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Size dependent microstructure for Ag–Ni nanoparticles
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Acta Materialia 59 (2011) 6501–6509 www.elsevier.com/locate/actamat
Size dependent microstructure for Ag–Ni nanoparticles C. Srivastava ⇑, S. Chithra, K.D. Malviya, S.K. Sinha, K. Chattopadhyay Department of Materials Engineering, Indian Institute of Science, Bangalore 560 012, India Received 23 May 2011; received in revised form 3 July 2011; accepted 10 July 2011 Available online 2 August 2011
Abstract The Ag–Ni system is characterized by large differences in atomic sizes (14%) and a positive heat of mixing (+23 kJ mol1). The binary equilibrium diagram for this system therefore exhibits a large miscibility gap in both solid and liquid state. This paper explores the sizedependent changes in microstructure and the suppression of the miscibility gap which occurs when free alloy particles of nanometer size are synthesized by co-reduction of Ag and Ni metal precursors. The paper reports that complete mixing between Ag and Ni atoms could be achieved for smaller nanoparticles (<7 nm). These particles exhibit a single-phase solid solution with face-centered cubic (fcc) structure. With increase in size, the nanoparticles revealed two distinct regions. One of the regions is composed of pure Ag. This region partially surrounds a region of fcc solid solution at an early stage of decomposition. Experimental observations were compared with the results obtained from the thermodynamic calculations, which compared the free energies corresponding to a physical mixture of pure Ag and Ni phases and a fcc Ag–Ni solid solution for different particle sizes. Results from the theoretical calculations revealed that, for the Ag–Ni system, solid solution was energetically preferred over the physical mixture configuration for particle sizes of 7 nm and below. The experimentally observed two-phase microstructure for larger particles was thus primarily due to the growth of Ag-rich regions epitaxially on initially formed small fcc Ag–Ni nanoparticles. Ó 2011 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Miscibility gap; Nanoparticles; Electron microscopy; Composition; Gibbs free energy
1. Introduction Efforts towards understanding the size–structure–property correlation for nanoscale entities have gained importance in recent years. In case of nano-sized features, large surface area and differences in the atomic coordination and chemistry of surfaces significantly alter the surface energy of a system [1–3]. The changes in surface energy produce substantial differences in properties between nanoparticles and their bulk counterparts for similar compositions [4]. This difference is manifested in phenomena such as changes in melting point [5], changes in attributes related to crystal order [6], surface plasmon resonance [7] and superparamagnetism [8]. The studies on the effect of nanometric size on alloys and in particular two-phase alloys are
⇑ Corresponding author. Tel.: +91 080 22932834.
E-mail address: [email protected] (C. Srivastava).
limited because of difficulties in measuring the compositions at small sizes. However, recent advances have allowed such a study. One interesting structural change at nanoscale is the formation of a solid solution between elements which at bulk scale show a miscibility gap [9–11]. The tendency towards retaining a single-phase microstructure can be due to two different effects, which must be understood precisely. They are (a) high surface curvature at smaller sizes enhancing the solid solubility through the Gibbs–Thompson effect and (b) decrease in the driving force for the nucleation and growth of second phase within a small particle. Increase in miscibility (or solid solubility) at nanoscale between elements that show tendency for phase separation at bulk scale has been reported for systems such as Ag–Pt [12], Au–Pt [13] and Pt–Ru [14]. A comprehensive theoretical and experimental analysis of various aspects of alloy formation between immiscible elements is provided in the review article by Ma [15].
1359-6454/$36.00 Ó 2011 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2011.07.022
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This paper presents an experimental and thermodynamic analysis of the tendency of Ag and Ni atoms to mix to form a solid-solution face-centered cubic (fcc) structure as a function of particle size, for nanoparticles synthesized by co-reduction of Ag and Ni metal precursors in water. It should be noted that at bulk scale, Ag–Ni system shows immiscibility in both solid and liquid phases [16]. Solid solubility of Ni in Ag is as low as 0.1 at.% even at 750 °C [17]. This high immiscibility results from the large difference in size (14%) between Ag and Ni atoms and a large positive heat of mixing (DH). For equiatomic Ag– Ni fcc solid solution, the DH value is +23 kJ mol1 [15]. Several researchers have reported both theoretical and experimental studies focused on nano-sized Ag–Ni alloys. He et al. [16] showed that sputtered Ag–Ni alloy films contain phases with compositions lying within the equilibrium (bulk) Ag–Ni miscibility gap. These phases exhibit a non-uniform, spinodal-like structure at an extremely fine scale. In another study, Zhang et al. [18] synthesized Ag–Ni nanoalloys by simultaneous reduction of Ag and Ni ions by c-irradiation. Results from their compositional analysis reveal homogeneous distribution of Ag and Ni atoms inside the as-synthesized particles 6 nm in size. Gaudry et al. [19] synthesized NiXAg100X clusters by laser-induced vaporization of rods of similar composition and subsequently condensing the vapors over a substrate under a continuous flow of helium. They reported that the clusters with compositions lying in the bulk miscibility gap region attained a core–shell structure. The core and shell were rich in Ni and Ag atoms, respectively. This kind of core–shell configuration is favorable as it minimizes the strain arising from pronounced lattice mismatch due to large difference in sizes between Ni and Ag atoms. The core–shell arrangement of atoms for Ag–Ni clusters is also confirmed by Baletto et al. [20]. They studied the growth process of 200–300 atoms Ag–Ni clusters by means of molecular dynamic simulations and concluded that a core–shell arrangement with Ni forming the core and Ag forming the shell is energetically and kinetically the most favored configuration for the Ag–Ni system. In all the studies cited above, investigators have focused primarily on analyzing the possibility of various structural arrangements such as solid solution (signifying complete miscibility) or core–shell (signifying immiscibility) which results when Ag and Ni atoms coexist in a fixed-sized nano-scale volume with overall composition lying within the bulk miscibility gap. Until now there have been no studies on the evolution of microstructure and, in particular, the composition of phases in Ag–Ni nanoparticles as a function of size. The present work investigates this issue and presents an experimental and theoretical analysis of size-dependent microstructure evolution for Ag–Ni bimetallic nanoparticles. 2. Experimental procedure To synthesize the nanoparticles, 0.54 g of nickel(II) nitrate (Ni(NO3)2), 0.5 g of silver nitrate (Ag(NO3)) and
1.36 g of polyvinyl pyrrolidone (PVP) were dissolved in 100 ml of distilled water. A separate solution containing 0.52 g of sodium borohydride (NaBH4) in 25 ml distilled water was also prepared. The precursor amounts were chosen with a target final average composition of 50 at.% Ag (or Ni). The mixture containing the metal precursors and PVP was stirred vigorously using a magnetic stirrer. Once this solution appeared clear, co-reduction of the metal precursors was facilitated by dropwise addition of the water solution of NaBH4 over a period of 10 min. Once the color of the reaction mixture turned black, stirring was stopped. The nanoparticle synthesis reaction was performed at room temperature and under ambient atmosphere. After the synthesis, the as-prepared particles were covered with PVP. The reaction byproducts that formed must be removed prior to analysis and characterization. To clean the nanoparticles, the reaction mixture was poured from the reaction flask into a beaker containing 100 ml ethanol and was left for more than 3 h. A black dispersion of particles collected at the bottom of the beaker and was then centrifuged at 5000 rpm for 10 min. The particles collected at the bottom of the centrifuge tube were then dispersed in distilled water for further analysis. Average composition of the nanoparticle dispersion was determined by the energy dispersive spectroscopy (EDS) technique and scanning electron microscopy (SEM) using a Quanta ESEM instrument operating at 20 kV. SEMEDS has a larger interaction volume, consequently yielding a larger sampling size for determining the average composition of the nanoparticle dispersion. The sample for SEMEDS analysis was prepared by drop drying the particle dispersion onto a glass plate. Transmission electron microscopy (TEM) with a 300 keV field emission FEI Tecnai F-30 was used for bright-field image acquisition and single-particle composition measurements. A highly dilute dispersion of the nanoparticle was drop dried onto a carbon-coated Au grid for the TEM-based analysis. For the size–composition correlation analysis, bright-field TEM micrographs were first captured on a gatan imaging filter (GIF) camera using the highest C2 aperture (150 lm diameter) setting and an FEI-designated spot size of 1 (biggest spot size). Bright-field micrographs were used to determine the sizes of the nanoparticles. After the acquisition of the bright-field image, the C2 aperture setting was changed to smallest (50 lm diameter) aperture size, and the beam spot size was reduced to 3 nm. With the new aperture and spot size settings, the electron beam was condensed over a nanoparticle, and the EDS signal was acquired from that particular particle. Background subtracted integrated intensity of peaks corresponding to the AgK and NiK lines in the EDS spectrum were used for the elemental quantification. To investigate the composition distribution inside a single particle, energy-filtered transmission electron microscopy (EFTEM)-based compositional mapping of a group of different sized particles was also performed using a GIF-2000 and a microscope high-tension voltage of 200 keV.
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3. Results and discussion TEM bright-field micrographs showed three different regions on the sample grid: (a) region containing isolated, nearly spherical, nanoparticles; (b) region containing isolated Ni oxide films; and (c) region with coexisting nanoparticles and Ni oxide films. A representative TEM brightfield image showing the isolated nanoparticles and the nanoparticle–Ni oxide film agglomerate is shown in Fig. 1a. The discussion henceforth only considers the structural and compositional data obtained from the isolated nanoparticles on the TEM grid. Histograms of size and composition distribution obtained from the analysis of individual isolated nanoparticles are shown in Fig. 1b and c, respectively. Mean values of size and composition of the particles (summation average of size and composition values for individual nanoparticles) were 10 nm and 25 at.% Ni respectively. SEM-EDS analysis of the nanoparticle dispersion revealed an average composition of 48 at.% Ni. The difference in Ni content between the average composition obtained from the measurements using SEM-EDS and that obtained by TEMEDS analysis can be attributed to the fact that, in the latter case only isolated nanoparticles were probed. The SEMEDS-based analysis, owing to its much greater interaction volume, considered compositional signals from both the nanoparticles and the nickel oxide film, yielding a relatively Ni-rich composition. Note that reports exist on simultaneous wide distribution of size and composition for chemically synthesized bimetallic nanoparticles [21]. However, in the present case, even though there was a simultaneous reduction of both Ag and Ni metal precursors, the nature of the distribution of size and composition among particles is distinctly different. The size distribution was observed to be significantly wide, while the composition distribution was relatively narrow (a high percentage of particles were Ag rich) as shown in Fig. 1b and c, respectively. This observation led to a speculation that the inherent immiscibility between Ag and Ni atoms might be the dominating factor controlling the co-reduction condition for the observed nature of size and composition distribution. To investigate a possible correlation between the immiscibility of the constituent elements and the observed variation in size and the corresponding compositional variability, compositions of individual nanoparticles were determined as a function of their sizes. From the size–composition correlation analysis, nanoparticles were grouped in three size ranges: (a) 3–7 nm, range 1; (b) 8–13 nm, range 2; and (c) 14–20 nm, range 3. Composition distribution histograms for particles in ranges 1, 2 and 3 are shown Fig. 2a, b and c, respectively. The average value and standard deviation of size and composition distribution for nanoparticles in each size range are presented in Table 1. The data presented in Table 1 reveal a large shift in the value of average composition from that of equiatomic to Ag-rich with the increase in size of the particles beyond 7 nm. Furthermore, from the values of the standard deviation for the
Fig. 1. (a) TEM bright-field micrograph showing two different regions on the specimen grid: a region containing isolated nearly spherical nanoparticles and a region containing nanoparticles embedded in a matrix. (b and c) Histograms for (b) size and (c) composition distribution between isolated Ag–Ni nanoparticles.
distribution of composition presented in Table 1 and the composition distribution histograms shown in Fig. 2, it is evident that the spread of composition significantly decreases with increase in size of the particles beyond the particle set included in range 1. The smaller particles (range 1) tend to possess relatively greater compositional variability compared with the larger ones (range 2 and 3). The above analysis data poses two important questions: (a) In what structural state do the atoms of Ag and Ni coexist and does it change with particle size, specifically for smaller
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Ag-rich with increase in the size of the particles beyond 7 nm. To address the above issues, high-resolution transmission electron microscopy (HRTEM)-based analysis of the nanoparticles was performed. HRTEM imaging revealed that the smaller particles (<7 nm) in the dispersion were essentially single phase. A representative HRTEM image of a 6 nm particle with lattice spacing of 0.22 nm is shown in Fig. 3a. It should be noted that the interplanar spacing of the (1 1 1) plane for pure Ni and Ag is 0.203 nm and 0.236 nm, respectively. From the relationship between lattice parameter and composition as estimated by Vegard’s law, the interplanar spacing of (1 1 1) plane corresponding to a solid solution between Ag and Ni atoms with composition 50 at.% Ag or Ni should be 0.220 nm. The observed single-phase microstructure and interplanar spacing of 0.22 nm for the representative 6 nm particle thus indicated the formation of a crystalline fcc solid solution between Ag and Ni atoms. HRTEM analysis of bigger particles (>10 nm) revealed a two-phase microstructure. A representative HRTEM image of a 15 nm particle is shown in Fig. 3b. The spacings of the planes measured from the lattice fringes revealed the identity of the two phases: (a) a phase with d spacing of 0.24 nm, which corresponds to the d spacing of (1 1 1) plane of a pure fcc Ag lattice; and (b) a phase with d spacing of 0.22 nm, which corresponds to the d spacing of (1 1 1) plane of Ag50Ni50 fcc solid solution. To further confirm the identity of different phases in Ag–Ni nanoparticles, EFTEM-based compositional mapping for a group of different sized particles was performed. Results from the EFTEM mapping experiment are shown in Fig. 4. Fig. 4a shows a bright-field TEM image of a set of nanoparticles. Fig. 4b and c shows mapping with Ni and Ag, revealing Ni-rich regions and Ag-rich regions, respectively. The sizes of the particles corresponding to numbers 1–3 in the bright-field micrograph (Fig. 4a) are 23 nm, 7 nm and 12 nm, respectively. From Fig. 4b and c, it can be seen that the particles numbered 1 and 3 contains two compositionally distinct regions. One of the regions contained both Ag and Ni atoms (the right edge of particle 1 and the upper half of particle 3). The second region, in contrast, is composed of only Ag atoms (left half of particle 1 and lower half of particle 3). In contrast, particle number 2, which has a size of 7 nm, does not show any distinctly compositionally phase separated regions. Results from the HRTEM and EFTEM analysis thus indicate that the miscibility between Ag and Ni atoms is restricted only for smaller sizes (<7 nm) and a two-phase microstructure essentially
Fig. 2. Composition distribution histograms for particles in (a) range 1 (3–7 nm), (b) range 2 (8–13 nm) and (c) range 3 (14–20 nm). About 40 individual particles were analyzed for each size range.
particles? (b) Why does the nature of composition distribution sharply change and significantly narrow down to
Table 1 Mean value and standard deviation for size and composition distribution for particles in size ranges 1, 2 and 3. Size range (nm)
Mean size (nm)
Standard deviation of size distribution
Mean composition (at.% Ni)
Standard deviation of composition distribution (at.% Ni)
3–7 8–13 14–20
6 10 15
1.1 1.5 2.1
48 17 11
26 14 9
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Fig. 3. HRTEM image of (a) 6 nm AgNi nanoparticle with a singlephase microstructure and a lattice fringes spacing of 0.223 nm and (b) 15 nm Ag–Ni nanoparticle with two-phase microstructure (the insert shows a low-magnification image of the particle). The two phases (separated by a dashed white line for ease of viewing) are (i) phase with d spacing 0.24 nm, which corresponds to the d spacing of (1 1 1) plane in a pure fcc Ag lattice, and (ii) phase with d spacing 0.22 nm, which corresponds to the d spacing of (1 1 1) plane of Ag50Ni50 fcc solid solution.
consisting of Ag on the fcc solid solution of Ag(Ni) nanoparticles develops for the bigger particles. In order to rationalize the experimental observations, a thermodynamic analysis was carried out. The analysis involved theoretically calculating the free energy of a physical mixture of Ag and Ni particles (designated Gmm) and solid solution (designated Gss) between Ag and Ni atoms for different sizes of particles. For all the particle sizes for which the Gss was less than Gmm, miscibility between Ag and Ni atoms with a resultant solid solution with fcc structure can be expected. The details are as follows. 3.1. Calculation of Gmm To calculate the Gmm, model particle geometry was chosen such that a spherical nanoparticle of diameter D contained coexisting pure Ag and Ni phase volumes with a heterophase interface. To calculate the value of Gmm as a function of particle size for a constant particle composition
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Fig. 4. Results from EFTEM compositional mapping experiment showing (a) bright-field image of nanoparticles, (b) nickel-rich regions and (c) silver-rich regions.
of Ag50Ni50, the curvature of the heterophase interface was changed with change in particle size in such a way that the atomic ratios of Ag and Ni remained 1:1. The volume fraction does not change with radius. The energy contributions to Gmm are due to: (a) the volumetric contributions from pure Ag and Ni phase volumes; (b) the interfacial energy contribution from the heterophase interface between the pure Ag and Ni regions; the interface was assumed to be a curved plane which is a frustum of another sphere with diameter D as that of the nanoparticle (since volume v is conserved); the thickness of the interface was assumed to ˚ ; and (c) the particle-size-dependent surface energy be 5 A contribution from the free surfaces of pure Ag and Ni phases volumes. It should be noted that the surface energies of the pure Ag and Ni surfaces are not constant and depend on the particle size (diameter of the model sphere). The geometry of the triple point where the mechanical equilibrium needs to be achieved was ignored in this treatment. A calculation presented below describes the approach
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adopted to calculate the size- and composition-dependent surface energies of pure and alloyed particles. Contributions to Gmm can be written mathematically as Gmm ¼ xAg GAg þ xNi GNi þ aAg S Ag cAg ðDÞ þ aNi S Ni cNi ðDÞ þ Gint ðDÞ 2
AAg ¼ 2pðD=2Þ ð1 cos hÞ; ANi ¼ A AAg aAg ¼
DV V Ag
ð1Þ ð2Þ ð3Þ
where xAg and xNi are the mole fractions of Ag and Ni, respectively; GAg and GNi are the molar free energies of pure Ag and Ni; AAg and ANi are the surface area of the pure Ag and pure Ni phase, respectively; A is the total surface area of the model sphere; aAg and aNi are the fractions of surface atoms Ag and Ni vs the total number of atoms in the bulk, respectively; SAg and SNi are the surface areas occupied by 1 mole of atoms Ag and Ni, respectively; cAg(D) and cNi are the size-dependent specific surface energies (surface energy per unit area) of pure Ag and Ni spherical surfaces (calculated in the following section and compared with the bulk c values [22]); D is the diameter of the particle (the model sphere); and Gint is the Gibbs free energy contribution from the interface between the pure Ag and Ni forming the model sphere. Numerical values for GAg and GNi were taken as 12.72 kJ mol1 [23] and 8.91 kJ mol1 [23], respectively. Numerical values for SAg and SNi were 4.35 104 m2 and 3.24 104 m2 respectively. As described by Turnbull [24], Gint has contributions from the geometrical (cgeo) and chemical factors (cche). Mathematically, Gint [25] can be written as Gint ¼ Sðcgeo þ cche Þ
ð4Þ
where cgeo ¼ ½0:33ðcAg ðDÞ þ cNi ðDÞÞ=2 cche ¼ fxAg DH AginNi =½C o ðV Ag Þ
2=3 þ
xNi DH NiinAg =½C o ðV Ni Þ
ð5Þ 2=3
g
ð6Þ where S is the surface area occupied by one mole of the interfacial atoms; DHAginNi (or DHNiinAg) is the heat of solution of Ag in Ni (or Ni in Ag) at infinite dilution; VAg and VNi are the molar volumes of Ag and Ni, respectively; and Co is a constant being 4.5 108. The multiplication factor of 0.33 in Eq. (3) is based on the assumption that the grain boundary energy is 30% of the surface energy at 0 K [26]. Details about the approach used for calculating the cche value (Eq. (4)) were provided by Miedema [22,27]. Numerical values for cAg(D) and cNi(D) were calculated from cohesive energy, and this is explained in the following section. Numerical values [26] for DHAginNi and DHNiinAg were taken as 68 kJ mol1 and 56 kJ mol1, respectively.
butions due to pure Ag and Ni, (b) excess free energy due to mixing and (c) size-dependent surface energy of the nanoparticle with solid solution fcc structure. Mathematically, Gss ¼ xAg GAg þ xNi GNi þ DGmix þ ð2css ðDÞV AgNi Þ=ðD=2Þ
ð7Þ
where xAg and xNi are the atomic fractions of Ag and Ni, respectively; GAg and GNi are the molar free energies of pure Ag and Ni, respectively; DGmix is the excess free energy of the alloy phase due to mixing; css(D) is the sizedependent specific surface energy (surface energy per unit area) of the nanoparticle with solid solution between Ag and Ni atoms; VAg–Ni is the molar volume of fcc AgNi solid solution; and D is the diameter of the particle. The free energy of an alloy phase due to mixing (DGmix) is given by DGmix ¼ DH mix T DS mix
ð8Þ
where DHmix and DSmix are the enthalpy and entropy of mixing, respectively. The entropy term for the solid solution was taken as that of an ideal solid solution given by DS mix ¼ R½xAg ln xAg þ xNi ln xNi
ð9Þ
where xAg and xNi are the atomic fraction of Ag and Ni, respectively, and R is the gas constant. According to the well-known Miedema model, the enthalpy of mixing (DHmix) can be expressed as a sum of chemical, elastic and structural contributions. A detailed description of the three components and the mathematical formula to calculate the numerical values corresponding to their energy contribution can be found in Refs. [28,29]. One important limitation to the application of Eq. (5) to calculate Gss is the absence of experimentally or theoretically determined size-dependent surface energy per unit area (css(D)) values for the solid solution Ag–Ni alloy in the literature. The methodology and the equations used to calculate the css(D) values are described below. To calculate css(D), a two-step approach was adopted. First, the particle-sizedependent cohesive energy of nanoparticles containing different atomic fractions of Ag and Ni atoms was calculated. Secondly, using the cohesive energy values obtained in the first step, the size- and composition-dependent surface energy of fcc metallic Ag–Ni nanoparticles was obtained. The details about the approach employed to derive the mathematical formula that yields the size- and composition-dependent cohesive energy (Ec(D)) values for alloyed nanoparticles was provided by Qi [30]. The mathematical formula for the calculation of Ec(D) is given as ! ! aD2 aD2 Ec ðDÞ ¼ xAg EAg 1 2 þ xNi ENi 1 2 xAg xNi X nd Ag nd Ni ð10Þ
3.2. Calculation of Gss
n ¼ fD3 =ðxAg d 3Ag þ xNi d 3Ni Þ
To calculate the Gss, the following approach was used. Energy contributions to Gss are from (a) volumetric contri-
where xAg and xNi are the molar fraction of Ag and Ni, respectively; EAg and ENi are the bulk cohesive energies
ð11Þ
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of Ag and Ni, respectively; a is the shape factor (defined as the surface area ratio of non-spherical and spherical nanoparticle of identical volumes); dAg and dNi are the atomic diameters of Ag and Ni, respectively; X is the interaction parameter with a value of 60 kJ mol1 (for Ag–Ni); and f is the packing factor (f = 0.74 for fcc structure). Numerical values for EAg and ENi are 283 kJ mol1 [22] and 428 kJ mol1 [22], respectively. Numerical values [31] for dAg ˚ and 2.49 A ˚ , respectively. It should be and dNi are 2.88 A noted that the mathematical formula for calculating the cohesive energy as provided by Qi [30] does not take into account the heat of mixing of component atoms, and terminates only after the first two terms on the rhs of Eq. (10). An extra term (third term after the minus sign) was added on the rhs of Eq. (10) which adds the energy contribution due to the heat of mixing of atoms of component elements. The approach adopted to calculate the size-dependent surface energy of solid solution nanoparticles was provided by Liu and Jiang [32]. Mathematical formula for the sizedependent specific surface energy (Es(D)) for a particle with a truncated octahedral (TC) geometry and size DTC (defined as the distance between two opposite fcc (1 1 1) planes in a TC geometry) is given as Es ðDÞ ¼ f2 ½Z s ðDÞ=Z b ½Z s ðDÞ=Z b
1=2
gEci ðDÞ=2
ð12Þ
where Eci ðDÞ ¼ Ec ðDÞ=f1 pðDÞf2 ½Z s ðDÞ=Z b ½Z s ðDÞ=Z b
1=2
g=2g
ð13Þ
where pðDÞ ¼ N s ðDÞ=N tot ðDÞ
ð14Þ
where Zs(D) is the size-dependent (DTC dependent) average surface coordination number, Zb is the average coordination of the internal atoms, and Ns(D) and Ntot(D) are the total number of atoms present on the surface and inside a particle of size DTC, respectively. The relation between css(D) (Eq. (7)) and Es(D) (Eq. (12)) is given as css ðDÞ ¼ N i Ec ðDÞ=paN A D2
ð15Þ
where Ni is the number of atoms on the surface of a particle of diameter D with fcc solid solution structure (the formulation for calculating the number of atoms on the surface of a particle of certain size is provided by Qi [33]), a is the shape factor (a = 1.24 for TC geometry), and NA is Avogadro’s number. css values for a number of pure fcc metal nanoparticles were calculated as a function of their sizes. It was observed that, for a particle size of 100 nm (which with respect to size can be approximated as bulk like), the calculated css(D = 100 nm) values were in close agreement with the reported bulk specific surface energy values for several pure fcc elements. This comparison for 10 fcc elements is provided in Table 2. Furthermore, few redundant observations were made when the css(D) values for several pure fcc metals were plotted for different particle sizes. A representative plot of this type for pure Au is
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Table 2 Comparison between calculated and bulk surface energy values for fcc elements. Element
Calculated surface energy (css(D)) for D = 100 nm (J m2)
Bulk surface energy (J m2)
Reference
Ag Ni Au Cu Pt Al Pb Sr Ir Rh
1.16 2.35 1.51 1.75 2.51 1.36 0.54 0.33 3.10 2.6
1.25 2.45 1.55 1.85 2.55 1.20 0.61 0.43 3.10 2.75
[22]
shown in Fig. 5a. These observations, as evident from the plot in Fig. 5a, are that (a) the css(D) increases as the size of the particle decreases and (b) the decrease in the value of css(D) with increasing particle size is relatively steeper for sizes <10 nm than for sizes >10 nm. These two observations suggest that the excess energy contribution from the surface is profound for smaller particle sizes (<10 nm) and the contribution substantially decreases with increase in particle sizes beyond 10 nm. Larger particles (>20 nm) show almost bulk-like behavior with respect to the surface energy. Using Eqs. (8)–(13), the css(D) values as a function of particle size and composition for solid solution fcc AgXNi(100X) nanoparticles were determined and are shown as a three-dimensional plot in Fig. 5b. It is evident from the Fig. 5b that the surface energy of fcc solid solution Ag–Ni nanoparticles decreases with decrease in the Ni content and increase in the size of the alloyed particles. The values for css(D) obtained from this graph were employed to calculate the Gss for different sizes and compositions of AgXNi(100X) nanoparticles using Eq. (7). Comparison between particle-size-dependent free energies of the physical mixture (Gmm) and the solid solution (Gss) between Ag and Ni atoms, as shown in Fig. 6, also validates the conclusions from the experimental observations. For a fixed overall composition of Ag50Ni50, the Gss values were less than the Gmm values for particle sizes up to 7 nm, indicating the energetic preference for the formation of solid solution over physical mixture below this size limit. Beyond the particle size of 7 nm, the free energy values and the corresponding lower energy preferred configuration flipped from solid solution to physical mixture. The experimental and theoretical results thus lead to the following possible mechanism, which produces the observed size-dependent microstructure for Ag–Ni nanoparticles. During the initial stages of the synthesis reaction, Ag and Ni atoms reduce and form small (<7 nm) AgNi solid solution clusters. As the synthesis progresses, the excess Ag atoms that are produced by the reduction of Ag precursor then grow over the exiting solid solution fcc nanoparticles, forming a two-phase microstructure for the bigger particles. Unlike Ag atoms, the excess Ni atoms that
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did not participate in the formation of small fcc Ag–Ni nanoparticles formed the Ni-oxide film. 4. Conclusion In the present work, Ag–Ni nanoparticles were synthesized by co-reduction of silver nitrate and nickel nitrate salts in water medium. Analysis on a single particle level revealed an opposite nature of size and composition distribution between nanoparticles. Size distribution was wide, but the composition distribution was fairly narrow. Size– composition correlation analysis showed that the bigger particles in the dispersion were primarily Ag rich, whereas the smaller particles (67 nm) had compositions lying in the broad range of 10–90 at.% Ag. Through thermodynamic calculations, a particle size limit was determined, below which enhanced miscibility leading to the formation of solid solution between Ag and Ni atoms is energetically favorable over a physical mixture configuration. The particle size limit determined was 7 nm. In accordance with the theoretical results, HRTEM- and EFTEM-based analysis of individual nanoparticles revealed that the smaller particles (67 nm) in the dispersion were single phased, with a solid solution Ag–Ni fcc structure, whereas particles with sizes beyond the theoretically determined size limit for miscibility were composed of two different phases, which were pure Ag phase and Ag–Ni fcc solid solution phase. The two-phase microstructure for larger particles was thus primarily due to the growth of Ag-rich regions on initially formed small fcc Ag–Ni nanoparticles. Fig. 5. (a) Plot of change in surface energy per unit area (css(D)) with particle size for pure Au and (b) plot of change in css(D) values as a function of particle size and composition for solid solution fcc AgXNi(100X) nanoparticles.
Acknowledgements One of the author (C.S.) would like to acknowledge the Centenary Post-Doctoral fellowship scheme of the Indian Institute of Science, Bangalore, India. One of the author (S.K. Sinha) would like to acknowledge the fellowship from CSIR, India. All the authors would like to acknowledge the microscopy facilities available at Advanced Centre for Microscopy and Microanalysis, Indian Institute of Science, Bangalore, India. Professor Srikanth Lele is thanked for discussions and for his suggestions that were incorporated in the thermodynamic calculations. References
Fig. 6. Comparison between theoretically calculated, particle-size-dependent free energies of physical mixture (Gmm) and solid solution (Gss) configuration between Ag and Ni atoms. The Gss values were less than the Gmm values for particle sizes up to 7 nm, indicating the energetic preference for the formation of solid solution over physical mixture below this size limit. Beyond the particle size of 7 nm, the free energy values and the corresponding lower energy preferred configuration flipped.
[1] Nanda KK, Maisels A, Kruis FE, Fissan H, Stappert S. Phys Rev Lett 2003;91:106102. 1–4. [2] Gellman AJ, Shukla N. Nat Mater 2009;8:87–8. [3] Huang WJ, Sun R, Tao J, Menard LD, Nuzzo RG, Zuo JM. Nat Mater 2008;7:308–13. [4] Yaghmaee MS, Shokri B. Smart Mater Struct 2007;16:349–54. [5] Jiang H, Moon KS, Dong H, Hua F, Wong CP. Chem Phys Lett 2006;429(4):492–6. [6] Chraska T, King AH, Berndt CC. Mater Sci Eng A 2000;286:169–78. [7] Jian Z, Yongchang W. Plasma Sci Technol 2003;5:1835–40. [8] Weller D, Moser A. IEEE Trans Magn 1999;35:4423–39. [9] Schamp CT, Jesser WA. Metall Mater Trans A 2006;37A:1825–9. [10] Yasuda H, Mori H. J Cryst Growth 2002;237:234–8.
C. Srivastava et al. / Acta Materialia 59 (2011) 6501–6509 [11] Yasuda H, Mori H. Phys Rev Lett 1992;69:3747–50. [12] Peng Z, Yang H. J Solid State Chem 2008;181:1546–51. [13] Mott D, Luo J, Smith A, Njoki PN, Wang L, Zhong CJ. Nanoscale Res Lett 2006;2:12–6. [14] Hills CW, Mack NH, Nuzzo RG. J Phys Chem B 2003;107:2626–36. [15] Ma E. Prog Mater Sci 2005;50:413–509. [16] He JH, Sheng HW, Schilling PJ, Chien CL, Ma E. Phys Rev Lett 2001;86:2826–9. [17] Tung CY, Lin HM, Gu JM, Lee PY. NanoStruct Mater 1997;9:117–20. [18] Zhang Z, Nenoff TM, Huang JY, Berry DT, Provencio PP. J Phys Chem C 2009;113:1155–9. [19] Gaudry M, Cottancin E, Pellarin M, Lerme´ J, Arnaud L, Huntzinger JR, et al. Phys Rev B 2003;67:15409. [20] Baletto F, Mottet C, Rapallo A, Rossi G, Ferrando R. Surf Sci 2004;566:192–6. [21] Srivastava C, Balasubramanian J, Thompson GB, Turner CH, Wiest JM, Bagaria HG. J Appl Phys 2007;102:104310.
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[22] Miedema AR. Z Metall 1978;69(5):287–92. [23] Barin I, Knache O, Kubaschewski O. Thermochemical properties of inorganic substances. Berlin: Springer Verlag; 1977. [24] Turnbull D. Impurities and imperfections. Ohio: American Society of Metals; 1955. p. 121. [25] Li XY, Li ZF, Liu BX. J Alloys Compd 2002;334:167–72. [26] Murr LE. Interfacial phenomenon in metals and alloys. London: Addison-Wilsey; 1975. [27] Miedema AR. Z Metall 1978;69:455. [28] Niessen AK, De Boer FR, Boom R, de Chatel PF, Matterns WCM, Miedema AR. Calphad 1983; 7: 51. [29] Miedema AR. J Less Common Metals 1976;46:67. [30] Qi HW. J Mater Sci 2006;41:5679–81. [31] Smithells metal handbook, 6th ed. London: Butterworths; 1983. [32] Liu D, Jiang Q. IEEE Trans 2008;30. [33] Qi WH. Solid State Commun 2006;137:536–9.
Acta Materialia 59 (2011) 6501–6509 www.elsevier.com/locate/actamat
Size dependent microstructure for Ag–Ni nanoparticles C. Srivastava ⇑, S. Chithra, K.D. Malviya, S.K. Sinha, K. Chattopadhyay Department of Materials Engineering, Indian Institute of Science, Bangalore 560 012, India Received 23 May 2011; received in revised form 3 July 2011; accepted 10 July 2011 Available online 2 August 2011
Abstract The Ag–Ni system is characterized by large differences in atomic sizes (14%) and a positive heat of mixing (+23 kJ mol1). The binary equilibrium diagram for this system therefore exhibits a large miscibility gap in both solid and liquid state. This paper explores the sizedependent changes in microstructure and the suppression of the miscibility gap which occurs when free alloy particles of nanometer size are synthesized by co-reduction of Ag and Ni metal precursors. The paper reports that complete mixing between Ag and Ni atoms could be achieved for smaller nanoparticles (<7 nm). These particles exhibit a single-phase solid solution with face-centered cubic (fcc) structure. With increase in size, the nanoparticles revealed two distinct regions. One of the regions is composed of pure Ag. This region partially surrounds a region of fcc solid solution at an early stage of decomposition. Experimental observations were compared with the results obtained from the thermodynamic calculations, which compared the free energies corresponding to a physical mixture of pure Ag and Ni phases and a fcc Ag–Ni solid solution for different particle sizes. Results from the theoretical calculations revealed that, for the Ag–Ni system, solid solution was energetically preferred over the physical mixture configuration for particle sizes of 7 nm and below. The experimentally observed two-phase microstructure for larger particles was thus primarily due to the growth of Ag-rich regions epitaxially on initially formed small fcc Ag–Ni nanoparticles. Ó 2011 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Miscibility gap; Nanoparticles; Electron microscopy; Composition; Gibbs free energy
1. Introduction Efforts towards understanding the size–structure–property correlation for nanoscale entities have gained importance in recent years. In case of nano-sized features, large surface area and differences in the atomic coordination and chemistry of surfaces significantly alter the surface energy of a system [1–3]. The changes in surface energy produce substantial differences in properties between nanoparticles and their bulk counterparts for similar compositions [4]. This difference is manifested in phenomena such as changes in melting point [5], changes in attributes related to crystal order [6], surface plasmon resonance [7] and superparamagnetism [8]. The studies on the effect of nanometric size on alloys and in particular two-phase alloys are
⇑ Corresponding author. Tel.: +91 080 22932834.
E-mail address: [email protected] (C. Srivastava).
limited because of difficulties in measuring the compositions at small sizes. However, recent advances have allowed such a study. One interesting structural change at nanoscale is the formation of a solid solution between elements which at bulk scale show a miscibility gap [9–11]. The tendency towards retaining a single-phase microstructure can be due to two different effects, which must be understood precisely. They are (a) high surface curvature at smaller sizes enhancing the solid solubility through the Gibbs–Thompson effect and (b) decrease in the driving force for the nucleation and growth of second phase within a small particle. Increase in miscibility (or solid solubility) at nanoscale between elements that show tendency for phase separation at bulk scale has been reported for systems such as Ag–Pt [12], Au–Pt [13] and Pt–Ru [14]. A comprehensive theoretical and experimental analysis of various aspects of alloy formation between immiscible elements is provided in the review article by Ma [15].
1359-6454/$36.00 Ó 2011 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2011.07.022
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This paper presents an experimental and thermodynamic analysis of the tendency of Ag and Ni atoms to mix to form a solid-solution face-centered cubic (fcc) structure as a function of particle size, for nanoparticles synthesized by co-reduction of Ag and Ni metal precursors in water. It should be noted that at bulk scale, Ag–Ni system shows immiscibility in both solid and liquid phases [16]. Solid solubility of Ni in Ag is as low as 0.1 at.% even at 750 °C [17]. This high immiscibility results from the large difference in size (14%) between Ag and Ni atoms and a large positive heat of mixing (DH). For equiatomic Ag– Ni fcc solid solution, the DH value is +23 kJ mol1 [15]. Several researchers have reported both theoretical and experimental studies focused on nano-sized Ag–Ni alloys. He et al. [16] showed that sputtered Ag–Ni alloy films contain phases with compositions lying within the equilibrium (bulk) Ag–Ni miscibility gap. These phases exhibit a non-uniform, spinodal-like structure at an extremely fine scale. In another study, Zhang et al. [18] synthesized Ag–Ni nanoalloys by simultaneous reduction of Ag and Ni ions by c-irradiation. Results from their compositional analysis reveal homogeneous distribution of Ag and Ni atoms inside the as-synthesized particles 6 nm in size. Gaudry et al. [19] synthesized NiXAg100X clusters by laser-induced vaporization of rods of similar composition and subsequently condensing the vapors over a substrate under a continuous flow of helium. They reported that the clusters with compositions lying in the bulk miscibility gap region attained a core–shell structure. The core and shell were rich in Ni and Ag atoms, respectively. This kind of core–shell configuration is favorable as it minimizes the strain arising from pronounced lattice mismatch due to large difference in sizes between Ni and Ag atoms. The core–shell arrangement of atoms for Ag–Ni clusters is also confirmed by Baletto et al. [20]. They studied the growth process of 200–300 atoms Ag–Ni clusters by means of molecular dynamic simulations and concluded that a core–shell arrangement with Ni forming the core and Ag forming the shell is energetically and kinetically the most favored configuration for the Ag–Ni system. In all the studies cited above, investigators have focused primarily on analyzing the possibility of various structural arrangements such as solid solution (signifying complete miscibility) or core–shell (signifying immiscibility) which results when Ag and Ni atoms coexist in a fixed-sized nano-scale volume with overall composition lying within the bulk miscibility gap. Until now there have been no studies on the evolution of microstructure and, in particular, the composition of phases in Ag–Ni nanoparticles as a function of size. The present work investigates this issue and presents an experimental and theoretical analysis of size-dependent microstructure evolution for Ag–Ni bimetallic nanoparticles. 2. Experimental procedure To synthesize the nanoparticles, 0.54 g of nickel(II) nitrate (Ni(NO3)2), 0.5 g of silver nitrate (Ag(NO3)) and
1.36 g of polyvinyl pyrrolidone (PVP) were dissolved in 100 ml of distilled water. A separate solution containing 0.52 g of sodium borohydride (NaBH4) in 25 ml distilled water was also prepared. The precursor amounts were chosen with a target final average composition of 50 at.% Ag (or Ni). The mixture containing the metal precursors and PVP was stirred vigorously using a magnetic stirrer. Once this solution appeared clear, co-reduction of the metal precursors was facilitated by dropwise addition of the water solution of NaBH4 over a period of 10 min. Once the color of the reaction mixture turned black, stirring was stopped. The nanoparticle synthesis reaction was performed at room temperature and under ambient atmosphere. After the synthesis, the as-prepared particles were covered with PVP. The reaction byproducts that formed must be removed prior to analysis and characterization. To clean the nanoparticles, the reaction mixture was poured from the reaction flask into a beaker containing 100 ml ethanol and was left for more than 3 h. A black dispersion of particles collected at the bottom of the beaker and was then centrifuged at 5000 rpm for 10 min. The particles collected at the bottom of the centrifuge tube were then dispersed in distilled water for further analysis. Average composition of the nanoparticle dispersion was determined by the energy dispersive spectroscopy (EDS) technique and scanning electron microscopy (SEM) using a Quanta ESEM instrument operating at 20 kV. SEMEDS has a larger interaction volume, consequently yielding a larger sampling size for determining the average composition of the nanoparticle dispersion. The sample for SEMEDS analysis was prepared by drop drying the particle dispersion onto a glass plate. Transmission electron microscopy (TEM) with a 300 keV field emission FEI Tecnai F-30 was used for bright-field image acquisition and single-particle composition measurements. A highly dilute dispersion of the nanoparticle was drop dried onto a carbon-coated Au grid for the TEM-based analysis. For the size–composition correlation analysis, bright-field TEM micrographs were first captured on a gatan imaging filter (GIF) camera using the highest C2 aperture (150 lm diameter) setting and an FEI-designated spot size of 1 (biggest spot size). Bright-field micrographs were used to determine the sizes of the nanoparticles. After the acquisition of the bright-field image, the C2 aperture setting was changed to smallest (50 lm diameter) aperture size, and the beam spot size was reduced to 3 nm. With the new aperture and spot size settings, the electron beam was condensed over a nanoparticle, and the EDS signal was acquired from that particular particle. Background subtracted integrated intensity of peaks corresponding to the AgK and NiK lines in the EDS spectrum were used for the elemental quantification. To investigate the composition distribution inside a single particle, energy-filtered transmission electron microscopy (EFTEM)-based compositional mapping of a group of different sized particles was also performed using a GIF-2000 and a microscope high-tension voltage of 200 keV.
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3. Results and discussion TEM bright-field micrographs showed three different regions on the sample grid: (a) region containing isolated, nearly spherical, nanoparticles; (b) region containing isolated Ni oxide films; and (c) region with coexisting nanoparticles and Ni oxide films. A representative TEM brightfield image showing the isolated nanoparticles and the nanoparticle–Ni oxide film agglomerate is shown in Fig. 1a. The discussion henceforth only considers the structural and compositional data obtained from the isolated nanoparticles on the TEM grid. Histograms of size and composition distribution obtained from the analysis of individual isolated nanoparticles are shown in Fig. 1b and c, respectively. Mean values of size and composition of the particles (summation average of size and composition values for individual nanoparticles) were 10 nm and 25 at.% Ni respectively. SEM-EDS analysis of the nanoparticle dispersion revealed an average composition of 48 at.% Ni. The difference in Ni content between the average composition obtained from the measurements using SEM-EDS and that obtained by TEMEDS analysis can be attributed to the fact that, in the latter case only isolated nanoparticles were probed. The SEMEDS-based analysis, owing to its much greater interaction volume, considered compositional signals from both the nanoparticles and the nickel oxide film, yielding a relatively Ni-rich composition. Note that reports exist on simultaneous wide distribution of size and composition for chemically synthesized bimetallic nanoparticles [21]. However, in the present case, even though there was a simultaneous reduction of both Ag and Ni metal precursors, the nature of the distribution of size and composition among particles is distinctly different. The size distribution was observed to be significantly wide, while the composition distribution was relatively narrow (a high percentage of particles were Ag rich) as shown in Fig. 1b and c, respectively. This observation led to a speculation that the inherent immiscibility between Ag and Ni atoms might be the dominating factor controlling the co-reduction condition for the observed nature of size and composition distribution. To investigate a possible correlation between the immiscibility of the constituent elements and the observed variation in size and the corresponding compositional variability, compositions of individual nanoparticles were determined as a function of their sizes. From the size–composition correlation analysis, nanoparticles were grouped in three size ranges: (a) 3–7 nm, range 1; (b) 8–13 nm, range 2; and (c) 14–20 nm, range 3. Composition distribution histograms for particles in ranges 1, 2 and 3 are shown Fig. 2a, b and c, respectively. The average value and standard deviation of size and composition distribution for nanoparticles in each size range are presented in Table 1. The data presented in Table 1 reveal a large shift in the value of average composition from that of equiatomic to Ag-rich with the increase in size of the particles beyond 7 nm. Furthermore, from the values of the standard deviation for the
Fig. 1. (a) TEM bright-field micrograph showing two different regions on the specimen grid: a region containing isolated nearly spherical nanoparticles and a region containing nanoparticles embedded in a matrix. (b and c) Histograms for (b) size and (c) composition distribution between isolated Ag–Ni nanoparticles.
distribution of composition presented in Table 1 and the composition distribution histograms shown in Fig. 2, it is evident that the spread of composition significantly decreases with increase in size of the particles beyond the particle set included in range 1. The smaller particles (range 1) tend to possess relatively greater compositional variability compared with the larger ones (range 2 and 3). The above analysis data poses two important questions: (a) In what structural state do the atoms of Ag and Ni coexist and does it change with particle size, specifically for smaller
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Ag-rich with increase in the size of the particles beyond 7 nm. To address the above issues, high-resolution transmission electron microscopy (HRTEM)-based analysis of the nanoparticles was performed. HRTEM imaging revealed that the smaller particles (<7 nm) in the dispersion were essentially single phase. A representative HRTEM image of a 6 nm particle with lattice spacing of 0.22 nm is shown in Fig. 3a. It should be noted that the interplanar spacing of the (1 1 1) plane for pure Ni and Ag is 0.203 nm and 0.236 nm, respectively. From the relationship between lattice parameter and composition as estimated by Vegard’s law, the interplanar spacing of (1 1 1) plane corresponding to a solid solution between Ag and Ni atoms with composition 50 at.% Ag or Ni should be 0.220 nm. The observed single-phase microstructure and interplanar spacing of 0.22 nm for the representative 6 nm particle thus indicated the formation of a crystalline fcc solid solution between Ag and Ni atoms. HRTEM analysis of bigger particles (>10 nm) revealed a two-phase microstructure. A representative HRTEM image of a 15 nm particle is shown in Fig. 3b. The spacings of the planes measured from the lattice fringes revealed the identity of the two phases: (a) a phase with d spacing of 0.24 nm, which corresponds to the d spacing of (1 1 1) plane of a pure fcc Ag lattice; and (b) a phase with d spacing of 0.22 nm, which corresponds to the d spacing of (1 1 1) plane of Ag50Ni50 fcc solid solution. To further confirm the identity of different phases in Ag–Ni nanoparticles, EFTEM-based compositional mapping for a group of different sized particles was performed. Results from the EFTEM mapping experiment are shown in Fig. 4. Fig. 4a shows a bright-field TEM image of a set of nanoparticles. Fig. 4b and c shows mapping with Ni and Ag, revealing Ni-rich regions and Ag-rich regions, respectively. The sizes of the particles corresponding to numbers 1–3 in the bright-field micrograph (Fig. 4a) are 23 nm, 7 nm and 12 nm, respectively. From Fig. 4b and c, it can be seen that the particles numbered 1 and 3 contains two compositionally distinct regions. One of the regions contained both Ag and Ni atoms (the right edge of particle 1 and the upper half of particle 3). The second region, in contrast, is composed of only Ag atoms (left half of particle 1 and lower half of particle 3). In contrast, particle number 2, which has a size of 7 nm, does not show any distinctly compositionally phase separated regions. Results from the HRTEM and EFTEM analysis thus indicate that the miscibility between Ag and Ni atoms is restricted only for smaller sizes (<7 nm) and a two-phase microstructure essentially
Fig. 2. Composition distribution histograms for particles in (a) range 1 (3–7 nm), (b) range 2 (8–13 nm) and (c) range 3 (14–20 nm). About 40 individual particles were analyzed for each size range.
particles? (b) Why does the nature of composition distribution sharply change and significantly narrow down to
Table 1 Mean value and standard deviation for size and composition distribution for particles in size ranges 1, 2 and 3. Size range (nm)
Mean size (nm)
Standard deviation of size distribution
Mean composition (at.% Ni)
Standard deviation of composition distribution (at.% Ni)
3–7 8–13 14–20
6 10 15
1.1 1.5 2.1
48 17 11
26 14 9
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Fig. 3. HRTEM image of (a) 6 nm AgNi nanoparticle with a singlephase microstructure and a lattice fringes spacing of 0.223 nm and (b) 15 nm Ag–Ni nanoparticle with two-phase microstructure (the insert shows a low-magnification image of the particle). The two phases (separated by a dashed white line for ease of viewing) are (i) phase with d spacing 0.24 nm, which corresponds to the d spacing of (1 1 1) plane in a pure fcc Ag lattice, and (ii) phase with d spacing 0.22 nm, which corresponds to the d spacing of (1 1 1) plane of Ag50Ni50 fcc solid solution.
consisting of Ag on the fcc solid solution of Ag(Ni) nanoparticles develops for the bigger particles. In order to rationalize the experimental observations, a thermodynamic analysis was carried out. The analysis involved theoretically calculating the free energy of a physical mixture of Ag and Ni particles (designated Gmm) and solid solution (designated Gss) between Ag and Ni atoms for different sizes of particles. For all the particle sizes for which the Gss was less than Gmm, miscibility between Ag and Ni atoms with a resultant solid solution with fcc structure can be expected. The details are as follows. 3.1. Calculation of Gmm To calculate the Gmm, model particle geometry was chosen such that a spherical nanoparticle of diameter D contained coexisting pure Ag and Ni phase volumes with a heterophase interface. To calculate the value of Gmm as a function of particle size for a constant particle composition
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Fig. 4. Results from EFTEM compositional mapping experiment showing (a) bright-field image of nanoparticles, (b) nickel-rich regions and (c) silver-rich regions.
of Ag50Ni50, the curvature of the heterophase interface was changed with change in particle size in such a way that the atomic ratios of Ag and Ni remained 1:1. The volume fraction does not change with radius. The energy contributions to Gmm are due to: (a) the volumetric contributions from pure Ag and Ni phase volumes; (b) the interfacial energy contribution from the heterophase interface between the pure Ag and Ni regions; the interface was assumed to be a curved plane which is a frustum of another sphere with diameter D as that of the nanoparticle (since volume v is conserved); the thickness of the interface was assumed to ˚ ; and (c) the particle-size-dependent surface energy be 5 A contribution from the free surfaces of pure Ag and Ni phases volumes. It should be noted that the surface energies of the pure Ag and Ni surfaces are not constant and depend on the particle size (diameter of the model sphere). The geometry of the triple point where the mechanical equilibrium needs to be achieved was ignored in this treatment. A calculation presented below describes the approach
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adopted to calculate the size- and composition-dependent surface energies of pure and alloyed particles. Contributions to Gmm can be written mathematically as Gmm ¼ xAg GAg þ xNi GNi þ aAg S Ag cAg ðDÞ þ aNi S Ni cNi ðDÞ þ Gint ðDÞ 2
AAg ¼ 2pðD=2Þ ð1 cos hÞ; ANi ¼ A AAg aAg ¼
DV V Ag
ð1Þ ð2Þ ð3Þ
where xAg and xNi are the mole fractions of Ag and Ni, respectively; GAg and GNi are the molar free energies of pure Ag and Ni; AAg and ANi are the surface area of the pure Ag and pure Ni phase, respectively; A is the total surface area of the model sphere; aAg and aNi are the fractions of surface atoms Ag and Ni vs the total number of atoms in the bulk, respectively; SAg and SNi are the surface areas occupied by 1 mole of atoms Ag and Ni, respectively; cAg(D) and cNi are the size-dependent specific surface energies (surface energy per unit area) of pure Ag and Ni spherical surfaces (calculated in the following section and compared with the bulk c values [22]); D is the diameter of the particle (the model sphere); and Gint is the Gibbs free energy contribution from the interface between the pure Ag and Ni forming the model sphere. Numerical values for GAg and GNi were taken as 12.72 kJ mol1 [23] and 8.91 kJ mol1 [23], respectively. Numerical values for SAg and SNi were 4.35 104 m2 and 3.24 104 m2 respectively. As described by Turnbull [24], Gint has contributions from the geometrical (cgeo) and chemical factors (cche). Mathematically, Gint [25] can be written as Gint ¼ Sðcgeo þ cche Þ
ð4Þ
where cgeo ¼ ½0:33ðcAg ðDÞ þ cNi ðDÞÞ=2 cche ¼ fxAg DH AginNi =½C o ðV Ag Þ
2=3 þ
xNi DH NiinAg =½C o ðV Ni Þ
ð5Þ 2=3
g
ð6Þ where S is the surface area occupied by one mole of the interfacial atoms; DHAginNi (or DHNiinAg) is the heat of solution of Ag in Ni (or Ni in Ag) at infinite dilution; VAg and VNi are the molar volumes of Ag and Ni, respectively; and Co is a constant being 4.5 108. The multiplication factor of 0.33 in Eq. (3) is based on the assumption that the grain boundary energy is 30% of the surface energy at 0 K [26]. Details about the approach used for calculating the cche value (Eq. (4)) were provided by Miedema [22,27]. Numerical values for cAg(D) and cNi(D) were calculated from cohesive energy, and this is explained in the following section. Numerical values [26] for DHAginNi and DHNiinAg were taken as 68 kJ mol1 and 56 kJ mol1, respectively.
butions due to pure Ag and Ni, (b) excess free energy due to mixing and (c) size-dependent surface energy of the nanoparticle with solid solution fcc structure. Mathematically, Gss ¼ xAg GAg þ xNi GNi þ DGmix þ ð2css ðDÞV AgNi Þ=ðD=2Þ
ð7Þ
where xAg and xNi are the atomic fractions of Ag and Ni, respectively; GAg and GNi are the molar free energies of pure Ag and Ni, respectively; DGmix is the excess free energy of the alloy phase due to mixing; css(D) is the sizedependent specific surface energy (surface energy per unit area) of the nanoparticle with solid solution between Ag and Ni atoms; VAg–Ni is the molar volume of fcc AgNi solid solution; and D is the diameter of the particle. The free energy of an alloy phase due to mixing (DGmix) is given by DGmix ¼ DH mix T DS mix
ð8Þ
where DHmix and DSmix are the enthalpy and entropy of mixing, respectively. The entropy term for the solid solution was taken as that of an ideal solid solution given by DS mix ¼ R½xAg ln xAg þ xNi ln xNi
ð9Þ
where xAg and xNi are the atomic fraction of Ag and Ni, respectively, and R is the gas constant. According to the well-known Miedema model, the enthalpy of mixing (DHmix) can be expressed as a sum of chemical, elastic and structural contributions. A detailed description of the three components and the mathematical formula to calculate the numerical values corresponding to their energy contribution can be found in Refs. [28,29]. One important limitation to the application of Eq. (5) to calculate Gss is the absence of experimentally or theoretically determined size-dependent surface energy per unit area (css(D)) values for the solid solution Ag–Ni alloy in the literature. The methodology and the equations used to calculate the css(D) values are described below. To calculate css(D), a two-step approach was adopted. First, the particle-sizedependent cohesive energy of nanoparticles containing different atomic fractions of Ag and Ni atoms was calculated. Secondly, using the cohesive energy values obtained in the first step, the size- and composition-dependent surface energy of fcc metallic Ag–Ni nanoparticles was obtained. The details about the approach employed to derive the mathematical formula that yields the size- and composition-dependent cohesive energy (Ec(D)) values for alloyed nanoparticles was provided by Qi [30]. The mathematical formula for the calculation of Ec(D) is given as ! ! aD2 aD2 Ec ðDÞ ¼ xAg EAg 1 2 þ xNi ENi 1 2 xAg xNi X nd Ag nd Ni ð10Þ
3.2. Calculation of Gss
n ¼ fD3 =ðxAg d 3Ag þ xNi d 3Ni Þ
To calculate the Gss, the following approach was used. Energy contributions to Gss are from (a) volumetric contri-
where xAg and xNi are the molar fraction of Ag and Ni, respectively; EAg and ENi are the bulk cohesive energies
ð11Þ
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of Ag and Ni, respectively; a is the shape factor (defined as the surface area ratio of non-spherical and spherical nanoparticle of identical volumes); dAg and dNi are the atomic diameters of Ag and Ni, respectively; X is the interaction parameter with a value of 60 kJ mol1 (for Ag–Ni); and f is the packing factor (f = 0.74 for fcc structure). Numerical values for EAg and ENi are 283 kJ mol1 [22] and 428 kJ mol1 [22], respectively. Numerical values [31] for dAg ˚ and 2.49 A ˚ , respectively. It should be and dNi are 2.88 A noted that the mathematical formula for calculating the cohesive energy as provided by Qi [30] does not take into account the heat of mixing of component atoms, and terminates only after the first two terms on the rhs of Eq. (10). An extra term (third term after the minus sign) was added on the rhs of Eq. (10) which adds the energy contribution due to the heat of mixing of atoms of component elements. The approach adopted to calculate the size-dependent surface energy of solid solution nanoparticles was provided by Liu and Jiang [32]. Mathematical formula for the sizedependent specific surface energy (Es(D)) for a particle with a truncated octahedral (TC) geometry and size DTC (defined as the distance between two opposite fcc (1 1 1) planes in a TC geometry) is given as Es ðDÞ ¼ f2 ½Z s ðDÞ=Z b ½Z s ðDÞ=Z b
1=2
gEci ðDÞ=2
ð12Þ
where Eci ðDÞ ¼ Ec ðDÞ=f1 pðDÞf2 ½Z s ðDÞ=Z b ½Z s ðDÞ=Z b
1=2
g=2g
ð13Þ
where pðDÞ ¼ N s ðDÞ=N tot ðDÞ
ð14Þ
where Zs(D) is the size-dependent (DTC dependent) average surface coordination number, Zb is the average coordination of the internal atoms, and Ns(D) and Ntot(D) are the total number of atoms present on the surface and inside a particle of size DTC, respectively. The relation between css(D) (Eq. (7)) and Es(D) (Eq. (12)) is given as css ðDÞ ¼ N i Ec ðDÞ=paN A D2
ð15Þ
where Ni is the number of atoms on the surface of a particle of diameter D with fcc solid solution structure (the formulation for calculating the number of atoms on the surface of a particle of certain size is provided by Qi [33]), a is the shape factor (a = 1.24 for TC geometry), and NA is Avogadro’s number. css values for a number of pure fcc metal nanoparticles were calculated as a function of their sizes. It was observed that, for a particle size of 100 nm (which with respect to size can be approximated as bulk like), the calculated css(D = 100 nm) values were in close agreement with the reported bulk specific surface energy values for several pure fcc elements. This comparison for 10 fcc elements is provided in Table 2. Furthermore, few redundant observations were made when the css(D) values for several pure fcc metals were plotted for different particle sizes. A representative plot of this type for pure Au is
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Table 2 Comparison between calculated and bulk surface energy values for fcc elements. Element
Calculated surface energy (css(D)) for D = 100 nm (J m2)
Bulk surface energy (J m2)
Reference
Ag Ni Au Cu Pt Al Pb Sr Ir Rh
1.16 2.35 1.51 1.75 2.51 1.36 0.54 0.33 3.10 2.6
1.25 2.45 1.55 1.85 2.55 1.20 0.61 0.43 3.10 2.75
[22]
shown in Fig. 5a. These observations, as evident from the plot in Fig. 5a, are that (a) the css(D) increases as the size of the particle decreases and (b) the decrease in the value of css(D) with increasing particle size is relatively steeper for sizes <10 nm than for sizes >10 nm. These two observations suggest that the excess energy contribution from the surface is profound for smaller particle sizes (<10 nm) and the contribution substantially decreases with increase in particle sizes beyond 10 nm. Larger particles (>20 nm) show almost bulk-like behavior with respect to the surface energy. Using Eqs. (8)–(13), the css(D) values as a function of particle size and composition for solid solution fcc AgXNi(100X) nanoparticles were determined and are shown as a three-dimensional plot in Fig. 5b. It is evident from the Fig. 5b that the surface energy of fcc solid solution Ag–Ni nanoparticles decreases with decrease in the Ni content and increase in the size of the alloyed particles. The values for css(D) obtained from this graph were employed to calculate the Gss for different sizes and compositions of AgXNi(100X) nanoparticles using Eq. (7). Comparison between particle-size-dependent free energies of the physical mixture (Gmm) and the solid solution (Gss) between Ag and Ni atoms, as shown in Fig. 6, also validates the conclusions from the experimental observations. For a fixed overall composition of Ag50Ni50, the Gss values were less than the Gmm values for particle sizes up to 7 nm, indicating the energetic preference for the formation of solid solution over physical mixture below this size limit. Beyond the particle size of 7 nm, the free energy values and the corresponding lower energy preferred configuration flipped from solid solution to physical mixture. The experimental and theoretical results thus lead to the following possible mechanism, which produces the observed size-dependent microstructure for Ag–Ni nanoparticles. During the initial stages of the synthesis reaction, Ag and Ni atoms reduce and form small (<7 nm) AgNi solid solution clusters. As the synthesis progresses, the excess Ag atoms that are produced by the reduction of Ag precursor then grow over the exiting solid solution fcc nanoparticles, forming a two-phase microstructure for the bigger particles. Unlike Ag atoms, the excess Ni atoms that
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did not participate in the formation of small fcc Ag–Ni nanoparticles formed the Ni-oxide film. 4. Conclusion In the present work, Ag–Ni nanoparticles were synthesized by co-reduction of silver nitrate and nickel nitrate salts in water medium. Analysis on a single particle level revealed an opposite nature of size and composition distribution between nanoparticles. Size distribution was wide, but the composition distribution was fairly narrow. Size– composition correlation analysis showed that the bigger particles in the dispersion were primarily Ag rich, whereas the smaller particles (67 nm) had compositions lying in the broad range of 10–90 at.% Ag. Through thermodynamic calculations, a particle size limit was determined, below which enhanced miscibility leading to the formation of solid solution between Ag and Ni atoms is energetically favorable over a physical mixture configuration. The particle size limit determined was 7 nm. In accordance with the theoretical results, HRTEM- and EFTEM-based analysis of individual nanoparticles revealed that the smaller particles (67 nm) in the dispersion were single phased, with a solid solution Ag–Ni fcc structure, whereas particles with sizes beyond the theoretically determined size limit for miscibility were composed of two different phases, which were pure Ag phase and Ag–Ni fcc solid solution phase. The two-phase microstructure for larger particles was thus primarily due to the growth of Ag-rich regions on initially formed small fcc Ag–Ni nanoparticles. Fig. 5. (a) Plot of change in surface energy per unit area (css(D)) with particle size for pure Au and (b) plot of change in css(D) values as a function of particle size and composition for solid solution fcc AgXNi(100X) nanoparticles.
Acknowledgements One of the author (C.S.) would like to acknowledge the Centenary Post-Doctoral fellowship scheme of the Indian Institute of Science, Bangalore, India. One of the author (S.K. Sinha) would like to acknowledge the fellowship from CSIR, India. All the authors would like to acknowledge the microscopy facilities available at Advanced Centre for Microscopy and Microanalysis, Indian Institute of Science, Bangalore, India. Professor Srikanth Lele is thanked for discussions and for his suggestions that were incorporated in the thermodynamic calculations. References
Fig. 6. Comparison between theoretically calculated, particle-size-dependent free energies of physical mixture (Gmm) and solid solution (Gss) configuration between Ag and Ni atoms. The Gss values were less than the Gmm values for particle sizes up to 7 nm, indicating the energetic preference for the formation of solid solution over physical mixture below this size limit. Beyond the particle size of 7 nm, the free energy values and the corresponding lower energy preferred configuration flipped.
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