J. Phys. Chem. C 2008, 112, 2079-2085
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Strain Analysis of AuxCu1-x-Cu2O Biphase Nanoparticles with Heteroepitaxial Interface Kenji Koga*,† and David Zubia‡ Nanotechnology Research Institute, National Institute of AdVanced Industrial Science and Technology (AIST), 1-1-1 Higashi, Tsukuba, Ibaraki 305-8565, Japan, and Department of Electrical and Computer Engineering, UniVersity of Texas at El Paso, El Paso, Texas 79968 ReceiVed: September 13, 2007; In Final Form: NoVember 12, 2007
Epitaxially coherent AuxCu1-x-Cu2O biphase nanoparticles (x ) 0.83) were grown in free space by oxidizing AuyCu1-y alloy nanoparticles (y ) 0.46) above their melting temperature. Electron-microscopic studies revealed that Au0.83Cu0.17 and Cu2O dome-shape nanocrystals are conjunct via a (110) heteroepitaxial interface with no crystallographic rotation to form a prolate-spheroid shape. It was observed that the misfit strain from 6.5% lattice mismatch is taken up by locally deforming both Cu2O and Au0.83Cu0.17 near the interface. The observed strain profiles were reproduced quantitatively using continuum theory modified with a semiempirical fitting parameter.
1. Introduction It is anticipated that multiphase nanoparticles will play increasingly important roles as building blocks for electronic devices with enhanced or novel functionalities.1-7 Moreover, multiphase nanoparticles are of great importance for precise morphological control of industrial materials such as heterogeneous catalysts, sensors, gas separators, and also for biological applications.8 Multistep solution-mediated synthesis is usually employed to create multiphase nanoparticles, for example, biphase AuFe3O4 nanoparticles9,10 with several different morphologies such as core/shell, peanut-like, and dumbbell-like. In solution-phase processing, one can control the timing of nucleation and growth for each component under relatively lower temperatures, which enables a variety of metastable forms to be produced. However, in order to have wide applicability, each metastable form should have a high degree of morphological and interfacial stability. In this paper, we report on the production of biphase nanoparticles by the gas-phase method involving high-temperature processing, which likely yields thermodynamically stable morphologies and interfaces. In particular, we investigate the oxidation of binary Au-Cu alloy nanoparticles and report on their epitaxial structure. Oxidation and corrosion processes of binary alloys are complicated in comparison with single-element cases.11,12 When a binary alloy M-A, composed of relatively unreactive M and reactive A constituents, is exposed to an oxidizing environment, the A atoms are selectively oxidized leaving an M-rich phase adjacent to an oxidized-A phase. An extreme case is that the M component is a noble metal. Recently, the oxidation behavior of Au0.5Cu0.5 alloy thin films at high temperatures were observed by means of transmission electron microscopy (TEM).13,14 According to their results, the oxide (Cu2O) islands grow heteroepitaxially forming a Au-rich zone. It is, therefore, very interesting to investigate whether high-temperature oxidation of Au-Cu nanoparticles in the gas phase yields Au-Cu2O * Corresponding author. E-mail:
[email protected]. † National Institute of Advanced Industrial Science and Technology (AIST). ‡ University of Texas at El Paso.
biphase nanoparticles with core/shell or asymmetrically separated morphologies. In this work, we pay close attention to the oxidation behavior of the Au-Cu nanoparticles. 2. Experimental Section A schematic diagram of the apparatus used to produce and oxidize the Au-Cu nanoparticles is shown in Figure 1. The apparatus is composed of three major parts; a source chamber, heat bath, and deposition chamber. Au-Cu nanoparticles are produced by the inert-gas-aggregation (IGA) method in the source chamber and are then transported with a helium stream through the heat bath and into the deposition chamber. In the heat bath, the particles are heated (melted) to 1373 K and oxidized with gaseous oxygen. The oxidized particles are then cooled to room temperature at the bath exit and deposited onto an amorphous carbon film (carbon microgrid). The gas velocity in the heat bath can be regulated by adjusting a valve between the deposition chamber and vacuum pump. The apparatus has been used for the annealing and melting of gold nanoparticles in free space in previous studies.15,16 Au and Cu vapors created from the molten Au-Cu ingot (heated in a carbon crucible to 1533 K by an induction coil) are then cooled by a purified He gas stream and condensed into alloy nanoparticles. The He pressure is 3.2 kPa at an inlet flow rate of 0.92 Pa m3s-1 in the source chamber. Laboratory-grade purity was used for the source materials (Au, Cu) and gases (He, O2). A long quartz tube (1.5 m, 28 mm i.d.) surrounded by a tube furnace (1.2 m) is employed as the heat bath. Three independently controlled SiC heaters yield a flat temperature profile measuring 0.8 m in length. The oxygen gas is injected with a small quartz tube (4 mm i.d.) to the center of the heat bath at an inlet flow rate of 0.46 Pa m3s-1 (half of the He inlet rate). The total pressure (He and O2) in the heat bath is 2.2 kPa. The mean flow velocity of gases is estimated to be 1.0 m/s at room temperature (4.6 m/s at 1373 K) using the pressure, total gas inlet flow rate, and the inner diameter of the heat bath. The velocity of the particles is estimated to be 1.5 times the mean flow velocity of gases assuming Poiseuille laminar flow because particles are well concentrated at the center axis of the
10.1021/jp077360u CCC: $40.75 © 2008 American Chemical Society Published on Web 01/19/2008
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Figure 1. Schematic horizontal-plane view of the experimental setup: (1) gas filter, (2) needle valve for He inlet (V1), (3) induction coil, (4) carbon crucible, (5) source material, (6) thermocouple, (7) capacitance manometer (G1), (8) pickup nozzle (4 mm i.d. quartz tube), (9) source chamber, (10) transport tube (SUS), (11) needle valve for O2 inlet (V2), (12) heat bath (1.5 m, 28 mm i.d. quartz tube), (13) O2 introduction tube (4 mm i.d. quartz tube), (14) tube furnace (1.2 m), (15) three zone SiC heating elements, (16) thermocouples, (17) flight tube (SUS), (18) capacitance manometer (G2), (19) deposition chamber, (20) microgrid carbon, (21) pressure control valve (V3).
tube. The dwell time of the particles in the flat temperature zone at 1373 K is about 0.16 s. The ideal gas diffusion coefficient of He is estimated to be 0.0029 m2/s at 298 K. The diffusion time of a single He atom at 298 K from the cylindrical center to the heat bath wall is 0.03 s. Although the diffusivity of O2 in the present condition is about one order lower than that of He, a huge number of collisions with He (∼1026 s-1) helps to rapidly thermalize O2. It therefore takes an order of ∼0.01 s for establishing temperature equilibrium between the gases and the heat bath wall, during which the gases move only a length of ∼0.05 m. The temperature of the gases is thus thermalized quickly with the heat bath wall. The heat bath consists of two zones; the melting and oxidizing zones. In the melting zone, the particles are heated with pure He. In this zone, the He collision rate on a 10-nm spherical surface is approximately 2.4 × 1010 s-1 at 1373 K. In the oxidizing zone, they are oxidized with a hot gaseous mixture of O2 and He. The collision rates of He and O2 are estimated to be 1.6 × 1010 s-1 and 2.9 × 109 s-1, respectively. The temperature control of metal clusters by collisions with noble gas atoms has been studied by Westergren et al.17,18 According to their thermodynamic expression, the temperature of a cluster composed of N atoms rises from Tc(0) to Tc(m) after m collisions with the noble gas atoms at temperature Tg, as Tc(m) ) (Tc(0) - Tg)(1 - k/3NkB)m + Tg, where k and kB are the energy exchange constant and the Boltzman constant, respectively.17 In case of a 10-nm alloy particle (N ∼ 4 × 104), approximately 108 collisions are sufficient to reach thermal equilibrium with the buffer gas temperature assuming k is on the order of 10-6 eV/K.17 In the present experimental conditions, thermal equilibrium is achieved within ∼10 ms. Therefore, the temperature of nanoparticles is presumably controlled well by the buffer gases and regarded to be nearly equal to that of the nearby heat bath wall. Using an ingot of Au0.84Cu0.16 alloy as a source material, we obtained Au0.46Cu0.54 nanoparticles with a mean size of 11 nm (standard deviation of 2.4 nm). The average alloy composition of Au0.46Cu0.54 (Au content standard deviation of 0.02) is determined by measuring 20 different particles using a JEOL JEM-2010 high-resolution electron microscope equipped with an EDAX Phoenix energy-dispersive X-ray spectrometer (EDS). The average size was derived from size distribution measured directly from TEM negatives using ImageJ software.19 The
higher Cu concentration of the particles than the source alloy is due to the higher vapor pressure of Cu at 1533 K than that of Au. The deposition time was limited to obtain a sparse nanoparticle dispersion on the substrate. Structural characterizations of the deposited particles were performed using highresolution TEM (HRTEM) imaging with a 0.194 nm point-topoint resolution at 200 kV acceleration voltage and selectedarea electron diffraction (SAED) measurements with a camera length of 100 cm. 3. Results and Discussion 3.1. HRTEM and SAED Characterizations. Figure 2a shows a TEM image of Au0.46Cu0.54 nanoparticles that were prepared by the IGA method and passed through the heat bath at room temperature. The particles are not oxidized and show crystalline and multiply twinned morphologies such as icosahedral and decahedral structures; however, they appear more complicated compared to the pure Au case but have the usual spherical shape.20 In contrast, Figure 2b shows the oxidized nanoparticles obtained by passing the nanoparticles through the heat bath at 1373 K. Except for the temperature of the heat bath, all other conditions were nominally the same for both cases as described in the previous section. All of the oxidized particles show an asymmetrically phase-separated morphology with a sharp interface and commonly took on a prolate-spheriod shape. The overall average [Au]:[Cu] composition ratio of the oxidized particles was determined to be 0.55:0.45 (Au content standard deviation of 0.02) by measuring 20 different particles using EDS, which represents a 17% decrease in Cu content compared to the non-oxidized particles. This is attributed to vaporization during the oxidation reaction. Debye-Scherrer diffraction rings were recorded on Imaging Plates (IPs, FUJI PHOTO FILM) in SAED mode, and the plates were scanned at 25 µm resolution using FUJI FDL5000 IP reader. The radial integration of the ring data into onedimensional intensity profiles were carried out using the software PIP (Powder pattern analyzer for IP).21 The radius of each ring was then precisely determined via nonlinear profile fitting procedures. An evaporated TlCl standard sample (TAAB Laboratories Equipment) was used for calibration of the SAED mode. The lattice constant determinations were done by the modified Bragg approach including the higher order term.22,23 The SAED data from the oxidized particles were assigned to
Analysis of AuxCu1-x-Cu2O Biphase Nanoparticles
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Figure 2. TEM images of (a) unoxidized and (b) oxidized Au0.46Cu0.54 nanoparticles passed through the heat bath with He-O2 mixture at room temperature and at 1373 K, respectively. The particles in b are Au0.83Cu0.17-Cu2O biphase nanoparticles as determined by SAED measurements. The scale bar is 50 nm.
Figure 3. HRTEM images of Au0.83Cu0.17-Cu2O biphase nanoparticles along (a) [11h0], (b) near [001], (c) near [11h0], and (d) [11h2] orientations, along with their power spectrum on the right. In all of the particles, the Cu2O/Au0.83Cu0.17 heteroepitaxial interface occurred along the (110) plane. The scale bar in the HRTEM images and the power spectra are 5 nm and 5 nm-1, respectively.
two types of crystalline structures. One is the Cu2O phase (primitive cubic) with 0.4248 ( 0.0003 nm, which is measured slightly smaller than the literature value24 of 0.42696 nm, and the other is the face-centered cubic (fcc) Au0.83Cu0.17 phase with 0.4019 ( 0.0002 nm. The alloy composition was determined from the lattice parameter using Vegard’s law corrected with a deviation factor.25 According to the above results, the oxidized particles with the phase-separated morphology are characterized to be Au0.83Cu0.17-Cu2O. A similar biphase morphology with Au0.9Cu0.1-Cu2O generated by annealing Au0.5Cu0.5 particles isolated in a silica matrix nearly at their melting point for 15 min has also been reported.26 HRTEM images of Au0.83Cu0.17-Cu2O nanoparticles are displayed in Figure 3a-d together with their power spectra (the squared modulus of the Fourier transform of each image) processed using the ImageJ software19 on the right. A particle
in Figure 3a shows two sets of lattice fringes seen in both darker (lower) and brighter (upper) regions. Each set of fringes is parallel throughout the two regions. From the corresponding power spectrum, the lattice spacings in the darker and brighter regions were found to accord well with d111 of Au0.83Cu0.17 and Cu2O crystals, respectively, indicating that dome-shaped Au0.83Cu0.17 and Cu2O nanocrystals are combined heteroepitaxially to form a prolate-spheroid-shaped particle. A sharp interface plane between the Au0.83Cu0.17 and Cu2O parts was clearly seen, and the angle between the interface and (111h) or (111) lattice fringes was found to be about 35°. On account of the crystallographic planes of the cubic lattices of Au0.83Cu0.17 and Cu2O, the two crystals are connected via a (110) plane with no rotation because the angle between the {111} planes and the (110) plane is 35.3°. The crystallographic orientation of this particular particle is thus [11h0]. Figure 3b shows another
2082 J. Phys. Chem. C, Vol. 112, No. 6, 2008 orientation case. The lattice fringes running through Au0.83Cu0.17 and Cu2O across the interface were found to be the (200) plane of the corresponding materials. An angle between the lattice fringes and the interface is about 45°. Hence, the interface is the (110) plane, which is the same as that in Figure 3a. This particle is slightly misoriented from [001] because the (020) lattice fringes should emerge symmetrically on the exact [001] orientation. The present situation on the no crystallographic rotation of heteroepitaxy between the two materials is similar to that reported of electrodeposited Cu2O epilayers on low-index Au surfaces.27,28 Figure 3c and d displays two Au0.83Cu0.17-Cu2O nanoparticles oriented nearly along [11h0] and [11h2] (or [1h12]) directions, respectively. Lattice fringes of (111h) and (1h11) (or (11h1)) planes are clearly observed in Figure 3c and d, respectively. Again, in both cases, the Au0.83Cu0.17 and Cu2O interface lies in the (110) plane. The lattice mismatch between the two materials is 5.7% from the SAED measurement results, where Au0.83Cu0.17 is regarded as a “substrate”. As indicated by the arrows in Figure 3d, Cu2O lattices are largely contracted near the interfacial plane and finally connected directly to the alloy lattices without generating any edge dislocations, while the alloy lattices are slightly dilated near the interface. Clearly the Cu2O and the Au0.83Cu0.17 parts are strained under compressive and tensile stresses, respectively. The common feature among the power spectra throughout Figure 3a-d is that the Au0.83Cu0.17 spots are very sharp while the Cu2O spots diffuse radially and tangentially. The tangential diffuseness of the Cu2O spots is fairly larger on the [001] and [11h2] orientations than on the [11h0]. This indicates there is anisotropic strain relaxation in the (110) interfacial layer. A theoretical analysis on relief of pseudomorphic strain in the fcc (110) epilayer has been done by Pashley.29 There are two slip planes of (111) and (111h) to contribute to strain relaxations on the (110) epilayers. Strains along [001] are readily relieved by glide on these {111} planes, whereas those along the [11h0] direction cannot be relieved by these basic slip systems because both planes intersect the (110) interface along the [11h0] direction. The (110) plane is composed of close-packed rows along [11h0], which are aligned with a distance x2 times greater than the nearest-neighbor distance. Therefore, pseudomorphism is more easily taken place along [001]. Regarding the above anisotropy on the (110) strain relaxation, the smaller diffuseness of Cu2O power spectra spots observed on the [11h0] orientation in Figure 3a and c can be attributed to the ease of strain relief along [001]. The larger diffuseness of Cu2O power spectra spots seen in the [001] orientation in Figure 3b is probably due to absence of the normal {111} slip systems to relief strains of the [11h0] close-packed rows. That also appears in the [11h2] orientation as shown in Figure 3d, along which the strained [11h0] rows inclined by 54.7° from the beam direction are projected. The oxidation reaction takes place at a heat-bath temperature of 1373 K, which is significantly higher than the melting temperatures of the Au-Cu system.30 The melting point of bulk Cu2O is, however, 130 K higher than 1373 K, and the solid Cu2O phase is stable under the present O2 partial pressure (0.72 kPa) at 1373 K.30 Hence, the following formation scheme can be considered. The oxidation reaction of a melted Au0.46Cu0.54 nanoparticle at 1373 K brings about a solid Cu2O part that is wetted by the Au-rich liquid. During the cooling process, the Au-rich liquid solidifies. The oxygen partial pressure, temperature, and time determine the final composition of the Au-rich phase (Au0.83Cu0.17). The above scheme, however, does not explain how the crystals formed into the asymmetric phase-
Koga and Zubia separated morphology with perfect (coherent) interface. This can be explained by considering the effect of postannealing on frozen structures. The strain energy is directly correlated to the interfacial area in nanoscale coherent heterostructures.31 From an energetic point of view, the asymmetrically phase-separated morphology with a smaller interfacial area (rather than other forms such as the core/shell geometry) is probably the most favorable. The reason the system prefers the {110} interface rather than {111} or {100} is considered qualitatively as follows. The in-plane coordination numbers of the {111}, {100}, and {110} plane are 6, 4, and 2, respectively. Driven by the strain energy minimization, the {110} interface is presumably preferred. 3.2. Strain Measurements. Careful observation of the [11h2] oriented particle in Figure 3d directly shows strain of {111} planes perpendicular to the (110) interface. The lattice spacing varies with distance to the interface, and parallelism of the lattice fringes becomes worse from the center to the edge. This feature is much more prominent in the Cu2O part and slightly observed in the alloy part near the interface. Figure 4a and b contains images of a small (10 × 9 nm) and a large (16 × 13 nm) particle in the same [11h2] orientation as Figure 3d. Both particles show clear lattice fringes running throughout both materials without generating any misfit dislocations. Using the ImageJ software,19 we extracted d111 values as a function of normal distance from the interface as shown in Figure 4c and d for the particle of Figure 4a and b, respectively.32 In the image analysis, a conversion factor transforming from pixel to the real scale was estimated. We determined it by applying the alloy d111 value from the SAED measurement, that is, a0(Au0.83Cu0.17)/x3 ()0.2320 nm), to the averaged d111 width of the alloy part in the HRTEM image. Figure 4c and d clearly shows that the oxide part carries a large compressive strain while the alloy part has a slight tensile strain. The fully relaxed d111 value of Cu2O, which might be found around the oxide edge (dome top), is expected to be 0.2465 nm (the bulk Cu2O lattice parameter24 (0.42696 nm) divided by x3). We see in Figure 4c and d that the d111 value at the oxide edge nearly shows this value. On the alloy side, the fully relaxed d111 value can be estimated by averaging the data in the straindamped region. On the basis of these fully relaxed values for both sides, we obtained the strain profiles with (d111 - drelaxed 111 )/ and are plotted in Figure 4e and f for the particle of drelaxed 111 Figure 4a and b, respectively. Using the fully relaxed widths, the accurate value of the lattice mismatch is calculated to be 6.5%, which is slightly larger than the value (5.7%) estimated from the SAED measurement. 3.3. Strain Analysis Based on Elasticity Theory. In this section, we describe the theoretical analysis of the strain profiles obtained above. Zubia and Hersee have briefly analyzed strain in selective-area heteroepitaxy in which an epilayer is nucleated on a nanoscale island.33,34 In such a case, the lattice deformation occurs three-dimensionally. Moreover, strain is partitioned (shared) between the epilayer and the island-shaped substrate, resulting in a considerable increase in the critical thickness (thickness at which strain is relieved by the generation of misfit dislocations). According to Luryi and Suhir, a coherent island of lateral extent (Di) on a rigid substrate will have a three-dimensional strain distribution in which the biaxial strain decays away from the interface with a characteristic length of decay proportional to the lateral extent.31 In the present analysis, we use the assumption of Zubia and Hersee that the strain is partitioned between the epilayer and substrate. The stresses in the epitaxial
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J. Phys. Chem. C, Vol. 112, No. 6, 2008 2083
Figure 4. HRTEM image of (a) smaller and (b) larger Au0.83Cu0.17-Cu2O nanoparticles along [11h2] orientation. (c and d) Mean width of {111} lattice fringes as a function of normal distance from the interface for a and b particles, respectively. (e and f) Misfit strain as a function of normal distance from the interface for a and b particles, respectively. Solid lines in e and f denote fitting results by the elasticity theory modified with a semiempirical parameter on strain damping.
layer (referred by the subscript “e”) and substrate (referred by the subscript “s”) will then have the form31
σe(y,z) ) 0e
Ye (1 - νe)
χ(y,z) exp
( ) -πz g Di
(1a)
( )
(1b)
and
σs(y,z) ) 0s
Ys (1 - νs)
χ(y,z) exp
πz g Di
where 0e and 0s are the yet to be determined partitioned strain of the epilayer and the substrate at the interface, Y is Young’s modulus, ν is Poisson’s ratio, z is the coordinate normal to the
planar interface with origin on it, y is the lateral coordinate, and χ(y,z) describes the lateral variation of stress. χ(y,z) deviates from unity only near the edges,35,36 and we therefore assume that χ(y,z) is uniformly equal to unity. This assumption was evaluated using finite element analysis and shown to be reasonable for first-order calculations. Moreover, the HRTEM images (Figure 3a-e and Figure 4a and b) show that this is a reasonable assumption. The exponential term in eqs 1a and b models the exponential decay of stress in bilayers of finite lateral extent. In the present particle case, we treat Di as a diameter of the interface. To determine the partitioned strains at the interface, we follow the approach of Zubia et al.37 However, our analysis optimal for a nanowire heterojunction is approximately applied to a nanodome junction in the present nanoparticle case.
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Moreover, we introduce a semiempirical parameter g in order to obtain a good quantitative fit with our experimental strain profiles because the exponential damping term in the original theory was given qualitatively.31 Under static equilibrium conditions, forces in the epilayer and substrate satisfy the following equilibrium relation
∫0h σe(z) dz + ∫-h0 σs(z) dz ) 0 e
(2)
s
where he and hs are the thickness of the epilayer and the substrate, respectively, and are considered positive quantities. Substituting eqs 1a and b into eq 2, and integrating with respect to z, and then rearranging and solving using 0e ) (ai - ae)/ae and 0s ) (ai - as)/as, where ae and as are the epilayer and substrate lattice parameters, and ai is the interfacial lattice parameter, we derive the interfacial epilayer and substrate strains, respectively, as
0e )
(as - ae)(1 - e
-πhsg/Di
)
ae(1 - e-πhsg/Di) + Kas(1 - e-πheg/Di)
(3a)
and
0s )
K(ae - as)(1 - e-πheg/Di) ae(1 - e-πhsg/Di) + Kas(1 - e-πheg/Di)
(3b)
where K ) Ye(1 - νs)/Ys(1 - νe) is the elastic compliance ratio. Unlike previous models that relied on the total mismatch strain (T),38 eqs 3a and b depend only on material properties and the lateral and vertical dimensions of the structure. Finally, the variation of strain as a function of normal distance from the interface, z is given as
( )
e ) 0e exp
-πz g Di
(4a)
Figure 5. Semiempirical parameters g on the strain damping as a function of interfacial diameter, that were obtained form analyses of four different Au0.83Cu0.17-Cu2O nanoparticles along [11h2] orientation. The g parameter shows a mean value (a solid line) of 3.10 ( 0.08 with no interfacial diameter dependence.
parameter as R ) (πg)-1) is ∼0.13.41 The decay constant in our case shows R j ) 0.103 ( 0.003, which is close to their result. The fitted curves in Figure 4e and f reproduce the experimental strain profiles very well. This suggests that the strain profiles in the present biphase nanoparticles are explained perfectly by the elasticity theory modified with the semiempirical g parameter showing no interfacial diameter dependence. According to theory of critical thickness in standard thinfilm heteroepitaxy, a lattice mismatch of 6.5% in Cu2O/Au0.83Cu0.17 is too large to support a psudomorphic interface.42 However, by reducing the lateral extent down to the 10-nm range, a psudomorphic heterojunction of such a large mismatch combination can be realized by three-dimensional deformation in both materials. 4. Conclusions
and
s )
0s
( )
πz exp g Di
(4b)
We have obtained excellent fits of the strain profiles using eqs 4a and b as shown by solid lines in Figure 4e and f. In the calculation, Cu2O and Au0.83Cu0.17 are defined to be the epilayer and the substrate, respectively, and the following parameters are used; YCu2O ) 30 GPa, YAu ) 79 GPa, νCu2O ) 0.45, and νAu ) 0.42,39,40 where the Young’s modulus and the Poisson’s ratio of Au are employed approximately for Au0.83Cu0.17. We used distances from the interface to the particle edges for hAu-Cu and hCu2O. The semiempirical parameter g was found to be g ) 3.28 ( 0.33 and 3.15 ( 0.11 for Figure 4e and f, respectively. Two more particles in the same orientation were analyzed, and the g parameters are plotted as a function of interfacial diameter as shown in Figure 5. We found the g parameters show no size dependence in 8-12 nm range, and its mean value is gj ) 3.10 ( 0.08. Because every particle takes a similar shape with a nearly constant g parameter, the interfacial strains for the Cu2O and Au0.83Cu0.17 sides show almost common values of -0.044 and 0.017, respectively, indicating that the oxide side accommodates 72% of the strain at the interface. Recently, Ertekin et al. carried out theoretical and finite-element-analysis studies on nanowire heterojunctions and found that the strain decay constant R (which was defined in relation to our g
The gas-phase reaction of melted Au0.46Cu0.54 alloy nanoparticles with oxygen yields homogeneously the prolate-spheroid Au0.83Cu0.17-Cu2O biphase nanoparticles with a coherent alloy/ oxide interface. The present HRTEM observations revealed that the two cubic lattices are connected via a (110) interface with no crystallographic rotation, and the strains arising from the 6.5% lattice mismatch are taken up by deforming both materials without generation of misfit dislocations. The observed strain partitioning is similar to the three-dimensional misfit stress relief mechanism in the nanoheteroepitaxy situation (a nanoscale epilayer island on a nanoscale-patterned substrate) that has been described by Zubia and Hersee.33 We have seen successful reproductions of the experimental strain profiles with the original elasticity theory31,33 modified by introducing a semiempirical parameter g into the strain damping exponential term. The present experiment demonstrates that biphase nanoparticles with a heteroepitaxial interface can be homogeneously generated by the high-temperature oxidation of noble-metal alloy nanoparticles in free space. The precise structural control of nanoscale heteroepitaxy will allow us to provide an ideal situation for understanding of various nanocomposite properties, such as catalytic, electronic, magnetic, gas-sensing properties, and so forth. Acknowledgment. K.K. is grateful to Y. Fujihisa for modification of the PIP software for the SAED data analysis.
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