Electrical Resistivity as a Characterization Tool for Nanocrystalline Metals
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Table I. Specific grain boundary resistivities (SGBR) for various polycrystalline materials. Material
I SGBR
Reference
General Boundaries 2
Copper Aluminum Aluminum Aluminum
2
3.12 x 10"| fcm 2.45 x 10-"2 cm2 2.40 x 10-"92 cm2 3.26 x 10-122cm 2
SpecialBoundaries 1.5 x 10-12tcm2 2 2
Copper (Twin Boundary, Z3) Aluminum (Twin Boundary, E3 )
1.48 x10-10 cm
[2] [2] [3] [5]
I
[4] [5]
EXPERIMENTAL The bulk nanocrystalline nickel (fcc), cobalt (hcp) and nickel-iron (disordered fcc) materials tested in the present study were produced by an electrodeposition process described elsewhere [11,12]. Specimens were electrodeposited onto a titanium substrate to a uniform thickness (between 30 and 150Anm) and subsequently stripped for structural characterization and electrical measurements on free-standing, deformation-free samples. For the nickel and cobalt materials the electroplating parameters were varied to produce specimens with mean grain sizes between 10 and 55nm. For the Ni-Fe samples a range of grain sizes was obtained through various annealing treatments. The average grain size for the nickel and nickel iron alloys was determined using X-ray line broadening and Scherrer's method [13]. TEM micrographs were used to determine the average grain size for the cobalt samples. Electrical resistivity measurements were made using a four-point probe between 4 and 300K. Isothermal high temperature electrical resistivities as a function of annealing time for Ni-Fe were measured in a salt bath. RESULTS DeterminingSpecific Grain Boundary Resistivity An example for the temperature dependence of the electrical resistivity of various nanocrystalline materials for the case of nickel ranging in grain size from 22 nm to 300 Am is shown in figure 1. As expected, the curves show an increase in the electrical resistivity with decreasing grain size. Figure 2 plots the electrical resistivity of the various nickel samples against the grain boundary area per unit volume at 4 K and 295 K. The grain boundary surface area per unit volume (S/V) was calculated using a tetrakaidecahedron as the grain shape which gives a S/V of 2.37/d, where d is the average grain diameter [14]. The SGBRs determined for nickel, cobalt and various nickel-iron alloys at 4 K are given in table II. Table II. Specific grain boundary resistivities determined from nanocrystalline samples at 4K. Material Nickel
Grain Size Range 17nm - 55 nm
Cobalt
1Onm - 30 nm
Ni- 16% Fe Ni- 31% Fe Ni- 34% Fe
l5nm- 300pm 14nm - 300gm l3nm - 30011m
SGBR 2.82 x 10-12 fcmI 3.26 x 10-12fncmM 3.01 x l1012 g2cm 3.09 x 10,12 C2cm 2.99 x 10,"12!cm
462
14 *
-. 12
14
55-,,
0- 30rim ...................................... . ".,
1I0 --I v
22 •
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o0
50
(
... . ........
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100
150
200
250
....... ............. 0 .. Qcm 2 2.74 x 10.12.............. ,Rl= ps
., 12
10 ......................... ....... .............
...
~ ........
27u
300
295 K
..................... . . ........... .. ... ..... ..... . . ..
0.1
4 -O0.0z
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