ISSN 10637834, Physics of the Solid State, 2013, Vol. 55, No. 1, pp. 1–4. © Pleiades Publishing, Ltd., 2013. Original Russian Text © R.Kh. Khisamov, I.M. Safarov, R.R. Mulyukov, Yu.M. Yumaguzin, 2013, published in Fizika Tverdogo Tela, 2013, Vol. 55, No. 1, pp. 3–6.
METALS
Effect of Grain Boundaries on the Electron Work Function of Nanocrystalline Nickel R. Kh. Khisamov, I. M. Safarov, R. R. Mulyukov, and Yu. M. Yumaguzin Institute for Metals Superplasticity Problems, Russian Academy of Sciences, ul. Khalturina 39, Ufa, 450001 Bashkortostan, Russia email:
[email protected] Received May 11, 2012
Abstract—The electron work function of nickel with various grain sizes has been studied. It has been shown that the work function decreases as the specific length of grain boundaries in nickel increases with decreasing average grain size. It has been found that the transformation of grain boundaries from a nonequilibrium to equilibrium state leads to an increase in the electron work function by 0.15 eV. DOI: 10.1134/S1063783413010186
1. INTRODUCTION A decrease in the electron work function in a metal is a topical problem from the standpoint of application in electronic engineering. In [1–4], it was shown that the formation of a nanocrystalline structure in a metal decreases the electron work function. The work func tion decreases due to an increase in the grain boundary fraction with decreasing average grain size and so called nonequilibrium state of the boundaries in a nanocrystalline metal [5, 6]. However, the separation of the influences of these factors remains unknown. Therefore, we studied the effect of various average grain sizes, specific length of the grain boundaries, and their state on the electron work function in nickel.
difference with an electron beam (Anderson method) [1, 2, 11]. In the experiment, we measured the depen dence of the retarding current Ir on the retardation potential Ur. Immediately prior to the measurements, the sample surface was subjected to in situ ionic clean ing. First, the measurements were performed for the nanocrystalline samples; then, the samples were annealed to change their structure, and the measure ments were performed under the same conditions. All the measurements were performed in vacuum no worse than 10–3 Pa. The difference between the nickel work function in each state ϕi and the work function of coarsecrystalline (annealed at the maximum temper ature) nickel ϕ0 was found from the shift of the corre sponding Iri(Uri) curve with respect to the Ir(Ur) curve along the potential axis for the coarsecrystalline sam ple: ϕi – ϕ0 = eΔUri. The difference in the work func tions was determined accurate to 0.05 eV.
2. SAMPLE PREPARATION AND EXPERIMENTAL TECHNIQUE We studied a 99.99%purity nickel. The nanocrys talline structure of the nickel samples was prepared by deformation nanostructuring using the method of tor sion under quasihydrostatic pressure of 4 GPa [5–7]. The sample structure was changed by annealings at temperatures from 373 to 973 K. The samples were annealed in a furnace that was preliminarily heated to desired temperature for a half an hour. This temperature range was chosen, since it is precisely the temperatures at which nanocrystalline nickel undergoes structural transformations [8, 9]. The structure of the samples pre pared was studied using a JEM2000EX transmission electron microscope. The average grain size and spe cific length of the grain boundaries were found by the linearintercept method [10] using micrographs of the microstructure regions containing no less than 200 grains. In this case, the error did not exceed 5%. The electron work function of the samples was determined by measurement of the contact potential
3. RESULTS OF MEASUREMENTS AND DISCUSSION The electron microscopy studies show that the deformation nanostructuring forms in the nickel sam ples a nanocrystalline structure with the average grain size about 150 nm (Fig. 1a). The diffuse contrast at the grain boundaries and the bend extinction contours in the grain body demonstrate a nonequilibrium state of the grain boundaries. Hereinafter, the nonequilibrium state implies the grain boundary state with a higher energy that is due to the existence of elastic distortions and extrinsic lattice dislocations [12, 13]. In general case, a nanocrystalline structure is characterized ther modynamically by a nonequilibrium nanocrystalline state [5, 6]. Annealing of the nanocrystalline sample at temperatures to 423 K increases the average grain size to 200 nm. In this case, a band contrast that is charac 1
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100 nm (b)
(а)
100 nm
1 µm
(c)
Fig. 1. Microstructure of nickel samples: (a) nanocrystalline sample, (b) nanocrystalline sample after annealing at 473 K, and (c) nanocrystalline sample after annealing at 973 K.
teristic of equilibrium state appears at the boundaries, and the bend extinction contours in the grain body become less noticeable. This fact testifies that the level of elastic distortions in the boundaries and in grain body decreases during return process, and the degree of boundary nonequilibrium decreases.
During heating to 448 K, the grains grow monoton ically to 250 nm. During annealing to a temperature higher than 448 K, the structure is sharply changed because of recrystallization processes. After annealing at 473 K, the average grain size increases to 1.7 μm (Fig. 1b), but the structure conserves regions with nonrecrys
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EFFECT OF GRAIN BOUNDARIES ON THE ELECTRON WORK FUNCTION 0.8
4 3
0.6 Ir, arb. units
d, μm
3
2 1
1 2 345 6
0.4
0.2 0
400
600
800
1000
T, K 0 2
Fig. 2. Dependence of the average grain size in nanocrys talline nickel on the annealing temperature.
tallized structure. Further increase in the annealing temperature leads to the completion of the processes of formation of new grains; a collective recrystallization is developed, and the structure is transformed to equilib rium state. In this case, the average grain size increases to 4 μm at 973 K. The structure in these states has a view characteristic of the wellannealed coarsecrystalline material with equilibrium grain boundaries (Fig. 1c). Based on the results of the structural studies, we plotted the dependence of the average grain size in the nickel samples on the annealing temperature (Fig. 2). The results of measurements of the contact poten tial difference of the nickel samples with various aver age grain sizes are shown in Fig. 3. The zero potential was taken arbitrarily. The difference in the electron work functions for the samples with various structures was judged from the relative shift of the curves along the potential axis at the current equal to a half of the maximum value. The sample has the minimum electron work func tion in the nanocrystalline state (curve 1). The increase in the average grain size shifts the Iri(Uri) curve toward higher potentials. Curve 6 corresponding to the sample with the average grain size d = 4 μm has the maximum shift relative to the first state. Further increase in the average grain size does not cause any marked shift as compared to curve 6. Thus, the measurements per formed show the decrease in the electron work func tion with a decrease in the average grain size. As is shown in [5, 6], the main factor determining the changes in the properties as a result of formation of a nanocrystalline structure in the material is the appearance of a large fraction of the grain boundaries existing in nonequilibrium state. In terms of the twophase model [5], a nanocrystal line metal can be represented as a combination of two phases (the grain and grain boundary phases); the former phase has the work function common for single crystal and coarsecrystalline materials; the latter phase PHYSICS OF THE SOLID STATE
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4 Ur, V
5
6
Fig. 3. Dependence of the retardation current on retarda tion potential for nickel samples with grain sizes d = (1) 150 nm, (2)180 nm, (3) 200 nm, (4) 250 nm, (5) 1.7 µm, and (6) 4 µm.
has lowered work functions [14, 15]. The physical width of the grain boundary phase δ exceeds the crystallo graphic grain boundary width by an order of magnitude and is about 10 nm [13, 16, 17]. Then, according to the spot theory [18, 19], the integral work function is summed from the local work functions of grain bound ary ϕGB and grain body ϕ0 in proportion to the fraction of the emitting surface occupied by each of the phases G
ϕi = s ϕ0 + s sG
GB
GB
ϕi ,
(1)
sGB
where and are the specific areas of the grain and grainboundary phases at the emitting surface. The specific area of the grain boundary phase can be repre sented as GB
(2) s i = pδ, where p is the specific grain boundary length. Let us construct the dependence of the electron work function on the specific grain boundary length (Fig. 4). The absolute value of the work function was found taking into account that the work function of usual coarsecrystalline nickel is 4.5 eV, according to the reference data [20]. Then, in particular, the work function of the nanocrystalline sample is 3.9 eV (Fig. 4). It is seen that the dependence of the work function on the specific grain boundary length is obeyed to a linear law, which agrees with Eqs. (1) and (2). In this case, the jump is observed in the range of varying p from 8.8 to 7.9 μm/μm2. Thus, several segments can be separated in the obtained dependence. We consider them successively beginning from the nanocrystalline state that is characterized by the largest specific grain boundary length. In segment I, the work function increases linearly from 3.93 to 4.05 eV in the range of the specific grain
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4. CONCLUSIONS The formation of a nanocrystalline structure in nickel decreases the electron work function in it. The work function decreases due to the increase in the specific grain boundary length. A nonequilibrium state of the grain boundaries additionally decreases the work func tion. In nanocrystalline nickel with the average grain size about 200 nm, the additional decrease is 0.15 eV.
4.6
ϕ, eV
4.4
T = 773 K T = 473 K
III
4.2
T = 448 K T = 423 K T = 373 K II
4.0 3.8 0
2
4
6 8 p, µm/µm2
NC
I
d 10
REFERENCES 12
14
Fig. 4. Dependence of the electron work function of nickel on the specific grain boundary length.
boundary lengths from 12.5 to 8.8 μm/μm2. This stage corresponds to the annealing of the nanocrystalline sample in the temperature range from room tempera ture to 373 K. In this case, the work function increases due to the decrease in the specific grain boundary length with conservation of the grain boundary nonequilibrity. In segment II, in the temperature range from 373 to 423 K, the specific length decreases insignificantly from 8.8 to 7.9 μm/μm2 which corresponds to the insignificant increase in the average grain size from 180 to 200 nm. In this case, the work function is sharply changed from 4.05 to 4.20 eV. The jumpwise change in the work function at this stage correlates with the changes in the grain boundary state observed in the structural studies, as well as with their transfor mation from a nonequilibrium to equilibrium state. In this case, their physical width ceases to be elevated; it is comparable to the crystallographic width, and their decreasing contribution to the work function decreases sharply. In segment III, the work function increases linearly from 4.2 to 4.4 eV as the specific grain boundary length decreases to 1.3 μm/μm2. The structural studies show that the primary recrystallization accompanied by the formation of new grains and their growth is developed in the temperature range 448–473 K. After annealing at a temperature of 473 K corresponding to the end of segment III, the relatively coarsecrystalline structure forms; the grain growth becomes less intense and does not lead to a significant decrease in the specific grain boundary length. At the specific length of 0.5 μm/μm2 and below, the work function increases to 4.5 eV, which is due to the end of the recrystallization process over entire sample volume and almost complete return of the nonequilibrium defect structure. The performed studies of the electron work func tion in nickel samples with various average grain sizes show that the work function is influenced by both the specific grain boundary length and their nonequilib rium state.
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