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Size effect on evaporation temperature of nanocrystals
Materials Chemistry and Physics 111 (2008) 293–295
Contents lists available at ScienceDirect
Materials Chemistry and Physics journal homepage: www.elsevier.com/locate/matchemphys
Size effect on evaporation temperature of nanocrystals T.H. Wang, Y.F. Zhu, Q. Jiang ∗ Key Laboratory of Automobile Materials, Ministry of Education, and Department of Materials Science and Engineering, Jilin University, Changchun 130022, China
a r t i c l e
i n f o
Article history: Received 6 December 2007 Received in revised form 1 April 2008 Accepted 4 April 2008 Keywords: Nanocrystals Size effect Evaporation temperature
a b s t r a c t Based on our model for size-dependent cohesive energy, the size-dependent evaporation temperature of nanocrystals has been modeled without any adjustable parameter. The model predicts a decrease of the evaporation temperature of nanocrystals with decreasing size. The model predictions are in good agreement with available experimental results for Ag, Au and PbS nanocrystals. © 2008 Elsevier B.V. All rights reserved.
1. Introduction Studies of basic phase transitions in nanoscale materials are of great fundamental importance to modern condensed matter physics. One of the striking features of a nanocrystal is that the transition temperatures for phase transitions, such as solid–liquid, liquid–vapor, magnetic–paramagnetic, ferroelectric–paraelectric transitions, are no longer constant but are tunable with the diameter D of nanocrystals in divergent ways [1–6]. According to Kelvin equation [7], the vapor pressure of nanoparticles due to their curved surface is higher than that of a flat surface. Thus, the vapor pressure and the related evaporation of nanocrystals are size-dependent. As predicted by Kelvin equation, the evaporation temperature Tev (D) of nanocrystals is experimentally found indeed to be size-dependent and decreases with decreasing size, being similar to the function of the size-dependent melting temperature of nanocrystals [8–12]. From the technological point of view, it is possible to evaporate different materials at the same temperature by taking different nanomaterials with distinct sizes. This is meaningful for the synthesis of nanoparticles or thin films of compounds from a single temperature source. Thus, knowing Tev (D) function of nanocrystals is valuable in industry. Assuming the energy required to remove one atom from a nanoparticle to vacuum can be scaled to Tev (D), Tev (D) has been deduced as [9], 2h3 Tev (D) =1− Tev (∞) 3EB (∞)D
∗ Corresponding author. Fax: +86 431 85095876. E-mail address: [email protected] (Q. Jiang). 0254-0584/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.matchemphys.2008.04.010
(1)
where is the surface energy, and h is the atomic or molecular diameter, ∞ denotes the bulk size, EB is the atomic cohesive energy, and D is defined as diameter of nanoparticles and nanorods, or thickness of thin films. Originally, the equation is used to calculate and EB (∞) by experimental data of Tev (D). Whereas if , Tev (∞) and EB (∞) are known, Tev (D) can be deduced although the determination of suffers difficulty and uncertainty. Recently, based on the bond order-length-strength correlation mechanism, Sun et al. [10] have established a model for Tev (D) function
Tev (D) i (zib ci −m(zi ) − 1) =1+ Tev (∞)
(2)
i≤3
where subscript i denotes the i-th atomic layer, which may be counted up to three from the outermost atomic layer to the centre of the solid. ci = hi /h = 2/{1 + exp[(12 − zi )/(8zi )]} shows a coordination number dependent reduction of h, zib = zi /zb with zi and zb being the coordinates with and without coordination number imperfection, respectively, and i = 2hci /D is the portion of the atoms in the i-th atomic layer from the surface compared to the total number of atoms of the entire solid with = 1, 2, 3 corresponding to thin films, nanorods and nanoparticles, respectively. The power index m is an indictor for the bond nature [10]. Although many efforts have been made on the study of evaporation of nanoparticles and thin films, they mostly focus on the mechanism, process and kinetics of the evaporation. The study on Tev (D) itself is less although it is important in both science and technology. Thus, further effort is needed to develop a model without any free parameter, which should benefit our understanding on the physics behind the evaporation phenomena of nanocrystals.
294
T.H. Wang et al. / Materials Chemistry and Physics 111 (2008) 293–295
In this contribution, a simple thermodynamic model, free of any adjustable parameter, is developed for Tev (D) function of nanocrystals. It is found that the model predictions agree with available experimental results for Ag, Au and PbS nanocrystals. 2. Model Based on the Lindemann’s criterion of melting, an expression for the bulk melting temperature Tm (∞) of crystals is derived [13], which shows that Tm (∞) is proportional to EB (∞), or Tm (∞) characterizes the bond strength [14–16]. The fact that Tm (∞) varies linearly with EB (∞) agrees with experimental data for metals [17]. According the Trouton’s rule [18], the ratio of latent heat of vaporization Hv (∞) to the liquid–vapor transition temperature Tv (∞) is a constant or vaporization entropy Sv . As results, Hv (∞) ∝ Tv (∞). It is known that compared with the gas, the bond strength and coordination number of liquid are similar to the crystal and their energetic differences are very small where Hv (∞) ≈ EB (∞) and Tv (∞) ≈ Tev (∞) [19,20]. Since EB (∞) is directly equal to the product of the bond number and the bond energy, which is the energy that divides a crystal into isolated atoms by destroying all bonds. This is just the energetic requirement for the solid–vapor transition. Thus, similar to Tm (∞) and Tv (∞), Tev (∞) characterizes even better the bond strength and Tev (∞) ∝ EB (∞) [9,10]. This relationship has been extended to nanosize [9,10] Tev (D) EB (D) = . Tev (∞) EB (∞)
(3)
Based on a model for the latent heat with a similar consideration of the above, EB (D)/EB (∞) function has also been deduced as [21]
EB (D) 1 = 1− EB (∞) (2D/h) − 1
2S (∞) B
exp −
3R
1 (2D/h) − 1
(4)
where SB (∞) = EB (∞)/Tev (∞) is the bulk solid–vapor transition entropy, R is ideal gas constant. It is evident from Eq. (4) that EB (D) increases (the absolute value decreases) with a decrease in size, which reflects the instability of nanocrystals in comparison with the corresponding bulk crystals. This trend is expected since the surface/volume ratio increases with decreasing size while the surface atoms have lower coordinates and thus higher energetic state, and consequently EB (D) as a mean value of all atoms increases [21]. Using Eq. (4), EB (D) values of W and Mo nanoparticles are predicted and are in agreement with the experimental results [21]. Substituting Eq. (4) into Eq. (3), we get
Tev (D) 1 = 1− Tev (∞) (2D/h) − 1
2S (∞) B
exp −
3R
1 . (2D/h) − 1
(5)
Fig. 1. Tev (D) functions for Ag, Au and PbS nanocrystals where the solid lines denote the model prediction of Tev (D) in terms of Eq. (5) and the symbols (), () and (䊉) show the experimental data of Ag, Au and PbS nanocrystals, respectively [9]. The necessary parameters used in Eq. (5) are listed in Table 1. The dashed lines show the theoretical results based on Eq. (2) where the original parameters have been cited from the original Ref. [10]. Since Ref. [10] has not discussed the case of Au nanocrystals, the same i and values for Ag are taken because of the similarity of Au and Ag. And the dash dotted lines denote the theoretical results based on Eq. (1) where the original parameters have been cited from the original Ref. [9].
increases, and prediction of Eq. (5) agrees well with the experimental results except Au. The experimental results of Au are slightly higher than the prediction of Eq. (5). This is induced by the fact that the measured Tev (∞) value of Au is lower than the real one due to the existence of surface melting [9]. The calculated results show that although the vapor pressure of Ag at 953 K is much higher than that of Au, the former is lower to latter when Au is surrounded by a liquid layer [22]. Thus, the surface melting significantly increases the evaporation of Au and this effect for the evaporation behavior of Au cannot be neglected [22]. As shown in Fig. 1, Eq. (1) gives good agreement with experimental results when (D) > (∞) is taken although the evident difference of (D) and (∞) used in Ref. [9] is not clear. The predictions of Eq. (2) are consistent with the experimental results when i = 3 and = 1 for Ag and Au and i = 3 and = 3 for PbS are taken as used in the original work [10]. Since values used are different while all considered nanocrystals are nanoparticles, the exact physical basis of is unknown. Considering the mathematical relation of exp(−x) ≈ 1 − x when x is small enough as a first order approximation, Eq. (5) can be rewritten as
3. Results and discussion
Tev (D) hSB (∞) ≈1− . 3RD Tev (∞)
Fig. 1 presents comparisons of Tev (D) between the model predictions in light of Eq. (5) with parameters listed in Table 1 and available experimental results for Ag, Au and PbS nanocrystals. Other two theoretical results based on Eqs. (1) and (2) are also shown. As shown in Fig. 1, Tev (D) decreases as D drops or as 1/D
Eq. (6) is in agreement with a general consideration that the drop of any size-dependent thermodynamic amount is proportional to 1/D or the surface/volume ratio [23,24]. This linear relationship has also been found in Eq. (1) [9] and in Eq. (2) when the surface layer number is considered to be one. By fitting the
(6)
Table 1 Several parameters of Ag, Au and PbS being needed in Eq. (5) where SB (∞) = EB (∞)/Tev (∞) ≈ Hv (∞)/Tv (∞)
Ag Au PbS
h (nm)
Hv (∞) (kJ mol−1 )
Tv (∞) (K)
SB (∞) (J mol−1 K−1 )
Tev (∞)a (K)
0.2889 [25] 0.2884 [25] 0.2970 [26]
255 [25] 330 [25]
2435 [25] 3129 [25]
105 105.5 13R [5]
1097 [9] 953 [9] 805 [9]
a For comparing the prediction of Eqs. (1), (2) and (5) with the experimental results [9], Tev (∞) used as denominator in Eqs. (1), (2) and (5) is cited from the experimental fitting results in Ref. [9], because Ag, Au and PbS nanoparticles sublimate from solid to vapor directly while the larger particles evaporate at much lower temperature as compared to the corresponding melting or boiling temperatures [9].
T.H. Wang et al. / Materials Chemistry and Physics 111 (2008) 293–295
experimental data into straight lines, they get slopes of −1158 ± 55, −895 ± 25 and −1138 ± 78 nmK for Ag, Au and PbS, respectively [9]. Through Eq. (6), we get slopes of −1334, −1153 and −1036 nmK for Ag, Au and PbS, which are close to experimental results. Tev (∞) used for calculating the slope values by Eq. (6) is cited by the experimental results [9] where Ag, Au and PbS nanoparticles sublimate from solid to vapor directly while larger particles evaporate at much lower temperature as compared to the corresponding Tm (D) or Tv (D) [9]. However, as D further decreases to a size about several nanometers, the difference between Eqs. (5) and (6) becomes evident where the energetic state of interior atoms of the nanocrystals increases too [6]. 4. Conclusions In conclusion, a simple model for Tev (D) function of nanocrystals, free of any adjustable parameter, has been established based on our model for EB (D) function. Reasonable agreement between the model predictions and experimental data of evaporation temperature for Ag, Au and PbS nanocrystals has been found.
295
References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22]
Acknowledgements
[23] [24]
Financial supports by National Key Basic Research and Development Program (Grants No. 2004CB619301) and by the 985 Project of Jilin University are acknowledged.
[25] [26]
H.K. Christenson, J. Phys.: Condens. Matter 13 (2001) R95. J.G. Dash, Rev. Mod. Phys. 71 (1999) 1737. M. Alcoutlabi, G.B. McKenna, J. Phys.: Condens. Matter 17 (2005) R461. V.N. Singh, B.R. Mehta, J. Nanosci. Nanotechnol. 5 (2005) 431. C.C. Yang, Q. Jiang, Acta Mater. 53 (2005) 3305. Q. Jiang, H.X. Shi, M. Zhao, J. Chem. Phys. 111 (1999) 2176. W. Thomson, Philos. Mag. 42 (1871) 448. F.E. Kruis, K. Nielsch, H. Fissan, Appl. Phys. Lett. 73 (1998) 547. K.K. Nanda, Appl. Phys. Lett. 87 (2005) 021909. C.Q. Sun, Y. Shi, C.M. Li, S. Li, T.C. Au Yeung, Phys. Rev. B 73 (2006) 075408. M. Blackman, N.D. Lisgarten, L.M. Skimmer, Nature (London) 217 (1968) 1245. M. Shimada, T. Seto, K. Okuyama, AIChE J. 39 (1993) 1859. J. Tateno, Solid. State. Commun. 10 (1972) 61. C.Q. Sun, Y. Wang, B.K. Tay, J. Phys. Chem. B 106 (2002) 10701. J.H. Rose, J. Ferrante, J.R. Smith, Phys. Rev. Lett. 47 (1981) 675. W.H. Qi, M.P. Wang, M. Zhou, X.Q. Shen, X.F. Zhang, J. Phys. Chem. Solids 67 (2006) 851. B. Pluis, D. Frenkel, J.F. van der Veen, Surf. Sci. 239 (1990) 282. F.T. Trouton, Philos. Mag. 18 (1884) 54. D.C. Wallace, Phys. Rev. E 56 (1997) 4179. J.H. Han, D.Y. Kim, Acta Mater. 51 (2003) 5439. Q. Jiang, J.C. Li, B.Q. Chi, Chem. Phys. Lett. 366 (2002) 551. K.K. Nanda, A. Maisels, F.E. Kruis, B. Rellinghaus, Europhys. Lett. 80 (2007) 56003. M. Hasegawa, K. Hoshino, M. Watabe, J. Phys. F: Met. Phys. 10 (1980) 619. H.K. Kim, S.H. Hum, J.W. Park, J.W. Jeong, G.H. Lee, Chem. Phys. Lett. 354 (2002) 165. http://www.webelements.com/. Joint Committee of Power Diffraction Standards (JCPDS) 05-0592 and 411049.
Contents lists available at ScienceDirect
Materials Chemistry and Physics journal homepage: www.elsevier.com/locate/matchemphys
Size effect on evaporation temperature of nanocrystals T.H. Wang, Y.F. Zhu, Q. Jiang ∗ Key Laboratory of Automobile Materials, Ministry of Education, and Department of Materials Science and Engineering, Jilin University, Changchun 130022, China
a r t i c l e
i n f o
Article history: Received 6 December 2007 Received in revised form 1 April 2008 Accepted 4 April 2008 Keywords: Nanocrystals Size effect Evaporation temperature
a b s t r a c t Based on our model for size-dependent cohesive energy, the size-dependent evaporation temperature of nanocrystals has been modeled without any adjustable parameter. The model predicts a decrease of the evaporation temperature of nanocrystals with decreasing size. The model predictions are in good agreement with available experimental results for Ag, Au and PbS nanocrystals. © 2008 Elsevier B.V. All rights reserved.
1. Introduction Studies of basic phase transitions in nanoscale materials are of great fundamental importance to modern condensed matter physics. One of the striking features of a nanocrystal is that the transition temperatures for phase transitions, such as solid–liquid, liquid–vapor, magnetic–paramagnetic, ferroelectric–paraelectric transitions, are no longer constant but are tunable with the diameter D of nanocrystals in divergent ways [1–6]. According to Kelvin equation [7], the vapor pressure of nanoparticles due to their curved surface is higher than that of a flat surface. Thus, the vapor pressure and the related evaporation of nanocrystals are size-dependent. As predicted by Kelvin equation, the evaporation temperature Tev (D) of nanocrystals is experimentally found indeed to be size-dependent and decreases with decreasing size, being similar to the function of the size-dependent melting temperature of nanocrystals [8–12]. From the technological point of view, it is possible to evaporate different materials at the same temperature by taking different nanomaterials with distinct sizes. This is meaningful for the synthesis of nanoparticles or thin films of compounds from a single temperature source. Thus, knowing Tev (D) function of nanocrystals is valuable in industry. Assuming the energy required to remove one atom from a nanoparticle to vacuum can be scaled to Tev (D), Tev (D) has been deduced as [9], 2h3 Tev (D) =1− Tev (∞) 3EB (∞)D
∗ Corresponding author. Fax: +86 431 85095876. E-mail address: [email protected] (Q. Jiang). 0254-0584/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.matchemphys.2008.04.010
(1)
where is the surface energy, and h is the atomic or molecular diameter, ∞ denotes the bulk size, EB is the atomic cohesive energy, and D is defined as diameter of nanoparticles and nanorods, or thickness of thin films. Originally, the equation is used to calculate and EB (∞) by experimental data of Tev (D). Whereas if , Tev (∞) and EB (∞) are known, Tev (D) can be deduced although the determination of suffers difficulty and uncertainty. Recently, based on the bond order-length-strength correlation mechanism, Sun et al. [10] have established a model for Tev (D) function
Tev (D) i (zib ci −m(zi ) − 1) =1+ Tev (∞)
(2)
i≤3
where subscript i denotes the i-th atomic layer, which may be counted up to three from the outermost atomic layer to the centre of the solid. ci = hi /h = 2/{1 + exp[(12 − zi )/(8zi )]} shows a coordination number dependent reduction of h, zib = zi /zb with zi and zb being the coordinates with and without coordination number imperfection, respectively, and i = 2hci /D is the portion of the atoms in the i-th atomic layer from the surface compared to the total number of atoms of the entire solid with = 1, 2, 3 corresponding to thin films, nanorods and nanoparticles, respectively. The power index m is an indictor for the bond nature [10]. Although many efforts have been made on the study of evaporation of nanoparticles and thin films, they mostly focus on the mechanism, process and kinetics of the evaporation. The study on Tev (D) itself is less although it is important in both science and technology. Thus, further effort is needed to develop a model without any free parameter, which should benefit our understanding on the physics behind the evaporation phenomena of nanocrystals.
294
T.H. Wang et al. / Materials Chemistry and Physics 111 (2008) 293–295
In this contribution, a simple thermodynamic model, free of any adjustable parameter, is developed for Tev (D) function of nanocrystals. It is found that the model predictions agree with available experimental results for Ag, Au and PbS nanocrystals. 2. Model Based on the Lindemann’s criterion of melting, an expression for the bulk melting temperature Tm (∞) of crystals is derived [13], which shows that Tm (∞) is proportional to EB (∞), or Tm (∞) characterizes the bond strength [14–16]. The fact that Tm (∞) varies linearly with EB (∞) agrees with experimental data for metals [17]. According the Trouton’s rule [18], the ratio of latent heat of vaporization Hv (∞) to the liquid–vapor transition temperature Tv (∞) is a constant or vaporization entropy Sv . As results, Hv (∞) ∝ Tv (∞). It is known that compared with the gas, the bond strength and coordination number of liquid are similar to the crystal and their energetic differences are very small where Hv (∞) ≈ EB (∞) and Tv (∞) ≈ Tev (∞) [19,20]. Since EB (∞) is directly equal to the product of the bond number and the bond energy, which is the energy that divides a crystal into isolated atoms by destroying all bonds. This is just the energetic requirement for the solid–vapor transition. Thus, similar to Tm (∞) and Tv (∞), Tev (∞) characterizes even better the bond strength and Tev (∞) ∝ EB (∞) [9,10]. This relationship has been extended to nanosize [9,10] Tev (D) EB (D) = . Tev (∞) EB (∞)
(3)
Based on a model for the latent heat with a similar consideration of the above, EB (D)/EB (∞) function has also been deduced as [21]
EB (D) 1 = 1− EB (∞) (2D/h) − 1
2S (∞) B
exp −
3R
1 (2D/h) − 1
(4)
where SB (∞) = EB (∞)/Tev (∞) is the bulk solid–vapor transition entropy, R is ideal gas constant. It is evident from Eq. (4) that EB (D) increases (the absolute value decreases) with a decrease in size, which reflects the instability of nanocrystals in comparison with the corresponding bulk crystals. This trend is expected since the surface/volume ratio increases with decreasing size while the surface atoms have lower coordinates and thus higher energetic state, and consequently EB (D) as a mean value of all atoms increases [21]. Using Eq. (4), EB (D) values of W and Mo nanoparticles are predicted and are in agreement with the experimental results [21]. Substituting Eq. (4) into Eq. (3), we get
Tev (D) 1 = 1− Tev (∞) (2D/h) − 1
2S (∞) B
exp −
3R
1 . (2D/h) − 1
(5)
Fig. 1. Tev (D) functions for Ag, Au and PbS nanocrystals where the solid lines denote the model prediction of Tev (D) in terms of Eq. (5) and the symbols (), () and (䊉) show the experimental data of Ag, Au and PbS nanocrystals, respectively [9]. The necessary parameters used in Eq. (5) are listed in Table 1. The dashed lines show the theoretical results based on Eq. (2) where the original parameters have been cited from the original Ref. [10]. Since Ref. [10] has not discussed the case of Au nanocrystals, the same i and values for Ag are taken because of the similarity of Au and Ag. And the dash dotted lines denote the theoretical results based on Eq. (1) where the original parameters have been cited from the original Ref. [9].
increases, and prediction of Eq. (5) agrees well with the experimental results except Au. The experimental results of Au are slightly higher than the prediction of Eq. (5). This is induced by the fact that the measured Tev (∞) value of Au is lower than the real one due to the existence of surface melting [9]. The calculated results show that although the vapor pressure of Ag at 953 K is much higher than that of Au, the former is lower to latter when Au is surrounded by a liquid layer [22]. Thus, the surface melting significantly increases the evaporation of Au and this effect for the evaporation behavior of Au cannot be neglected [22]. As shown in Fig. 1, Eq. (1) gives good agreement with experimental results when (D) > (∞) is taken although the evident difference of (D) and (∞) used in Ref. [9] is not clear. The predictions of Eq. (2) are consistent with the experimental results when i = 3 and = 1 for Ag and Au and i = 3 and = 3 for PbS are taken as used in the original work [10]. Since values used are different while all considered nanocrystals are nanoparticles, the exact physical basis of is unknown. Considering the mathematical relation of exp(−x) ≈ 1 − x when x is small enough as a first order approximation, Eq. (5) can be rewritten as
3. Results and discussion
Tev (D) hSB (∞) ≈1− . 3RD Tev (∞)
Fig. 1 presents comparisons of Tev (D) between the model predictions in light of Eq. (5) with parameters listed in Table 1 and available experimental results for Ag, Au and PbS nanocrystals. Other two theoretical results based on Eqs. (1) and (2) are also shown. As shown in Fig. 1, Tev (D) decreases as D drops or as 1/D
Eq. (6) is in agreement with a general consideration that the drop of any size-dependent thermodynamic amount is proportional to 1/D or the surface/volume ratio [23,24]. This linear relationship has also been found in Eq. (1) [9] and in Eq. (2) when the surface layer number is considered to be one. By fitting the
(6)
Table 1 Several parameters of Ag, Au and PbS being needed in Eq. (5) where SB (∞) = EB (∞)/Tev (∞) ≈ Hv (∞)/Tv (∞)
Ag Au PbS
h (nm)
Hv (∞) (kJ mol−1 )
Tv (∞) (K)
SB (∞) (J mol−1 K−1 )
Tev (∞)a (K)
0.2889 [25] 0.2884 [25] 0.2970 [26]
255 [25] 330 [25]
2435 [25] 3129 [25]
105 105.5 13R [5]
1097 [9] 953 [9] 805 [9]
a For comparing the prediction of Eqs. (1), (2) and (5) with the experimental results [9], Tev (∞) used as denominator in Eqs. (1), (2) and (5) is cited from the experimental fitting results in Ref. [9], because Ag, Au and PbS nanoparticles sublimate from solid to vapor directly while the larger particles evaporate at much lower temperature as compared to the corresponding melting or boiling temperatures [9].
T.H. Wang et al. / Materials Chemistry and Physics 111 (2008) 293–295
experimental data into straight lines, they get slopes of −1158 ± 55, −895 ± 25 and −1138 ± 78 nmK for Ag, Au and PbS, respectively [9]. Through Eq. (6), we get slopes of −1334, −1153 and −1036 nmK for Ag, Au and PbS, which are close to experimental results. Tev (∞) used for calculating the slope values by Eq. (6) is cited by the experimental results [9] where Ag, Au and PbS nanoparticles sublimate from solid to vapor directly while larger particles evaporate at much lower temperature as compared to the corresponding Tm (D) or Tv (D) [9]. However, as D further decreases to a size about several nanometers, the difference between Eqs. (5) and (6) becomes evident where the energetic state of interior atoms of the nanocrystals increases too [6]. 4. Conclusions In conclusion, a simple model for Tev (D) function of nanocrystals, free of any adjustable parameter, has been established based on our model for EB (D) function. Reasonable agreement between the model predictions and experimental data of evaporation temperature for Ag, Au and PbS nanocrystals has been found.
295
References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22]
Acknowledgements
[23] [24]
Financial supports by National Key Basic Research and Development Program (Grants No. 2004CB619301) and by the 985 Project of Jilin University are acknowledged.
[25] [26]
H.K. Christenson, J. Phys.: Condens. Matter 13 (2001) R95. J.G. Dash, Rev. Mod. Phys. 71 (1999) 1737. M. Alcoutlabi, G.B. McKenna, J. Phys.: Condens. Matter 17 (2005) R461. V.N. Singh, B.R. Mehta, J. Nanosci. Nanotechnol. 5 (2005) 431. C.C. Yang, Q. Jiang, Acta Mater. 53 (2005) 3305. Q. Jiang, H.X. Shi, M. Zhao, J. Chem. Phys. 111 (1999) 2176. W. Thomson, Philos. Mag. 42 (1871) 448. F.E. Kruis, K. Nielsch, H. Fissan, Appl. Phys. Lett. 73 (1998) 547. K.K. Nanda, Appl. Phys. Lett. 87 (2005) 021909. C.Q. Sun, Y. Shi, C.M. Li, S. Li, T.C. Au Yeung, Phys. Rev. B 73 (2006) 075408. M. Blackman, N.D. Lisgarten, L.M. Skimmer, Nature (London) 217 (1968) 1245. M. Shimada, T. Seto, K. Okuyama, AIChE J. 39 (1993) 1859. J. Tateno, Solid. State. Commun. 10 (1972) 61. C.Q. Sun, Y. Wang, B.K. Tay, J. Phys. Chem. B 106 (2002) 10701. J.H. Rose, J. Ferrante, J.R. Smith, Phys. Rev. Lett. 47 (1981) 675. W.H. Qi, M.P. Wang, M. Zhou, X.Q. Shen, X.F. Zhang, J. Phys. Chem. Solids 67 (2006) 851. B. Pluis, D. Frenkel, J.F. van der Veen, Surf. Sci. 239 (1990) 282. F.T. Trouton, Philos. Mag. 18 (1884) 54. D.C. Wallace, Phys. Rev. E 56 (1997) 4179. J.H. Han, D.Y. Kim, Acta Mater. 51 (2003) 5439. Q. Jiang, J.C. Li, B.Q. Chi, Chem. Phys. Lett. 366 (2002) 551. K.K. Nanda, A. Maisels, F.E. Kruis, B. Rellinghaus, Europhys. Lett. 80 (2007) 56003. M. Hasegawa, K. Hoshino, M. Watabe, J. Phys. F: Met. Phys. 10 (1980) 619. H.K. Kim, S.H. Hum, J.W. Park, J.W. Jeong, G.H. Lee, Chem. Phys. Lett. 354 (2002) 165. http://www.webelements.com/. Joint Committee of Power Diffraction Standards (JCPDS) 05-0592 and 411049.