Letter pubs.acs.org/NanoLett
Synthesis and Modeling of Hollow Intermetallic Ni−Zn Nanoparticles Formed by the Kirkendall Effect Subhra Jana, Ji Woong Chang, and Robert M. Rioux* Department of Chemical Engineering, Pennsylvania State University, University Park, Pennsylvania 16802, United States S Supporting Information *
ABSTRACT: Intermetallic Ni−Zn nanoparticles (NPs) were synthesized via the chemical conversion of nickel NPs using a zerovalent organometallic zinc precursor. After the injection of a diethylzinc solution, Ni NPs progressively transformed from a solid to a hollow Ni−Zn intermetallic structure with time. During the transformation of Ni NPs to intermetallic structures, they retained their overall spherical morphology. The growth mechanism for the solid-to-hollow nanoparticle transformation is ascribed to the nanoscale Kirkendall effect due to unequal diffusion rates of Ni and Zn. We develop a diffusion model for nonreactive, homogeneous, diffusioncontrolled intermetallic hollow NP formation including moving boundaries at the interfaces of void−solid and solid−bulk solutions. Apparent diffusion coefficients for both metals and vacancy were evaluated from modeling the time-dependent growth of the void. The apparent diffusion coefficients obtained in this system compared favorably with results from measurement at grain boundaries in bulk Ni−Zn. This study represents the first combined experimental modeling of the formation of hollow nanostructures by the nanoscale Kirkendall effect. KEYWORDS: Intermetallic, Ni−Zn, Kirkendall effect, hollow nanoparticle, diffusion, moving boundary model
T
Inorganic hollow nanostructures have attracted considerable interest compared to their solid counterparts due to enhanced structural features (e.g., lower densities and a higher surface-tovolume ratio) and potential utilization in a number of diverse applications.18,19 The reduction of the amount of materials decreases their poisoning effect for in vivo applications.18,20 The large fraction of void space in hollow structure endows them with the ability to encapsulate materials such as drugs and biological molecules in their interior cavity for targeted delivery applications. Their properties make them potentially suitable materials for catalysis,21,22 sensing,23 drug delivery,20,23 and energy storage application.24 A variety of chemical methods have been employed to synthesize inorganic hollow NPs, for example, emulsion/ interfacial polymerization methods,25,26 self-assembly techniques,27 heterophase polymerization/combined with sol−gel processing,28 and surface living polymerization reactions.29,30 The sacrificial template method (e.g., SiO2,31−33 C spheres,34 polymers,35,36 vesicles37,38) is the most commonly used. In metal template-based methods, the metal itself acts as a reactant in the synthetic route.39 Generally, two operable mechanisms have been proposed to explain the formation of hollow nanostructures: Kirkendall effect and galvanic displacement.40,41 Galvanic displacement involves a replacement
his Letter describes the synthesis and modeling of the formation of voids in nanostructured Ni−Zn intermetallic nanoparticles (NPs) and provides estimates of diffusivity for both metals and vacancies that are in good agreement with bulk diffusivity measurements at defects. Alloys and intermetallic compounds are of great interest for their catalytic, magnetic, optical, and magneto-optical properties.1,2 Intermetallic compounds are atomically ordered alloys which have well-defined compositions and crystal structures that differ from their constituent elements.3,4 Their properties depend not only on their composition but also their size and geometric structure. Bulk intermetallic compounds are fabricated using hightemperature techniques which include powder metallurgy, arc melting, and induction heating where long annealing times are required to overcome the low atomic mobility present during solid−solid diffusion5 and grinding steps are necessary for powder preparation. The preparation of intermetallics at milder temperature is accomplished using solvothermal techniques,6 electrodeposition,7 molten-flux synthesis,4 high-energy ball milling,8−10 chemical vapor deposition,11,12 and gas-phase condensation routes.13 Low-temperature solution-phase synthesis represents one of the most attractive strategies and has been utilized to produce bulk and nanoscale intermetallics, including a number of new metastable phases.14−17 Access to methods that enable the production of nanoscale intermetallics broadens their potential applications due to enhanced or unique properties typically observed at the nanometer dimensions. © 2013 American Chemical Society
Received: April 23, 2013 Revised: June 24, 2013 Published: July 5, 2013 3618
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reaction between a lower electrode potential metal template and a metal salt precursor containing a metal with a relatively higher electrode potential, whereas the Kirkendall effect arises due to unequal diffusion rates of the atoms across a boundary of two materials under thermally activated conditions. The Kirkendall effect was first observed in a bulk diffusion couple between Cu and Zn to form brass.40 The nanoscale Kirkendall effect was first proposed by Yin et al. to explain the formation of hollow NPs of cobalt oxide and chalcogenides through the reaction of colloidal Co with oxygen, sulfur, and selenium.19 Following similar strategies, inorganic hollow NPs such as CoSe,42 ZnO,43,44 magnetic iron oxide,45 and transition metal phosphides46,47 have been synthesized. A Kirkendall effect in a thin-film geometry for a post transition metal−transition metal48 has also been reported. Though researchers have reported the formation of d−d hollow nanostructures by a galvanic displacement reaction,49,50 we could find no report on the synthesis of hollow d−d intermetallic NPs via a Kirkendall effect. Mathematical models for component diffusion, vacancy production, and the formation of the void, coalescence of vacancies, have been developed for heterogeneous (consisting of two or more phases) alloys.51−53 For homogeneous (consisting of a single phase) alloys, a model for vacancy production has been developed in the fixed boundary system.54 Models for metal−metal oxide systems incorporating growing boundaries have been described.55−57 A model for metal−metal interdiffusion with a growing boundary and the formation of Kirkendall void has not been reported to date. We report a synthetic procedure for the production of intermetallic Ni−Zn NPs using a solution-mediated reaction route with transition metal salts. With commercially available reagents, Ni NPs are synthesized in a hot organoamine solvent followed by the injection of diethylzinc (DEZ). Spherical hollow Ni−Zn intermetallic NPs have been synthesized through a nanoscale Kirkendall effect. We formulate a diffusion model of metals and vacancies based entirely on experimental observation for the time-dependent formation of hollow NPs based on Fick’s laws and evaluate the diffusivity of Ni, Zn, and vacancy in the NPs. The diffusivities of the metals and vacancies are evaluated under the synthesis conditions by fitting the temporal evolution of the void size. Results and Discussion. Characterization of the NPs. Transmission electron microscopy (TEM) images for the Ni and corresponding Ni−Zn NPs are presented in Figure 1. A TEM micrograph of Ni NPs isolated from the reaction mixture immediately before the addition of DEZ is shown in Figure 1A. Ni NPs exhibit nearly monodisperse spherical morphology with an average particle size of 10 ± 0.5 nm. Solid Ni−Zn NPs (Figure 1B) were observed 10 min after the injection of DEZ to the reaction mixture containing Ni NPs at 250 °C. The crystal structure of the samples was measured using powder X-ray diffraction (XRD; inserts in Figure 1A and B). The XRD patterns of the as-synthesized Ni NPs indicate facecentered cubic (fcc) Ni. The characteristic peaks observed in the XRD pattern correspond to the (111), (200), and (220) crystal planes of fcc Ni (PDF No. 01-089-7128). No diffraction peaks attributed to other phases (e.g., nickel oxides) were observed in these XRD patterns, demonstrating the NPs consist of a pure fcc phase. From the corresponding XRD patterns and TEM images, we have seen that Ni−Zn contains a ZnO impurity. Simulated XRD patterns of ZnO, α-Ni−Zn, and βNi−Zn are compiled in Figure S1. This is in accordance with
Figure 1. TEM micrographs of (A) 10 nm Ni and corresponding (B) Ni−Zn NPs. The scale bar is 50 nm. The inset is the XRD pattern for NP type.
the earlier observation by the Schaak group for M−Zn synthesis even under rigorously air-free conditions.58 Since our synthesis was conducted under air-free conditions, we believe the source of oxygen is most likely the acetylacetonate ligands associated with the Ni(II) complex. Effect of Reaction Temperature. Reaction temperature is a critical parameter with respect to the formation and growth of Ni−Zn nanostructures (both solid and hollow). First, we synthesized Ni NPs at 220 °C, followed by the injection of a DEZ-oleylamine solution to the reaction mixture under an argon atmosphere at 250 °C. If the reaction temperature during the injection of DEZ was higher than 250 °C, nickel phosphide formed. This observation is consistent with previous results from Schaak and co-workers.59 On the contrary, if the injection temperature is too low (220−240 °C), no reaction between Ni NPs and DEZ occurred. Therefore, 250 °C is the threshold temperature for this particular reaction to acquire Ni−Zn NPs. A very narrow operating window to form hollow Ni−Zn NPs exists for this system based on the chosen solvents. The influence of DEZ concentration on the formation of hollow Ni−Zn NPs at 250 °C has been described in the Supporting Information (Figure S2). Time Dependence of Particle and Void Formation. The growth of the nanostructures was measured ex situ by analyzing aliquots removed at increasing time increments following the injection of DEZ. We have studied the growth and the change in morphology of the nanostructures with TEM. Figure 2 represents the nanostructures obtained at 5, 10, and 30 min 3619
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Figure 2. TEM images of Ni−Zn NPs obtained from 10 nm Ni NPs (A) 5, (B) 10, and (C) 30 min after the injection of 1.0 mmol DEZ and (D) their corresponding XRD patterns. The scale bar represents 50 nm.
the morphology of the intermetallic M−Zn compounds (where M = metal) can be templated by the morphology of monometallic NPs.58,64 The present synthesis involved a twostep procedure: the formation of transition metal NPs by thermolysis of Ni precursors followed by transformation into Ni−Zn intermetallics due to the reaction with DEZ in a hot organoamine solvent. After the injection of DEZ, Zn(0) atoms diffuse to the solvated Ni NP surface and form intermetallic Ni−Zn compounds. The formation of void in the center of the particle can be described by the Kirkendall effect. In our reaction system, we eliminate the possibility of galvanic displacement because Ni does not have a counteranion in solution to stabilize Ni2+ species that would form as a result of galvanic replacement. Additionally, the overall electrode potential of reaction (Ni(0) + Zn2+ → Ni2+ + Zn(0)) is negative (standard electrode potential for Ni2+/Ni0 and Zn2+/Zn0 is −0.25 and −0.76 eV, respectively). Therefore, void formation is not a result of galvanic displacement. We believe void formation in the center of the particle was induced by a nanoscale Kirkendall effect, similar to that observed by Yin et al.19 The void in the center of the particles is observed by ex situ TEM from samples removed from the flask ∼10 min after the injection of DEZ. Approximately 30 min after the injection of DEZ, the size of the void in the center of the particles does not change. Diffusion Model for Intermetallic Hollow NPs Formation with Moving Boundaries. We have established a rigorous model considering the formation of solid as well as hollow Ni− Zn NPs and evaluated the diffusivities of both metals and the vacancy in the hollow particles formed by the Kirkendall effect. The Ni−Zn NPs were synthesized from Ni NPs (particle size ∼10 nm), followed by the injection of DEZ (1 mM) at 250 °C.
after the injection of the DEZ solution into the reaction mixture containing 10 nm Ni NPs. Five minutes after the injection, only solid Ni−Zn NPs exist in the reaction mixture (Figure 2A). After 10 min, we observed continual evolution of the solid Ni− Zn NPs (Figure 2B), and by 30 min after the DEZ injection, hollow Ni−Zn NPs formed (Figure 2C). XRD analysis confirmed that the solid Ni−Zn NPs retain their structure when transforming to hollow Ni−Zn NPs with time (Figure 2D). The composition of Zn lies to the right beside the phase boundary of α-phase and a mixture of α- and β-phases.60−62 This indicates that the Ni−Zn NPs consist of a majority of αphase and a small amount of β-phase. Since ZnO was observed as a byproduct, the majority of the particles will be α-phase, but we have found β-phase particles in the product. The HR-TEM images of well-ordered β-phase Ni−Zn NPs show lattice fringes in both the solid (Supporting Information, Figure S3A) and hollow (Supporting Information, Figure S3B) Ni−Zn NPs, whereas the dominant α-phase of the NPs has a disordered structure. The atomic planes exhibit an atomic separation of 0.196 nm corresponding to the (110) face of tetragonal Ni−Zn whose zone axis is [001̅]. The EDX patterns of the solid as well as hollow Ni−Zn NPs (Supporting Information, Figure S4) confirm the presence of both Ni and Zn in the particles. A histogram for the overall and void size of hollow Ni−Zn NPs 45 min after the injection of DEZ has been provided in the Supporting Information (Figure S5). Mechanism of Particle Formation. Zero-valent organometallic precursors and long-chain organoamine solvents are widely used for the synthesis of monometallic NPs with controlled particle morphology.63 However, the control of morphology in multimetallic systems is more challenging than the monometallic counterpart. Utilizing a two-step procedure, 3620
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To measure the time-dependent growth of Ni−Zn NPs and corresponding voids, 15 aliquots were taken at various stages during the NP synthesis. The interdiffusion of a bimetallic NP consisting of a core of Ni with a growing (nonfixed boundaries) Zn shell structure was considered as the basis for model development and numerical evaluation of the solution. The colloidal synthesis of the hollow NP alloy involves the addition of DEZ solution to the initial NP solution. Due to the growth of both the inner phase (i.e., void) and the solid phase in spherical coordinates, a numerical solution with moving boundaries (solid−void and solid−bulk solution interfaces) rather than fixed boundaries is required. In the model, only Ni initially exists, but as the Zn shell grows, Zn diffuses into the Ni core. During the interdiffusion, the vacancies generated by the difference in mobility of the main components (Ni and Zn) move inward due to the faster outward flux of nickel. In this case, the void formed due to the Kirkendall effect arises in the middle of the NP. Analysis of the TEM images demonstrated the Ni−Zn NPs possessed singular voids only. Therefore, multiple void evolution65 is not considered in our model. We assume that the partial molar volume of species i is constant and that the isothermal compressibility is zero.56 The molar volume of the mixture, Vm, becomes
Vm =
∑ xiVi i
Figure 3. PDF of hollow Ni−Zn NPs and RMC fit of Ni−Zn NP assuming a perfect fcc lattice. The peak locations for perfect fcc Ni are marked (▼).
Scheme 1. Geometry of the Hollow NPs and the Corresponding Concentration Profiles
(1)
where xi is the mole fraction of species i and Vi is partial molar volume of i. We also introduce the concentration, Ci, measured in moles per unit volume of mixture. The total concentration is defined as
C=
∑ xiCi i
(2)
where Ci = xiC. It is clear from their respective definitions that C = 1/Vm. The equilibrium vacancy concentration is neglected by using an excess of vacancies, CV (i.e., vacancy supersaturation). Thus, CV = CVT −CVE, where CVT is the total concentration of vacancies and CVE is the equilibrium concentration of vacancies. The dependence of the physical properties on the temperature and pressure, such as the thermal expansion of Ni and Zn and the vacancy equilibrium concentration, are ignored since the synthesis of intermetallic Ni−Zn NPs is conducted under isothermal and isobaric conditions. The pair distribution function (PDF) analysis by a reverse Monte Carlo (RMC) simulation of high-energy X-ray diffraction data by fitting calculated PDFs to the experimental PDF via random adjustment of atomic position distribution66 demonstrates the hollow NPs are α-phase with an average disorder of 0.60 ± 0.31 Å. The disorder is defined as the average position difference between fcc Ni atoms and Ni atoms calculated by RMC (Figure 3). Therefore, we model the NPs as a homogeneous alloy since the α-phase is dominant. The structure of the system is depicted in Scheme 1. The system is described by the radius of the void, RV, initial radius R0, and outer radius of the hollow NP, R. The radius of the void and the outer radius of the NP vary as a function of time. The void size is constrained by the generation of vacancies, and the outer radius is constrained by the growth rate of Zn. The growing boundary is expressed as the following.
4π 4π 3 4π R(t )3 = R0 + R V(t )3 + VG(t ) 3 3 3
(3)
where VG(t) is the volume of the growing Zn shell on the NP. The growth kinetics of Zn on the surface of NPs depends on the rate of DEZ decomposition, diffusion of Zn from the bulk solution to the NP surface, and the rate of the surface reaction for Zn adatom formation. For simplicity, we assume the growth kinetics of the Zn shell obeys first-order kinetics, that is; −
s dCZn (t ) s = kCZn dt
(4)
where CsZn is the concentration of Zn in the bulk solution and k is the rate constant for the growth process. The rate of volume increase due to the growth of Zn is expressed by the rate of Zn consumption in the solution. 3621
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Nano Letters s ∂VG(t ) d C s (t ) V s s V = − Zn VZn = kCZn VZn ∂t dt n n
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Scheme 2. Scheme of the Apparent Vacancy Flux Based on the Gradient of Vacancy Supersaturationa
(5)
where Vs is the volume of the solution and n is the number of NPs in the solution. In our analysis of interdiffusion during the formation of hollow NPs, we assume the following: (1) particles are spherical, (2) an intermetallic particle is an ideal solid solution and a homogeneous alloy according to the phase diagram and the PDF analysis, (3) supersaturation vacancy, Cv is generated only by the Kirkendall effect, (4) gradients in the vacancy supersaturation concentration is the only contribution to flux that leads to the formation of Kirkendall voids, (5) a single void forms at the center of NP for the convenience of modeling (no multiple voids and no random locations), (6) a void forms when the flux of vacancies is high enough to form an irreversible size of void (i.e., larger than single atomic volume), (7) vacancies accumulate at the center of the body before a void forms, and (8) void shrinkage is ignored since it is a much slower process compared to the process of formation.67 For the analysis, we describe the system in spherical coordinates with no angular dependence and formulate the problem in terms of concentrations of Ni, Zn, and vacancies. From the conservation of lattice sites68 and the ideal solid solution assumption of two metals of different atomic volumes, the convective flow is the sum of the volume fluxes,53 so that the molar average velocity, v, is v = VNiJNi + VZnJZn + Vm JV = 0
a
by simultaneous outward diffusion of atoms because the main components diffuse out more easily by exchanging with vacant sites when compared to diffusion through packed atoms.69 Therefore, two different partial differential equations (PDEs) are used depending on the sign of the gradient of the vacancy supersaturation. Vacancy diffusion is allowed when the gradient of the vacancy concentration is positive so that vacancies move isotropically to the center of the NP (eq 9a). In eq 9b, the vacancy concentration increases as much as the total number of vacancies generated because there is no vacancy flux (i.e., slope of the gradient of the vacancy concentration is negative).
(6)
where JNi, JZn, and JV are the molar fluxes of Ni, Zn, and the vacancy, respectively. Accounting for mass diffusion without convective flow leads to ∂Ci(r , t ) ∂C (r , t ) ⎞ 1⎛∂ = 2 ⎜ r 2Di i ⎟ ∂t ∂r ⎠ r ⎝ ∂r
Refer to Scheme 1 for a description of the radial dimension.
(7)
∂C VG(r , t ) ∂C V(r , t ) ∂C (r , t ) ⎞ 1⎛∂ = 2 ⎜ r 2D V V ⎟+ ⎠ ∂t ∂r ∂t r ⎝ ∂r
where Di is the apparent diffusion coefficient of the main components, t is time, and r is the radial coordinate. The generation rate of the vacancy concentration can be obtained by the conservation of lattice sites, which is the sum of the rate of outward diffusion of Ni and the rate of inward diffusion of Zn, that is,
(9a)
subject to ∂C V(r , t ) >0 ∂r
⎛ ∂C (r , t ) ∂VmC VG(r , t ) ∂C (r , t ) ⎞ = −⎜VNi Ni − VZn Zn ⎟ ⎠ ⎝ ∂t ∂t ∂t
∂C VG(r , t ) ∂C V(r , t ) = ∂t ∂t
(8)
where CVG is the vacancy concentration generated by diffusion of the main components (Ni and Zn). The left-hand side in eq 8 is the rate of change of concentration of vacancies; the first term on the right-hand side is the rate of change of concentration of Ni, and the second term is the rate of change of concentration of Zn. The difference in diffusion rates between the metals leads to vacancy generation in the NP, and the faster outward diffusion rate of Ni causes the vacancies to diffuse inward. Therefore, there is no vacancy flux outward during the diffusion of Ni and Zn. Scheme 2 is a schematic of diffusion of vacancy supersaturation depending on the sign of the gradient of the vacancy supersaturation without consideration of vacancy generation. If the sign is positive, the excess vacancies diffuse into the center of NPs because the direction of the flux of excess vacancy is opposite to the direction of the flux of atoms. Otherwise, outward diffusion of vacancies is hindered
(9b)
subject to ∂C V(r , t ) ≤0 ∂r
Initial and boundary conditions are given below in order to solve the PDEs (eqs 6−9). The initial geometry is a solid Ni particle with zero void volume, no vacancy supersaturation in the body of the solid, and no Zn growth at t = 0. The moving boundary conditions are applied during particle growth and void formation. At r = R(t), there is no flux of Ni or vacancy from the bulk solution inward toward the center of the nanoparticle by using eqs 3−5 for the addition of Zn to NPs, and there is no flux of any species from the NPs outward toward the bulk solution. Therefore, the boundary conditions at r = R(t) become 3622
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= r=R
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∂CZn ∂r
= r=R
∂C V ∂r
references above varies from 5 h to 200 days, which is longer than the nanoscale diffusion observed here (
