67.3 W/m-K, respectively. Analysis shows that for the nanocrystalline Ni, the change in the values of thermal conductivity and electrical resistivity is mainly due to grain boundary contributions with limited impurity effects. Furthermore, the thermoelectrical transport behavior agrees well with the Wiedemann–Franz law. The corresponding Lorenz numbers varied only in a narrow range from 2.30  108 to 2.37  108 W X/K2 for the nanocrystalline Ni and were well within the experimentally measured value range of 2.12–2.44  108 W X/K2 for coarsegrained Ni reported in the literature. Ó 2016 Elsevier Ltd. All rights reserved.

1. Introduction Nanocrystalline Ni materials are widely used in many engineering applications where the thermal conduction plays an important role in materials performance e.g. [1,2]. In comparison with intensive investigations on properties such as mechanical behavior and thermal stability e.g. [3–12], very few studies have looked at the effects of grain size on thermal transport in bulk nanocrystalline Ni or any other bulk nanocrystalline metals. However, many investigations associated with nanostructure were conducted on thin Ni films having thicknesses down to the nanometer range. For example, measurements were done on thin Ni films sputtered onto quartz substrates with thicknesses ranging from 400 nm to 8 lm (no grain sizes given) and a relatively constant room temperature thermal conductivity, j, of approximately 90 W/m-K, was reported [13]. For thin Ni films fabricated by electron beam physical vapor deposition (e-beam deposition), the experimentally measured j values were found to be 47.5 W/m-K for a 1 lm thick Ni film [14] and 52.7 W/m-K for a 100 nm thick Ni film [15], respectively. Moreover, a free-standing electrodeposited 4 lm thick Ni microbridge showed a j value of 78.8 W/m-K in a recent study [16]. Again, no grain sizes were given in these studies. Apparently in the thickness range from 100 nm to 8 lm of the Ni thin films, there were significant variations of j values from 47.5 W/m-K to ⇑ Corresponding author. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2016.04.068 0017-9310/Ó 2016 Elsevier Ltd. All rights reserved.

90 W/m-K but there was no clear correlation between thermal conductivity and the Ni film thickness as predicted in previous theoretical studies e.g. [17,18]. Computer simulation studies have shown a significant effect of film thickness on thermal conductivity at room temperature for thin Ni films. For a given nano-grain sized Ni film and assuming coarse-grained thick Ni to have j = 91 W/m-K, the room temperature thermal conductivity is expected to decrease from approximately 80 W/m-K to 64 W/m-K as the Ni film thickness decreases from 100 nm to 20 nm e.g. [17,18]. It is possible that grain size may have played a crucial role in the discrepancy between the experimental observations and theoretical predictions for the thermal conductivity as a function of Ni thin film thickness. Generally, grain boundaries are expected to impede thermal transport in materials, creating a temperature discontinuity across the boundaries, a phenomenon quantified as Kapitza resistance of grain boundaries in previous theoretical studies e.g. [19,20]. However, the lack of grain size information precludes an assessment of grain boundary contributions to the discrepancies among the various Ni thin film studies. On the other hand, thermal conductivity of metals is often alternatively assessed from the relatively straightforward measurement of the corresponding electrical resistivity using the wellestablished Wiedemann–Franz (W–F) law. Based on the fact that electrons serve as the dominant energy carrier in both electrical and thermal transport in conventional coarse-grained metals, the classic Wiedemann–Franz law states that the thermal and electrical conductivities are related as follow:

H.J. Cho et al. / International Journal of Heat and Mass Transfer 100 (2016) 490–496

L ¼ j=rT

ð1Þ

where L is a constant known as the Lorenz number, j, r and T are thermal conductivity, electrical conductivity and temperature, respectively [21,22]. Assuming free electrons in solids move like in an ideal gas and using Fermi–Dirac statistics, the theoretical value of the Lorenz number has been determined to be 2.44  108 W X/K2 [22]. For coarse-grained metals, the Lorenz numbers can be readily found in the literature, and the W–F law has been widely employed to estimate thermal conductivity from resistivity measurements for conventional coarse-grained metals e.g. [23]. For nanocrystalline metals, the same approach is also used in some studies to obtain the corresponding j values e.g. [16,18]. However, the validity of the W–F law has not been generally established for nanocrystalline metals, which exhibit many properties that are fundamentally different from their coarse-grained counterparts due to the contribution to properties from considerable fractions of atoms residing in grain boundary regions, e.g. increasing followed by decreasing hardness/strength at smaller grain sizes e.g. [3,24], significant changes in magnetic coercivity [25] and grain size dependent Young’s modulus at very small grain sizes e.g. [26–28]. Regarding thermoelectrical transport, results from previous studies suggested that the W–F law may break down for metals having structural feature lengths on the nanometer scale. For example, the Lorenz number, L, was found to be several times higher than the value of the coarse-grained counterpart, L0, over the temperature range from 80 K up to room temperature in gold films made by e-beam deposition with film thicknesses of 21–37 nm and average grain sizes approximately 70% of the film thickness [29]. In a recent study on gold films of less than 100 nm in thicknesses, deviations from the W–F were observed at room temperature with L values 1.3–1.8 higher than for coarse-grained bulk gold, while the breakdown of the W–F law occurred at T < 40 K with L values several times higher than for bulk gold [30]. The room temperature L value for a free-standing 28 nm thick e-beam deposited film of Pt was substantially enhanced, approximately twice as high as that of coarse-grained bulk Pt [31]. Furthermore, measurements on a Ni nanowire also indicated some deviation from the W–F law [32]. These experimental observations suggest that there may be some fundamental differences in thermoelectrical transport between nanocrystalline metals and their conventional polycrystalline counterparts. This paper focuses on the thermal transport of bulk nanocrystalline Ni produced by electrodeposition, a common synthesis approach to fabricate fully dense nanocrystalline metals [33]. Grain size effects and the validity of the Wiedemann–Franz law at room temperature will be addressed for a series of thick (300 lm) electrodeposited nanocrystalline Ni samples with grain sizes below 50 nm. Thick and large area samples were used in an effort to separate grain size effects from thin film effects. The study is an extension of our previous work [34] and will also address the effect of impurities on thermal conductivity in Ni.

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ness measurements were made on each sample at 100 g load and 10 s dwelling time to determine the average hardness. Commercially available Ni 200 supplied by Special Metals Corporation was used as a coarse-grained counterpart in the current study. Prior to property measurements, the coarse-grained Ni 200 sheet was subjected to annealing treatment in a tube furnace under argon atmosphere for 2 h at 800 °C to obtain a fully recrystallized structure. Samples were then mechanically ground and polished down to 2400 grit SiC paper, followed by 1 lm alumina cloth polishing. The polished surfaces were etched in a solution consisting of 10 g CuSO4, 50 ml HCl and 50 ml H2O at room temperature for 30 s. The microstructure was examined using optical microscopy and the average grain size was obtained based on grain diameter measurements using ImageJ. Thermal conductivity of each material, j, was determined from the measurement of thermal diffusivity at room temperature according to the equation,

j ¼ D a cp

ð2Þ

where D, a and cp are density, thermal diffusivity and specific heat, respectively. Measurements of the thermal diffusivity at room temperature were carried out on 1 cm  1 cm sample coupons according to the ASTM E-1461 [36]. Using the laser flash method (Netzsch LFA 447 Nanoflash Instrument), high-intensity and short duration energy pulses are directed towards the front surface of the sample with a thickness of h. As a result of energy absorption, heat is generated first at the front surface and subsequently propagates through the sample, causing a temperature increase on the rear surface. This temperature change at the rear surface is monitored as a function of time, and the correspondent plot is employed to determine the thermal diffusivity, a, according to the following equation [36],

a ¼ 0:1388h2 =t1=2

ð3Þ

Here h is the sample thickness, and t1/2 is the time required for the rear face temperature rise to reach one half of its maximum value, i.e. the half-rise time. Essentially, the determination of the thermal diffusivity corresponds to the measurements of two fundamental parameters, sample thickness h and half-rise time t1/2. The former was obtained using a micrometer screw gauge, while the latter was measured through the software/hardware package associated with the laser flashing equipment. Based upon the determined a value, the thermal conductivity, j, is obtained at given values of D and cp, i.e. density and specific heat, respectively, as per Eq. (2) [36]. Electrical resistivity was measured at room temperature on 3 cm  0.4 cm strip samples, using the conventional four-point probe technique, whereby the potential drop was measured at a resolution of 1  109 V with constantly supplied DC current of 150 mA. For each sample, two measurements were made, one with forward and the other with reverse electric current, and the average value was taken as the sample electrical resistivity.

2. Experimental

3. Results and discussion

Fully-dense and more than 99.9% pure bulk nanocrystalline nickel materials (300 lm thick) were produced at Integran Technologies, using the electrodeposition process [33,35]. Sample microstructures were examined using transmission electron microscopy (TEM). The average grain size was obtained based on grain diameter measurements on multiple TEM micrographs using ImageJ and approximately 200 grains were measured for each nanocrystalline Ni sample. The Vickers micro–hardness of the materials was measured according to ASTM Standard E384-99 using a Buehler Micromet 5103 Microhardness Tester. Five hard-

3.1. Microstructure and hardness Fig. 1a shows a representative microstructure of the fully annealed coarse-grained nickel sample, the Ni 200. The material consists of well-annealed grains that are equi-axed in shape and separated by clearly defined grain boundaries. A detailed analysis was carried out on a series of optical micrographs, and a total of 257 grains were measured. The details are shown in the grain size distribution histogram in Fig. 1b, which is log-normal with the normal skewed tail to the right of the

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(a)

(b)

Average grain size 57 ± 19 µm

250 µm

Fig. 1. Microstructure of the coarse-grained Ni 200, (a) Optical micrograph, and (b) grain size distribution histogram.

maximum. The average grain size was determined to be 57 lm with a standard deviation of ±19 lm (Fig. 1b). The majority of grains fall within one standard deviation of the average value, i.e. within the range from 38 lm to 76 lm. The nanocrystalline Ni samples were made by the well established electrodeposition process [3,8,33]. Through controlling the operating parameters, e.g. current density and waveform, at given plating bath chemical composition, the samples with various nanostructure as represented by different average grain size and distribution, were synthesized. The microstructures of the nanocrystalline Ni materials were examined using TEM. Fig. 2 shows a set of representative TEM micrographs for one of the nanocrystalline nickel samples: bright field, dark field and selected area diffraction (SAD) images. The grains exhibited an equi-axed shape with relatively small aspect ratio as per bright and dark field images (Fig. 2a, b), typical for nanocrystalline electrodeposits. The SAD pattern (Fig. 2c) demonstrates concentric diffraction rings with relatively uniform intensity on each ring, suggesting a fine grain matrix with more or less even distribution of crystallographic orientations. The rings correspond to the f.c.c crystalline structure of nickel. The other nanocrystalline Ni samples exhibited basically the same features in the microstructure, e.g. fine grains with equi-axed grain shape. Fig. 3 shows the grain size distributions of the nanocrystalline Ni samples used in the current study. All three samples display log-normal grain size distributions. The average grain sizes and standard deviations were determined to be 47 nm ± 18 nm, 36 nm ± 14 nm and 28 nm ± 11 nm, respectively (Fig. 3a–c). As average grain size decreases from 47 nm to 28 nm, the size distribution becomes tighter and more grains fall within one standard deviation of the average value.

(a)

(b)

Table 1 summarizes the average grain sizes for the samples used in the current study together with the corresponding hardness values and the volume fractions of interface or grain boundary atoms, fIN, obtained as per Eq. (4) [37,38] and assuming an average grain boundary thickness of 1 nm and a regular 14-sided tetrakaidecahedron as the ideal grain shape,

 3 1:055D f IN ¼ 1  1  d

ð4Þ

where D and d are the average grain boundary thickness and grain size, respectively. It should be noted that the 14-sided tetrakaidecahedron is often used as an ideal grain shape to describe the polyhedral nature of equi-axed grain structure [8,39,40]. As for grain boundary thickness, many previous studies have shown that highangle grain boundaries achieve an orientation change from one grain to another over a width of approximately 1 nm [41–44]. Clearly, the grain boundary volume fraction is negligible for the Ni 200 with less than 100 ppm. For the nanocrystalline counterparts, orders of magnitude higher fractions of atoms reside in grain boundaries with the values of fIN ranging from 6.6% to 10.9%. Given the volume fraction values, considerable contributions from grain boundaries are generally expected for many properties of the nanocrystalline Ni e.g. [8]. Hardness values follow the general trend of grain size strengthening, displaying higher strength with finer grain size in accordance with the classic Hall–Petch relationship [45,46],

kHP H ¼ H0 þ pffiffiffi d

ð5Þ

where H is the sample hardness, d is the sample average grain size; H0 and kHP are constants specific to materials. The hardness starts at

(c)

Fig. 2. Microstructure of a representative nanocrystalline sample with average grain size of 28 nm, (a) TEM bright field, (b) TEM dark field, and (c) TEM selected area diffraction pattern.

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Fig. 4. Hall–Petch plot of the nickel samples.

1.94 GPa for the coarse-grained Ni (57 lm Ni 200) and shows a substantial increase as grain size decreases into the nanocrystalline region; specifically, the 47 nm Ni exhibits a microhardness of 3.81 GPa, while the 28 nm Ni shows 4.44 GPa. Fig. 4 shows the Hall–Petch plot of the hardness values for all Ni samples. This trend of increasing hardness with decreasing grain size is in general agreement with earlier studies on electrodeposited nanocrystalline materials [3,47,48]. 3.2. Thermal and electrical transport in nanocrystalline Ni

Fig. 3. Grain size distributions for the three nanocrystalline Ni samples with average grain sizes of (a) 47 nm, (b) 36 nm, and (c) 28 nm, respectively.

Table 1 Grain size, hardness and grain boundary volume fractions for all Ni samples.

Thermal conductivity of each sample, j, was obtained based on measured thermal diffusivity, a, using Eq. (2). Previous studies have shown little dependence of both density and specific heat e.g. [49–51] of Ni on grain size. In fact, their values remain more or less the same for the grain size ranging from 20 nm to 100 lm. Therefore, the handbook values [52] at room temperature for density (D = 8.9 g/cm3) and specific heat (cp = 0.444 J/g°C) of Ni were used in the current study. The room temperature thermal conductivities are summarized in Table 2, together with the electrical resistivity values q, for all samples. The resistivity shows a clear increasing trend from 9.37 to 10.2 lX cm as grain size decreases from 57 lm to 28 nm. For the Ni 200, the measured resistivity of 9.37 lX cm lies well within the reported room temperature q value range of 7.0–9.5 lX cm for coarse-grained Ni in the literature e.g. [52–55]. The wide q value range suggests considerable sample differences among various studies in the literature. Given the very small variations in grain boundary volume fractions among the various coarsegrained materials as per Eq. (4), grain size is likely a minor contributor to this wide q range. Rather, different impurity levels among the various materials are more likely the major contributor, which will be discussed in more details in Section 3.3. For the nanocrystalline Ni electrodeposits, the q range in the current study agrees well with the reported 9.4–10.4 lX cm for the Ni samples with grain size range of 55–30 nm and fabricated through the same Integran electrodeposition process [8,56]. Higher resistivity of 11.5 lX cm was reported for a Ni electrodeposit with 230 nm grain size in another study [57]. Table 2 Room temperature thermal conductivity and electrical resistivity for all Ni samples.

Material

Grain size

Grain boundary volume fraction,%

Vickers hardness (GPa)

Material

Grain Size

Thermal conductivity (W/m-K)

Electrical resistivity (l X cm)

Ni 200 n-Ni 1 n-Ni 2 n-Ni 3

57 ± 19 lm 47 ± 18 nm 36 ± 14 nm 28 ± 11 nm

0.0056 6.6 8.5 10.9

1.94 ± 0.10 3.81 ± 0.07 4.24 ± 0.04 4.44 ± 0.03

Ni-200 n-Ni 1 n-Ni 2 n-Ni 3

57 ± 19 lm 47 ± 18 nm 36 ± 14 nm 28 ± 11 nm

77.9 74.7 73.2 67.3

9.37 9.42 9.63 10.20

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Regarding the room temperature thermal conductivity, j, a grain size effect is also evident; the Ni samples exhibit decreasing thermal conductivity from 77.9 to 67.3 W/m-K with decreasing grain size from 57 lm to 28 nm. The commercial Ni 200 sample exhibits a j value of 77.9 W/m-K, which is within the literature value range for coarse-grained Ni from 70 to 91 W/m-K e.g. [52– 55]. The uncertainty associated with thermal conductivity measurement may be one of the reasons for the wide range of the reported values. In the case of the current study, the two measured parameters are sample thickness h and half-rise time t1/2 as mentioned earlier in Section 2. The samples used in the current study have a thickness of hundreds of micrometers (300 lm). The accuracy of the micrometer screw gauge is 2 lm, leading to an uncertainty in the thickness (square) measurement at the level of less than 2% (Eq. (3)). On the other hand, the overall laser flashing equipment measurement resolution is reported to be approximately 3% [58], which is practically the maximum uncertainty due to the measurement of the half-rise time t1/2. Combining the two leads to the uncertainty of the diffusivity measurement at the level of about 5%. During the measurement, the sample specific heat and density remain essentially constant because of negligible sample temperature change [36]. Hence, the maximum uncertainty of the thermal conductivity measurement is practically the same as that of the thermal diffusivity, i.e. 5%, in the current study. Likely, this measurement uncertainty is a minor contributor to the wide range of the reported Ni thermal conductivity values. Instead, different impurity levels in the coarse-grained Ni samples are expected to be the dominant factor. For thick nanocrystalline Ni materials, reports on experimental measurements of thermal conductivity are scarce. The closest case was a study on 250 lm thick Ni electrodeposits having submicron grain sizes. In the asdeposited state, samples with grain size of 890 nm and 230 nm displayed thermal conductivity of 80.8 and 61.4 W/m-K, respectively [57]. The reported j of the 890 nm sample is close to the value of the Ni 200 in the current study. However, the 230 nm sample showed evidently a lower j value. On the other hand, quite a number of previous studies, theoretical as well as experimental, were done on thin Ni films. Usually, thermal conductivity was investigated as a function of film thickness, and the corresponding grain size was estimated based on an assumed ratio of film thickness over grain size. For example, grain size effects on thermal conductivity were assessed in computer simulations on room temperature thermal conductivity for Ni films at thickness below 100 nm with the ratios set at 1, 2 and 3 e.g. [17,18]. A clear trend of decreasing j with film thickness/grain size was observed [18], very similar to the current experimental observations. However, the calculated thermal conductivities generally exhibited values higher than the experimentally measured j in the current study. This may be attributed to the fact that simulation was conducted assuming pristine and structurally idealized Ni. Previous experimental studies on thin Ni films may provide further illustration on the multi-factor dependent nature of thermal conductivity. In the case of thin Ni films fabricated by electron beam physical vapor deposition, the experimentally measured j values at room temperature were found to be 47.5 W/m-K for a 1 lm thick Ni film [14] and 52.7 W/m-K for a 100 nm thick Ni film [15], respectively, considerably lower than the simulation values. In contrast, measurements performed on Ni films sputtered on quartz substrates with varying thicknesses from 400 nm to 8 lm, showed a thermal conductivity essentially independent of the film thickness, approximately 90 W/m-K [13]. Moreover, a free-standing electrodeposited 4 lm thick Ni micro-bridge exhibited a j value of 78.8 W/m-K in a recent study [16]. Evidently, these reported room temperature j values show no consistent correlation between j and film thickness among the various studies for thin Ni films, likely due

Fig. 5. Thermoelectrical transport of the nanocrystalline Ni at room temperature.

Table 3 Room temperature Lorenz number of Ni, current vs previous studies. Material

Thickness

Grain size

Lorenz number (108 W X/K2)

Source

Ni-200 n-Ni 1 n-Ni 2 n-Ni 3

300 lm

57 lm 47 nm 36 nm 28 nm

2.45 2.36 2.37 2.30

Current

Ni foil Ni foil

250 lm

890 nm 230 nm

2.16 2.37

[57]

Ni thin film Handbook Ni

4 lm N/A

N/A N/A

2.56 2.12–2.44

[16] [52,53,55,59–61]

to the contributions from multiple other factors. Hence, caution is recommended when comparing thermal conductivity values among various studies, even for the same sample shape/geometry (e.g. thin film) and/or synthesis method (e.g. e-beam deposition). In the current study, the samples have an approximate thickness of 300 lm. Unlike the thin film counterparts typically with thickness below 5 lm, these thick samples behave practically like bulk material with negligible effects of sample thickness on the measurement of thermoelectrical transport as demonstrated in previous studies [17,18]. Moreover, the grain size of these samples is essentially independent from their thicknesses because it is controlled by the deposition operating parameters, e.g. current density and wave form at given plating bath chemical composition, using the Integran process [33]. In other words, Table 2 and Fig. 5 show the evident grain size effects on the thermoelectrical transport for the bulk nanocrystalline Ni electrodeposits in the current study. Based on the measured thermal and electrical transport parameters, j and q, the corresponding Lorenz numbers, L, can be readily obtained as per Eq. (1), and are summarized in Table 3 for the Ni samples in the current study. Also included are the reported values obtained through experimental measurements on electrodeposited Ni foils [57], free standing Ni thin film [16] and coarse-grained conventional Ni [52,53,55,59–61]. The values of the Lorenz number derived from the measurements in the current study are close to each other with a narrow variation from 2.30 to 2.45  108 W X/K2, and are comparable to the theoretical value of 2.44  108 W X/K2 on the basis of free electron gas model [22]. Moreover, they agree well with the experimentally determined handbook value range from 2.12  108 W X/K2 to 2.44  108 W X/K2 for coarsegrained nickel [52,53,55,59–61]. Similar Lorenz numbers of 2.16  108 W X/K2 and 2.37  108 W X/K2 were observed in an

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experimental study on electrodeposited 250 lm Ni foils having grain sizes of 890 and 230 nm, respectively [57]. Slightly higher Lorenz number, 2.56  108 W X/K2, was reported in a recent study for a free standing 4 lm thin Ni film also synthesized by electrodeposition [16]. Overall, the experimental results on the Lorenz number among various studies agree well with each other despite the significant differences in sample shape/geometry (thin film vs bulk), and grain size (coarse-grained vs nanocrystalline), indicating the universal applicability of the Wiederman–Franz law for metallic Ni. In other words, free electrons function as the dominant energy carriers for both thermal and electrical transport in the nanocrystalline Ni essentially in the same way as in the coarse-grained counterpart at room temperature. From a practical point of view, using the Wiedermann–Franz law is therefore a legitimate approach to assess room temperature thermal conductivity for nanocrystalline Ni on the basis of much easier to perform electrical resistivity measurements. 3.3. Impurity effects on thermal conductivity in nickel As mentioned in the preceding section, a wide range of thermoelectrical transport values were reported in literature for coarse-grained Ni. According to Eq. (4), the grain boundary volume fraction variation is insensitive to grain size for coarse-grained Ni in the micrometer range. For example, the difference in volume fraction is very small, i.e. 3.2  105, between two hypothetical coarse-grained Ni samples with average grain sizes of 50 lm and 100 lm. This small difference unlikely results in the magnitude of the aforementioned thermal transport value range. On the other hand, a wide value range was observed in an early study on a series of coarse-grained Ni samples with different impurity contents [62]. It was found that the room temperature thermal conductivity was approximately 90 W/m-K for a sample labeled as very high purity, and about 80 W/m-K for a 99.5% pure sample. In contrast, one Ni sample exhibited a j value below 70 W/m-K, which was attributed to high impurity content [62]. Therefore, further examining impurity effects could provide a better understanding of the thermoelectrical values obtained in the current study. For the case of coarse-grained Ni, additional measurements were done on a high-purity 99.99% nickel (HP Ni) sample supplied by Alfa Aesar (main impurity: Fe). Using the same procedure as for the Ni 200 material, its grain size was experimentally determined to be 178 lm as per optical microscopy examination. For nanocrystalline Ni, the impurity effect was examined through measurements on an additional Integran-process sample, nNi 4, in two states, the as-deposited state and the annealed state, at 200 °C for 89 h. The nNi 4 had an as-deposited average grain size of 50 nm determined per TEM micrograph examination. Based on the Integran quality control standards, the sample has 99.9% purity (main impurities: S and C). In the Integran-process, one of the key quality control steps is to monitor and control the plating bath chemistry on a continuing basis to ensure sample impurity content below a certain level. Upon annealing, the as-deposited nNi 4 underwent grain growth due to substantial thermodynamic driving force to eliminate grain boundaries. For nanocrystalline Ni produced by the same method, previous studies showed that the grain boundaries become mobile at about 120 °C [12,63]. Generally at a given annealing temperature, grains in the nanocrystalline Ni electrodeposits initially undergo fast growth for some time, and gradually stabilize at an equilibrium size [64,65]. Usually, higher annealing temperature results in faster growth and larger equilibrium size for a given nanocrystalline Ni [64–66]. For the nNi 4, the annealing temperature was chosen at 200 °C to activate grain growth, while minimizing the potential oxidation effect on the subsequent transport measurement. The annealing time of 89 h provided time for sufficient grain growth

Table 4 Thermal conductivity at 298 K of commercial Ni 200 and high purity coarse-grained Ni as well as nanocrystalline Ni in the as-deposited and annealed states. Material

Sample state

Purity level (% Ni)

Grain size

Thermal conductivity (W/m-K)

Ni 200 HP Ni nNi 4 nNi 4

As-received As-received As-deposited Annealed [email protected] °C

99.0 99.99 99.9 99.9

57 lm 178 lm 50 nm 520 nm

77.9 92.3 77.2 89.0

as confirmed by the grain size examination. In the annealed state, the average grain size of the nNi 4 increased to 520 nm as per SEM examination. The results are summarized in Table 4, together with those of the commercial 99.0% Ni 200 (main impurities: Fe, Mn, Si and Cu according to the supplier data sheet). For the coarse-grained Ni, approximately two orders of magnitude increase in purity leads to a significant change in thermal conductivity. The HP Ni exhibits a room temperature thermal conductivity of 92.3 W/m-K, a significant enhancement from 77.9 W/m-K for the commercial Ni 200 and very close to the upper end of the handbook value of 91 W/m-K e.g. [53,54]. This magnitude of impurity effect is in line with the observation in an earlier study on Ni [62]. For the nNi 4, the as-deposited sample with a grain size of 50 nm exhibits 77.2 W/m-K for the room temperature j. This value is essentially the same as for coarse-grained commercial Ni 200. After annealing, the thermal conductivity increases significantly to 89 W/m-K, as the grain boundary volume fraction is reduced from 6.2% (at 50 nm grain size) to 0.6% (at 520 nm grain size) as per Eq. (4). During annealing, little variation in chemical composition was expected. Therefore, the change after annealing in thermal conductivity can be solely attributed to the grain boundary contribution. Since the post-annealing j value of the nNi 4 is close to that of the high purity Ni (Table 4), impurities are expected to play a minor role in the thermal transport of the nanocrystalline Ni at room temperature in this study. In other words, the measured reduced thermal conductivity values for the as-deposited nanocrystalline nickel are largely the result of grain boundary effects in the current study.

4. Summary Room temperature thermoelectrical transport was investigated on a series of thick (300 lm) fully-dense electrodeposited nanocrystalline Ni samples with grain sizes below 50 nm. A strong dependence on sample grain size was observed for both electrical resistivity and thermal conductivity. Specifically as grain size decreased from 47 to 28 nm, the resistivity increased from 9.42 to 10.2 lX cm, while the thermal conductivity decreased from 74.7 to 67.3 W/m-K. Furthermore, the two thermoelectrical transport parameters exhibited a proportional relationship in agreement with the Wiedemann–Franz law. The corresponding Lorenz number varied only in a narrow range from 2.30  108 to 2.37  108 W X/K2 for the nanocrystalline Ni and was very close to the theoretical value of 2.44  108 W X/K2 for coarse-grained Ni. Therefore, thermal conductivity of nanocrystalline nickel can be determined on the basis of much easier to perform electrical resistivity measurements. Analysis shows that for the nanocrystalline Ni in the current study, impurities played a minor role in the thermoelectrical transport, and the reduced thermal conductivities are mainly due to grain boundary effects.

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