NANO LETTERS
Size Effect on the Crystal Structure of Silver Nanowires
2006 Vol. 6, No. 3 408-412
Xiaohua Liu, Jun Luo, and Jing Zhu* Department of Materials Science & Engineering, Tsinghua UniVersity, Beijing 100084, China Received November 11, 2005; Revised Manuscript Received January 9, 2006
ABSTRACT A 4H structural silver nanowire (4H-AgNW) is discovered to coexist with a face-centered cubic (FCC) one prepared by electrochemical deposition and to have the highest concentration in the total of 4H- and FCC-AgNWs with diameters around 30 nm. Moreover, the concentration becomes smaller when the diameters deviate from 30 nm. This size effect arises from the fact that 4H-AgNW has a more favorable surface configuration but higher volume internal energy than FCC-AgNW, which is proved by our model.
As the size of materials goes small into nanoscale, with an increasing ratio of surface atoms, their structures and properties usually change and differ from those of their bulk counterparts.1-3 For example, some theoretical works have predicted that structures of thin metal nanowires, such as Au, Al, and Pb nanowires, differ from their bulk counterparts.4,5 For silver nanowire (AgNW), which has attracted much interest because of the high electric conductivity of its bulk counterpart, many groups proposed various methods to prepare AgNWs and widely studied the structures and properties of these AgNWs.6-9 In all of these works, the AgNWs have the face-centered cubic (FCC) structure, the same as that of bulk silver. That is to say, no difference between the structures of the AgNWs and bulk silver was found. Only in silver nanoparticles, 4H structural silver, whose structure is different from that of the bulk silver, was reported.10-12 In our work, it has been reported that 4H structural AgNWs (4H-AgNWs) exist.13 In this paper, we report further that 4H-AgNWs coexist with FCC-AgNWs, and investigate thoroughly the crystal structures of 4H- and FCC-AgNWs. As a result, a size dependence of crystal structure in AgNWs is discovered. The highest concentration of 4H-AgNWs in the total of 4H- and FCC-AgNWs is found to occur in the diameters around 30 nm, and this concentration decreases when the diameters become larger or smaller. Furthermore, the systemic energy of an individual AgNW, that is, the sum of internal energy and surface energy, is analyzed to validate that the existence of 4H-AgNW is reasonable. AgNWs are electrochemically deposited into porous anodized aluminum oxide (AAO) templates. Templates, with different pore diameters ranging from 10 to ∼100 nm but * Corresponding author. Phone: (8610) 62794026; fax: (8610) 62772507; e-mail:
[email protected]. 10.1021/nl052219n CCC: $33.50 Published on Web 02/11/2006
© 2006 American Chemical Society
similar lengths of ∼10 µm, are prepared by controlling the proper anodization process and by enlarging the pores.13-15 Architecture AAO (amorphous)-Al film-AAO of the template is formed. AgNO3 aqueous solution (5 g/L, pH ) 3 adjusted by H2SO4) served as the electrolyte. Alternating current (ac) plating is used at a voltage of 10 V. After the electrochemical depositions, the samples are taken to X-ray diffraction (XRD) studies by employing Cu KR irradiation (λ ) 1.5405 Å). In all of these XRD spectra, most of the diffraction peaks can be assigned to FCC-Ag and FCC-Al. Additionally, there are some peaks different from FCC-Ag and FCC-Al in these spectra. A set of XRD spectra from a set of AgNWs in AAO templates with different pore diameters are shown in Figure 1a, where a peak marked as Peak I exists at 2θ ) 35.89° in every spectrum except that from an empty template. This peak can be assigned to {101h0} or {0004} planes of 4H-Ag. This indicates that 4H-Ag exists in every sample containing AgNWs with diameters ranging from 8 to 75 nm. Another characteristic peak of 4H-Ag is also found to exist at 2θ ) 40.30°, marked as Peak II in Figure 1a. But, because of the weaker intensity of Peak II, it becomes invisible in the spectrum of the 75-nm sample, whereas Peak I still exists. This implies that 4H-Ag exists in the 75-nm sample but has a low concentration. Other peaks of 4H-Ag and FCC-Ag overlap a lot but can still be distinguished by surveying the peak shapes. To clarify whether these 4H-Ag peaks result from stacking faults in FCC-AgNW or from 4H-AgNW, further investigation is taken on released individual nanowires by transmission electron microscopy (TEM) including electron diffraction and high-resolution imaging. As a result, two kinds of AgNWs with FCC and 4H structures are found, respectively, and both are single crystalline. This indicates that the characteristic peaks of 4H-Ag in the XRD spectra in Figure 1a come from
Figure 1. (a) Set of XRD spectra from a set of AgNWs in AAO templates with different pore diameters of 8, 15, 30, 50, and 75 nm. “Empty template” means that the corresponding sample is an AAO template without any nanowires inside. The b symbol corresponds to the normalized peaks of FCC-Ag {111} planes. The solid arrows represent two characteristic peaks of 4H-Ag: Peak I corresponds to {101h0} or {0004} planes, whose spacings are both 2.500 Å; Peak II corresponds to {101h2} planes with spacing 2.236 Å. The intensities of Peaks I and II change with varying diameters of AgNWs, indicating relevant changes in concentrations of 4HAgNW between 14% and 52% by calculating the intensity ratio of XRD peaks. (b) The statistical distributions for the diameters of AgNWs according to TEM characterizations, where the 4H-AgNW has the highest concentration when the diameters are around 30 nm.
4H-AgNWs. Moreover, according to the TEM characterizations, we carried out statistics on about 130 released nanowires, which is shown in Figure 1b. Figure 1b shows that the 4H-AgNWs have the highest concentration, 65%, in the total of 4H- and FCC-AgNWs with diameters around 30 nm. This accords with the XRD data in Figure 1a, which show that the intensity of Peak I is getting its maximum in the spectrum from the 30-nm sample. By calculating the intensity ratio of peaks in the XRD spectrum of the 30-nm sample in Figure 1a, the maximum 4H-AgNW concentration is 52%. This value differs from the highest concentration, 65%, of the 4H-AgNWs in Figure 1b. The difference should be due to the fact that XRD gives the average information of millions of nanowires, whereas the statistical result from TEM studies is limited to a smaller volume of samples. Therefore, deviation and systematic errors should be larger in the statistics by TEM than in those by XRD, and the Nano Lett., Vol. 6, No. 3, 2006
analyses on the 4H-AgNW concentrations from the XRD data are more representative. Nevertheless, whichever of the two results by TEM and XRD indicates that the maximum concentration of the 4H-AgNWs occurs in the nanowires with diameters around 30 nm. Besides, the XRD data in Figure 1a show that the concentrations of 4H-AgNWs in the 75nm and 8-nm samples are 14% and 33%, respectively. Both of these values are much lower than the maximum concentration, 52%. This concrete result from the XRD data is also supported by the statistics from TEM results in Figure 1b, showing a reasonable trend that the 4H-AgNW concentration is highest around 30 nm and lower around 80 and 10 nm. Therefore, it is concluded that there is a size effect on the crystal structure in AgNWs and 4H-AgNWs prefer to exist at proper diameters around 30 nm. We have also examined the surface configuration of these two kinds of AgNWs. The longitudinal axes of FCC-AgNWs are usually [110], as shown in Figure 2a. Figure 2b shows the cross-section image of a FCC-AgNW. The cross-section TEM sample is prepared by microtomy after AgNWs are embedded into the resin. The cross-section image indicates that the FCC-AgNW is nearly cylindrically shaped and has the surfaces of {111}, {001}, and {110} crystal planes. For 4H-AgNWs, it is found that the axes of most nanowires are along 〈1h21h0〉 and the {101h1} planes are parallel to the axes, as shown in Figure 2c. Besides, the {0001} planes are also parallel to the axes of 〈1h21h0〉 according to geometrical relationship. Moreover, all of the {101h1} and {0001} planes of 4H-AgNW are facets with lower surface energy because of their higher density of atomic arrangement and larger spacing (all larger than FCC-Ag {111} planes). Thus, these planes may be the facets terminating the surfaces of a 4HAgNW to lower the surface energy. This is also supported by some calculations on the surface configuration of a 4HAgNW with the longitudinal axis of [1h21h0], whose details are shown later in this paper. The result of the calculations is shown in Figure 2d, which indicates that the surfaces of a 4H-AgNW with the longitudinal axis of [1h21h0] consist of {101h1} and {0001} planes. The internal energy of 4H and FCC structures may differ from each other as a result of different lattice symmetries and constants. Silver is well-known as a FCC metal in its bulk form because FCC-Ag has a lower internal energy when surface and interface effect can be neglected. Because the diameter of a nanowire is only several tens of nanometers, the surface effect should be taken into account. For simplification, we consider an individual nanowire approximately as a cylinder with a diameter D and a length L. The total systemic energy (E) should be expressed as the sum of its volume internal energy (U) and surface energy (Es) contributed by interior atoms and surface layers, respectively E ) U + Es
(1)
FCC-Ag served as a reference energy state. We calculate the difference ∆E defined by ∆E ) E4H - EFCC. When ∆E is negative, 4H-Ag rather than FCC-Ag is energetically favorable. 409
Figure 2. (a) High-resolution TEM image of a FCC-AgNW, whose longitudinal axis is [110]. The inset is an electron diffraction pattern from this nanowire indexed as FCC-Ag. (b) An image of the cross section of a FCC-AgNW. The cross section is perpendicular to the longitudinal axis [110] of the nanowire and shows that the surfaces of the nanowire are {111}, {001}, and {110} planes. Dashed lines represent some other facets consisting of planes with orientations close to the low-index planes (about 20° angles, indicated by elongate solid lines). (c) High-resolution TEM image of a single crystalline 4H-AgNW. The lower left inset is an electron diffraction pattern from the 4H-AgNW, where the two spots marked with two white arrows correspond to two crystal planes with spacings of 2.425 and 2.500 Å according to our measurement and calculation. Moreover, the angle between the reciprocal vectors of the two spots is 61°. The values of the spacings and the angle cause the two spots to be indexed only as (101h1) and (011h0) of 4H-Ag, not FCC-Ag. Thus, the zone axis of this electron diffraction pattern is [2h113]. Besides, the electron diffraction pattern shows that the (101h1) plane is parallel to the axis of the nanowire. The upper right inset is a magnification of the area marked by a white rectangle in c, where some jade-green dots are added to show the atomic projection of 4H-Ag along [2h113]. (d) The calculated cross section of a 4H-AgNW by the broken-bond rule and Wulff’s construction, where the surface energy curve is marked with a black arrow and the surfaces of the nanowire are marked with a red arrow and terminated by {0001} and {101h1} planes.
The close-packed {0001} planes of 4H-Ag have a hexagonal atomic arrangement similar to the FCC-Ag {111} planes but with a shorter Ag-Ag bond and a larger interplanar distance. So each atom in the FCC-Ag lattice has 12 nearest-neighbor atoms with a distance of r0 ) 2.8894 Å, whereas each atom in the 4H-Ag lattice has only 6 with a distance of r1 ) a4H-Ag ) 2.8862 Å in the identical basal plane, and the other 6 next-nearest-neighbor atoms lie in two adjacent basal planes with a distance of r2 ) 3.0044 Å. To estimate the change of internal energy of 4H-Ag compared to that of FCC-Ag, here we employ the Lennard-Jones (LJ) potential,16 which has been used widely in modeling FCC solids. The atoms with a distance of r interacted via the following LJ potential ULJ(r) ) 4
[(σr ) - (σr ) ] 12
6
(2-1)
where is the bond energy and σ is determined by the 410
distance of atoms.17 Reference 17 gives ) 0.3450 eV/atom and σ ) 2.644 Å. Here we use σmodified in our calculation; it is a refined σ to ensure that the FCC-Ag with its constant has the lowest volume internal energy in the case aFCC-Ag ) 4.0862 Å. The internal energy of a unit volume can be calculated as 1 UV ) NV 2
∑j
ULJ(rj) ) 2 NV
∑j
[( ) ( ) ] σ
rj
12
-
σ
rj
6
(2-2)
where NV is the number of atoms in the unit volume. For an FCC lattice with aFCC-Ag ) x2r0 ) 4.0862 Å, NV,FCC-Ag ) 3 ) 4/(x2r0)3 ) x2/r30. When the interaction 4/aFCC-Ag between nearest-neighbor atoms is considered, from the condition (dUV/dr)r)r0 ) 0 we get σmodified ) r0/(5/3)1/6 ≈ r0/1.09 ) 2.654 Å, which is used in our calculation and very close to the reported value.17 Then we can calculate the LJ potential on different bond lengths r (r0, r1, and r2, respectively): Nano Lett., Vol. 6, No. 3, 2006
ULJ(r0) ) 4 ULJ(r1) ) 4 ULJ(r2) ) 4
[( ) ( ) ] [( ) ( ) ] [( ) ( ) ] σ r0
12
-
σ r0
6
) -0.960
σ r1
12
-
σ r1
6
) -0.957
σ r2
12
-
σ r2
6
) -0.997
(3)
Hence, the increment of internal energy in the unit volume is drawn out: ∆UV ) UV,4H - UV,FCC ) 2 NV,4H-Ag
∑ j ) 1,2
[( ) ( ) ] [( ) ( ) ] σ
12
-
rj
2 NV,FCC-Ag
σ
6
-
rj
σ
12
-
r0
σ
r0
6
(4)
As mentioned before, FCC-AgNWs are enclosed mainly by their {111}, {001}, and {110} planes, and 4H-AgNWs by {0001} and {101h1} planes. We use the average surface energy, γ j , of the corresponding planes as the surface energy of AgNWs: γ j FCC-Ag ≈
1 (γ + γ001 + γ110) 3 111
γ j 4H-Ag ≈
1 + γ101h1) (γ 2 0001
(5)
Here the subscripts are the corresponding indices of the planes. The surface energies of FCC-Ag planes are studied widely, but the reported values are very much different. Referencing the higher experimental values of free Ag nanoparticles,18 a set of specific surface energies of FCCAg is selected for our calculation,19 that is, γ111 ) 2.537 J/m2, γ001 ) 2.895 J/m2, and γ110 ) 4.360 J/m2. For the lack of experimental data of 4H-Ag, we estimate γ0001 and γ101h1 by applying the modified broken-bond rule.20 The broken bonds are divided into two groups according to the bond length, namely, r1 for nearest-neighbor atoms and r2 for nextnearest-neighbor atoms, weighted by their different bond strengths calculated in eq 3 based on a LJ interaction. Here we still use FCC-Ag as a reference state; we convert the total sum of broken bond strength in unit area of 4H-Ag into that of FCC-Ag to estimate the surface energy of 4HAg {hkil} planes, according to the following relation γhkil [Zr1‚ULJ(r1) + Zr2‚ULJ(r2)]/Ahkil ) γ111 Zr ‚ULJ(r0)/A111
Figure 2d. Afterward, by applying Wulff’s construction21 and analyzing the surface energy curve, it is found that {0001} and {101h1} planes are the terminating surfaces of a 4H-Ag crystallite (Figure 2d), which accords with our experimental observations mentioned above. Finally we obtain the average surface energy for FCC- and 4H-AgNW, respectively. And the difference of surface energy per unit area between 4Hand FCC-Ag NW, ∆γ, is also worked out: γ j FCC-Ag )
1 (γ + γ100 + γ110) ) 3.252 J/m2 3 111
γ j 4H-Ag )
1 + γ101h1) ) 2.511 J/m2 (γ 2 0001
∆γ ) γ j 4H-Ag - γ j FCC-Ag ) -0.741 J/m2
∆E ) E4H - EFCC ) V∆UV + Asurface∆γ
(6)
where Zrn represents the total number of broken bonds with a bond length of rn (n ) 0, 1, 2) in an area of a specific plane (Ahkil or A111). So we calculate the surface energy curve of 4H-Ag from eq 6. The surface energy curve is shown in
(7)
The total energy difference between 4H- and FCC-AgNWs can be deduced according to our model:
)π
0
Nano Lett., Vol. 6, No. 3, 2006
Figure 3. Difference between the systemic energies of an individual 4H-AgNW and an individual FCC-AgNW, ∆E ) E4H - EFCC, with varying diameters of nanowires. In the diameter range when ∆E < 0, 4H-AgNW is more energetically favorable. ∆E reaches its minimum at D* ) 25.5 nm, consistent with the experimental results that the highest concentration of 4H-AgNW appears at diameters around 30 nm.
)
(
(D2 ) L‚∆U 2
)
V
+ π DL‚∆γ
π L∆UV 2 D + (π L∆γ)D 4
(8)
The ∆E-D curve is plotted in Figure 3, where ∆E reaches its minimum, ∆Emin, at D*: 411
D* ) -
π L∆γ 2∆γ )) πL∆UV ∆UV 2 4 2(-0.741 J/m2) ) 25.5 nm (9) 5.811 × 107 J/m3
(
)
Figure 3 indicates that 4H-AgNW is energetically favorable in the diameter ranging 10-50 nm, of which the diameter of 25.5 nm is corresponding to energetically the most favorable case, and becomes unfavorable above 50 nm. This accords with the XRD spectra in Figure 1a showing that the 4H-AgNW concentration has the highest value (52%) in the 30-nm AgNWs and decreases from 52% to 17% in the 50-nm AgNWs and 14% in the 75-nm. These data from the XRD spectra show a trend that 4H-AgNW becomes more and more unfavorable with increasing diameters above 50 nm. This trend and the value of the diameter (30 nm) corresponding to the highest 4H-AgNW concentration agree well with the plotted curve and the value of D* (25.5 nm) in Figure 3. Furthermore, the shape of the plotted curve and the value of D* in Figure 3 are determined by two important parameters, the positive ∆UV and the negative ∆γ, in eqs 8 and 9. The positive ∆UV means that the volume internal energy of 4H-AgNW is higher than that of FCC-AgNW, and the negative ∆γ means that 4H-AgNW has a surface configuration of lower surface energy than FCC-AgNW. Therefore, it is concluded that the size effect on the crystal structure of AgNW arises from the fact that 4H-AgNW has a more favorable surface configuration but higher volume internal energy than FCC-AgNW. In summary, 4H-AgNW is discovered coexisting with FCC-AgNW in electrochemically deposited AgNWs. The 4H-AgNW concentration is highest (52%) in the AgNWs with diameters around 30 nm, decreases from 52% to 17% in the 50-nm AgNWs and 14% in the 75-nm, and is expected to approach zero when the nanowire diameters go even larger than 75 nm. This size effect arises from the fact that 4HAgNW has a more favorable surface configuration but higher volume internal energy than FCC-AgNW, which is proved by our calculation. Therefore, the surface energy plays an
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important role in determining the crystal structure of AgNWs. Similar phenomena may exist in some other systems, and the dynamical process needs further studies. Acknowledgment. This work was supported by the National 973 Project of China, the Chinese National Nature Science Foundation, and the National Center for Nanoscience and Technology of China. We thank W. Miao for X-ray diffraction and fruitful discussions. References (1) Kondo, Y.; Takayanagi, K. Science 2000, 289, 606. (2) Rodrigues, V.; Bettini, J.; Rocha, A. R.; Rego, L. G. C.; Ugarte, D. Phys. ReV. B 2002, 65, 153402. (3) Liang, H. Y.; Upmanyu, M.; Huang, H. Phys. ReV. B 2005, 71, 241403. (4) Diao, J. K.; Gall, K.; Dunn, M. L. Nat. Mater. 2003, 2, 656. (5) Gu¨lseren, O.; Ercolessi, F.; Tosatti, E. Phys. ReV. Lett. 1998, 80, 3775. (6) Sun, Y. G.; Yin, Y. D.; Mayers, B. T.; Herricks, T.; Xia, Y. N. Chem. Mater. 2002, 14, 4736. (7) Terabe, K.; Hasegawa, T.; Nakayama, T.; Aono, M. Nature 2005, 433, 47. (8) Chen, H. Y.; Gao, Y.; Yu, H. C.; Zhang, H. R.; Liu, L. B.; Shi, Y. G.; Tian, H. F.; Xie, S. S.; Li, J. Q. Micron 2004, 35, 469. (9) Sauer, G.; Brehm, G.; Schneider, S.; Graener, H.; Seifert, G.; Nielsch, K.; Choi, J.; Go¨ring, P.; Go¨sele, U.; Miclea, P.; Wehrspohn, R. B. J. Appl. Phys. 2005, 97, 024308. (10) Taneja, P.; Banerjee, R.; Ayyub, P.; Dey, G. K. Phys. ReV. B 2001, 64, 033405. (11) Novgorodova, D.; Gorshkov, A.; Mokhov, A. Zap. Vseross. Mineral. OVa. 1979, 108, 552. (12) Li, X. Y.; Yan, H. F.; Liu, B. X. J. Phys. Soc. Jpn. 2005, 74, 2007. (13) Luo, J.; Zhang, L.; Zhang, Y. J.; Zhu, J. AdV. Mater. 2002, 14, 1413. (14) Xu, Q.; Zhang, L.; Zhu, J. J. Phys. Chem. B 2003, 107, 8294. (15) Sauer, G.; Brehm, G.; Schneider, S.; Nielsch, K.; Wehrspohn, R. B.; Choi, J.; Hofmeister, H.; Go¨sele, U. J. Appl. Phys. 2002, 91, 3243. (16) Lennard-Jones, J. E. Proc. R. Soc. London, Ser. A 1924, 106, 463. (17) Guan, P.; Mckenzie, D. R.; Pailthorpe, B. A. J. Phys.: Condens. Matter 1996, 8, 8753. (18) Nanda, K. K.; Maisels, A.; Kruis, F. E.; Fissan, H.; Stappert, S. Phys. ReV. Lett. 2003, 91, 106102. (19) van Santen, R. A. Theoretical Heterogeneous Catalysis; World Scientific Press: Singapore, 1991; p 282. (20) Jiang, Q.; Lu, H. M.; Zhao, M. J. Phys.: Condens. Matter 2004, 16, 521. (21) Wulff, G. Z. Kristallogr. Mineral. 1901, 34, 449.
NL052219N
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