Article pubs.acs.org/JPCC
Size-Dependent Phase Transformations in Bismuth Oxide Nanoparticles. I. Synthesis and Evaporation Gerrit Guenther,†,§ F. Einar Kruis,‡ and Olivier Guillon*,§ †
Technische Universitaet Darmstadt, Institute of Materials Science, Petersenstr. 23, 64287 Darmstadt, Germany Universitaet Duisburg-Essen, Faculty of Engineering, Institute of Technology for Nanostructures and Center for Nanointegration Duisburg-Essen (CENIDE), Bismarckstr. 81, 47057 Duisburg, Germany § Friedrich-Schiller-Universitaet Jena, Otto Schott Institute of Materials Research, Loebdergraben 32, 07743 Jena, Germany ‡
S Supporting Information *
ABSTRACT: At the nanoscale material properties can be tuned by altering the size and shape of the specimen. Such effects are quite well investigated for metallic materials. On the other hand inorganic compounds have received relatively little interest due to the more demanding experimental procedures. While the size effects are similar for any kind of inorganic material, the degree of size-dependent changes depends on the bond strength and bond nature of the material at the surface: the higher the surface energy, the stronger the size dependence. These thoughts are demonstrated in this contribution by investigating the size-dependent thermodynamic properties of monodisperse, size-selected bismuth oxide (Bi2O3) nanoparticles in the range between 6 and 50 nm. This first part is mainly concerned with evaporation, while the second part (J. Phys. Chem. C 2014, 10.1021/jp509841s) covers size-dependent melting. Heating experiments up to the evaporation of the particles were performed with a new, custom method based on loss of matter caused by evaporation. The results in this part show the validity of the Kelvin equation and a size-dependent evaporation behavior of this oxide. A 1 1 ∝ 1/3 ∝ V D N
1. INTRODUCTION Promising cutting-edge applications of oxide materials, such as semiconductor quantum dots, transparent electronics for highefficiency solar cells, light emitters, photocatalysts, gas sensors, etc., all rely on their size-dependent properties. The success of nanoscience is based on the change of material properties at the nanoscale due to quantum-confinement effects and the increasing ratio of surface atoms to atoms in the volume. One of the most striking consequences of the increased surface to volume ratio are changes in the phase stabilities leading to size-dependent melting, evaporation, and other phase transformation temperatures. Such effects were experimentally and theoretically shown for numerous metals such as gold, silver, tin, indium, and lead.1−5 Two kinds of size-dependent effects exist in small systems: First, smoothly scaling effects related to the fraction of lowcoordinated atoms at the surface and, second, quantum effects due to the completion of shells which show discontinuous behavior. An illustrative example for the latter case is the sizedependent fluorescence effect due to quantum confinement in silicon particles smaller than 10 nm.6,7 In the scope of this work is the former kind which occurs in phase transformations of nanomaterials. The surface energy adds a total excess energy to a nano-object that is proportional to the surface area. The surface area A increases relative to the volume V of a particle © 2014 American Chemical Society
(1)
N is the number of atoms in the particle, and D is the diameter of a perfectly spherical particle. A material property which is influenced by the surface excess energy must follow this 1/D dependency. This is exactly the case for the depression of the melting and boiling point of gold nanoparticles.4,8 The excess contribution adds to the total free energy of the nanosized object. Therefore, less additional, thermal energy is needed to reach the melting or boiling point. Thus, the relative change of the melting and boiling temperature follows a 1 − 1/D dependency. The liquid−vapor phase transition is discussed in this part of the article. In part II,9 the emphasis is put on melting. If a spherical nanoparticle with radius r, liquid or solid, is in equilibrium with its vapor, the vapor pressure is greater than the same pressure of a planar surface. This was theoretically stated by Lord Kelvin in 187110 and found repeated experimental validation starting in the middle of the 20th century (e.g., ref 2 and references therein). It was initially derived for a liquid droplet for which the conditions of constant curvature, r, and constant surface energy, γ, are always fulfilled. The widely Received: December 21, 2013 Revised: October 9, 2014 Published: October 10, 2014 27010
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Bi2O3 shows a pronounced polymorphism.15,16 The common structures were summarized by Medernach and Snyder.17 The α-Bi2O3 as the stable room-temperature phase has a monoclinic structure of P21/c space group with 8 Bi3+ and 12 O2− atoms in the unit cell. A transformation at 1003 K yields the cubic δbismuth oxide. It has a calcium fluoride (CaF2) type structure in which 25% of the sites in the oxygen sublattice are vacant. It is an ongoing discussion whether the vacancies are statistically distributed.18 The unit cell contains 4 Bi3+ and 6 O2− atoms. Melting occurs at 1098 K from the δ-phase. In certain cases the bismuth oxide can adopt the metastable β-phase which has the same structure as the δ-phase but with ordered oxygen positions.19,20 It is described by a tetragonal unit cell ((P421c (114)). Finally, the boiling point of bismuth oxide is not clearly reported. Only 245 kJ/mol as an approximate value for the enthalpy of evaporation was given by Sidorov et al.22 At the nanoscale thin films of bismuth oxide were investigated by Zav′yalova et al.23,24 Due to the confinement other structures were observed and analyzed by X-ray diffraction at room temperature. Among them was the metastable β-phase and a distorted tetragonal β-like form with the stoichiometry Bi2O2.5. More recently Fan et al.25 showed that β-Bi2O3 as well as δ-Bi2O3 thin films could be deposited by reactive sputtering of Bi onto NaCl, Si, ZrO2, quartz, and glass substrates with controlled temperature. The films were polycrystalline with an average grain size of ≤20 nm. While the δ-phase only formed in a narrow temperature window around 473 K, the β- and α-phase were readily achieved at higher temperatures. There are a few letters and reports about synthesized bismuth oxide nanoparticles and needles from different groups.26−31 If reported the typical structure was β-Bi2O3. Only Han-Xiang et al. also prepared the δ-phase by a vacuum vapor-phase oxidation.32 Except XRD no further characterization of any of the particles took place. Hence no surface energies or other thermodynamic properties of bismuth oxide nanoparticles are known. The evaporation behavior of binary compounds is more complicated than the one of elements because a number of different gas components with different enthalpies of formation form. In the case of bismuth oxide, Bi, O2, BiO, Bi2, Bi4O6, Bi2O3, and many minor gases formed. The few studies conducted are very inconsistent.22,33−36The total vapor pressure of the material has to be calculated from an equilibrium containing the condensed matter as well as all the gas components. Special software calculating the thermodynamic equilibrium is used for such purposes.37,38 Furthermore, the stoichiometry and the evaporation rate in oxides often change under vacuum. Stoichiometry changes are due to decomposition by reduction reactions which involve p(O2) on the product side. Onyama et al.36 found that composition change also applies to bismuth oxide at 1023 K (δphase) in vacuum while being negligible in air. Hence the multiphase evaporation of bismuth oxide is increased in vacuum, accompanied by stoichiometric changes of the still condensed matter.
known Kelvin equation describes the increase in vapor pressure of small droplets (pp) compared to the planar surface of the bulk (ps). ⎛ pp ⎞ 4v γ m lv ln⎜⎜ ⎟⎟ = RTD ⎝ ps ⎠
(2) 11
However, Kaptay recently showed that this equation is based on an erroneous derivation. His derivation leads to the following formula ⎛ pp ⎞ 6v γ m lv ln⎜⎜ ⎟⎟ = p RTD ⎝ s⎠
(3)
A factor of 6 instead of 4 is the difference. The qualitative behavior remains the same. The goal of our work was to analyze the 1 − 1/D dependency of oxides in general. A distinction between eqs 2 and 3 was not possible. No systematic investigation of phase transformations including melting has been undertaken for oxides yet. This is due to experimental challenges and the lack of suitable characterization methods: For one, the synthesis of oxide particles has to be performed under an oxygen-rich atmosphere where most suitable characterization methods fail. For another, vacuum conditions which are necessary for the usually applied probe-beam methods could affect the stability of the compounds. All this complicates the experiments considerably and requires new methods and procedures to be developed. Nevertheless, a better knowledge of structural properties including the determination of phase stability domains as a function of sizeis of the utmost importance for the further development of reliable nanodevices. Bismuth oxide was exemplarily chosen for this work. Our goal is to systematically show the size effect of phase transition temperatures in bismuth oxide nanoparticles. This means we need to investigate the qualitative and quantitative differences of size effects in compounds with covalent/ionic bonds compared to metals. Together with transformations in copper sulfide and cadmium sulfide,12,13 it is the first report for inorganic compounds, and it is the only one for oxide materials. The study consists of two parts, separating the particle synthesis and evaporation measurements performed with an aerosol evaporation−condensation apparatus on the one hand and the melting experiments performed in situ in the transmission electron microscope (TEM) on the other hand. In the present paper (part I) is structured as follows: After an introduction to the material bismuth(III) oxide, the particle synthesis and the experimental procedure for measuring evaporation of the particles are described. Afterward the characterization of the particles and size-dependent evaporation measurements are presented followed by a short, preliminary discussion (of this part of the results). In the second part,9 melting of these bismuth oxide nanoparticles will be treated, and the results will be interpreted comprehensively. 1.1. Bismuth Oxygen System. The material under investigation is bismuth(III) oxide (Bi2O3). It was chosen because of its low melting temperature (1098 K14) combined with good crystallinity and a stable meltat least under atmospheric conditions. Furthermore, a low enthalpy of melting, Δ m H, promised a pronounced melting point depression at the nanoscale (see part II9). The important structural and thermodynamic properties, as reported in the literature, are summarized here.
2. EXPERIMENTAL SECTION 2.1. Particle Synthesis. The particles were synthesized by an aerosol-based evaporation−condensation process with a size-fractioning method at the Technology for Nanostructures group, University of Duisburg-Essen. Detailed treatment of similar synthesis processes is reported by Kruis et al.39 The schematic representation of the synthesis setup can be seen in 27011
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together with diffusion losses caused a reduction of the particle concentration in the fractionated portion by one to two orders of magnitude. The conditioned aerosol distribution could then be characterized by a scanning mobility particle sizer (SMPS). The experimental system used in this study consisted of an electrostatic classifier (model 3080, TSI Inc.), a differential mobility analyzer (model 3080n, TSI Inc.), and a condensation particle counter (model 3025, TSI Inc.). While stepping through the voltage range of the DMA the CPC enumerated the number of particles passing through the detector per unit volume in each size fraction. In this way a fractionated size− concentration distribution was measured. From the data the size-distribution function, mean, mode, and geometric standard deviation, σGSD, were calculated (e.g., Figure 4). For the evaporation experiments this procedure was sufficient. Additionally the fractionated particles were deposited by electrostatic precipitation (ESP) of the particles.41 They were deposited on TEM grids with amorphous silicon nitride (SiNx) support films for characterizing and melting them in the TEM (part II9). Depending on the particle size and the ESP voltage the deposition time varied between 3 and 50 min for polydisperse samples and between 1 and 40 h for sizefractionated samples. As accurate determination of the particle size was indispensable for this study, a calibration of the instruments was performed with reference particles (NIST, RM 8011−RM 8013) on TEM grids with SiNx membrane. These gold nanoparticles had the nominal sizes of 10, 30, and 60 nm with spherical shape and a very narrow size distribution. They were used for calibration of the SEM and TEM microscope in use. The images were taken under the same conditions and magnifications as (a) in the NIST reports about the reference materials and (b) used for the investigation of the Bi2O3 nanoparticles.42 2.2. Size-Dependent Evaporation. The evaporation of Bi2O3 nanoparticles was investigated by a new, custom method. Its basic principle is as follows: Due to the loss of matter the size of a droplet decreases when it evaporates. The evaporation rate (quantified as size change/shrinkage) depends on the temperature of the particles/droplets and their size. The sizes of the nanoparticles were measured with a special setup. Furthermore, the self-accelerating process was also simulated by a kinetic-theory model taken from nucleation theory. The initial and final states were compared to the experiment. This combination of measuring and simulating the droplet size during the evaporation process gives insight into the thermodynamic properties of the material under investigation.
Figure 1. Gas streams of 1.3 L/min N2 and 0.13 L/min O2, both with a purity of 99.99999%, were mixed and lead through
Figure 1. Synthesis and evaporation setup. In the top row sizefractionated particles were synthesized. These were used in two ways: (a) to perform size-dependent evaporation experiments by measuring the size distributions before and after an evaporation furnace and (b) to deposit on TEM grids for characterization and in situ TEM melting experiments (part II9).
the setup. In a first tube furnace (1253−1373 K) high purity (99.999%) Bi2O3 powder was evaporated from a zirconia crucible. Flowing with the carrier gas the vapor cooled rapidly, and nanoparticles nucleated from the supersaturated gas. In a second tube furnace the aerosol was annealed at lower temperatures (803 K) to form spherical, monocrystalline particles. When the particles are not spherical at the start of the evaporation experiments, it is not possible to distinguish between size reduction caused by solid-state sintering (leads to shrinkage due to compaction) and evaporation (leads to shrinkage due to loss of matter). An approximately log-normal size distribution of particles resulted from the thermally activated evaporation process. Passing through an ionizing radioactive source the particles were chargedusually with a single electron charge. Within a differential mobility analyzer (DMA40) charged particles were attracted to a negatively biased center electrode while experiencing a drag force by the carrier gas. Particles for which the electrical force balanced the drag force passed through a collection slit. In this way a narrow size fraction was separated from the initial distribution according to the mobility equivalent diameter (EMD). This size narrrowing
Figure 2. Scheme of the measurement method for analyzing the evaporation behavior. Monodisperse particles were synthesized and transported through a heating chamber as a low concentrated aerosol. The size distribution was sequentially measured before and after the evaporation event. The temperature of the chamber was changed in steps, and material properties were derived from the temperature-dependent shrinkage caused by evaporation. 27012
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the case of a spherical particle of volume ν = π/6D3 one can express the change of diameter, D, per unit time as follows
First the experimental part of the method will be described: The size distribution was measured before and after evaporation in a dedicated furnace. For that a special setup, similar to the one described by Nanda et al.,3 was built up: Behind the synthesis setup in Figure 1 an additional tube furnace was positioned which served as an evaporation chamber. The maximum temperature was measured by a thermocouple inside the tube. The synthesized, monodisperse aerosol flowed with 1.43 std L/min through the tube. The high oxygen content guaranteed congruent evaporation and no stoichiometric changes of the particles (see section 1.1). The parameters in section 2.1 were used to produce monodisperse sizes of 47, 29, 17, 8, and 6 nm, and for each of these initial sizes an evaporation experiment was conducted: As depicted in Figure 2 the size distribution was measured before and after the chamber. The dwell time in the chamber was calculated to be 2 s. Stepping through the temperatures between 373 and 1200 K, distributions were recorded and analyzed (Figure 3). Because evaporation causes shrinkage, the changing particle diameter could be used as a measure of evaporation rate.
2vm(p − pp ) dD = dt 2πmmRT
(4)
Here t is the time [s] spent in the heated region; T is the temperature [K] in that region; R is the gas constant [J mol−1 K−1]; νm is the molar volume (53.07 × 10−6 m3/mol at the bulk melting temperature44); and mm is the molar mass (465.96 g/ mol) of liquid Bi2O3. Bi2O3 is the only compound considered because its evaporation is congruent, and it is the only condensed matter which transforms into gaseous species. As the particle diameter is the measured quantity in the DMA, this equation can be directly used to simulate the evaporation at constant temperature in the heating chamber. The initial particle size D0 was known, and the size Dx after the dwell time (t = 2 s) in the heating chamber had to be calculated. If the partial pressure driving force p − pp is constant over time, which is true for large particles, this is simply done by integration D(t ) = D0 +
∫0
t
2vm(p − pp ) 2πmmRT
dt (5)
However, for nanoparticles the Kelvin correction (eq 2 or 3) has to be applied. Now eq 4 gets more complicated (here with eq 2) dD = dt
⎛ ⎡ 4vmγlv ⎤⎞ 2vm ⎜p − ps exp⎢ ⎥⎟ ⎣ RTD(t ) ⎦⎠ 2πmmRT ⎝
(6)
This is a differential equation. Because of the exponential expression this had to be solved numerically in constant time steps. In the present case the gas phase is composed of several bismuth oxide species (see section 1.1); however, the one which has to be considered for the evaporation is only the species which can take part in the evaporation or condensation events, namely, Bi2O3. The presence of other species leads to a lower ps of Bi2O3 (g), but what is required for the present evaporation study is only the effective value on the surface of Bi2O3 (l) and not the total vapor pressure of all the Bi−O species. So the expression was approximated by using the Clausius−Clapeyron equation
Figure 3. Example of evaporating (e.g., shrinking) Bi2O3 droplets with an initial size of 47 and 17 nm.
Second, the theoretical model will be described: A first evaluation method was proposed by Nanda et al.3−5 Similar to determining the onset of an event in a differential scanning calorimeter they determined an onset temperature for evaporation which changed with initial size. With the help of the Kelvin equation (eq 2) and a bulk reference they determined a mean value for γ of PbS, Ag, and Au. However, ΔvH and γlv can not be obtained from such a graph. Here, a new evaluation method derived from kinetic theory was developed. It simulates the dynamic shrinking of the nanoparticles in the evaporation chamber. Its mathematical base will now be derived. For analyzing the measured size changes a model is necessary which relates the size change to the evaporation rate and hence to the physical properties of the particles. The Hertz−Knudsen equation (eq 4) was used for that purpose. The driving force is the pressure difference p − pp between the partial pressure of Bi2O3 p and the vapor pressure at the surface of the droplet, pp [Pa]. This difference has to be negative for evaporation because a material can only evaporate if the vapor pressure is higher than the partial pressure in the surrounding atmosphere. For
d ln(ps ) dT
=
Δv H RT 2
(7)
One can integrate from pressure p1 at T1 to pressure p2 at T2 if one assumes that the enthalpy of evaporation ΔvH is approximately temperature-invariant in the respective temperature range ⎡ −Δ H ⎛ 1 1 ⎞⎤ v p2 = p1 exp⎢ ⎜ − ⎟⎥ ⎢⎣ R ⎝ T2 T1 ⎠⎦⎥
(8)
Used in the differential eq 6 this finally gives the equation that had to be solved (here with eq 2) 27013
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dD = dt +
Article
⎛ ⎡ −Δ H ⎛ 1 1⎞ v ⎜⎜p − p exp⎢ ⎜ − ⎟ 1 ⎢⎣ R ⎝ T T1 ⎠ ⎝
4vmγlv ⎤⎞ ⎥⎟ RTD(t ) ⎥⎦⎟⎠
(9)
The same equation holds when applying eq 3 instead of eq 2, only with factor 6 instead of 4. As the concentration of the nanoparticles was low (0.8. Only the largest size distribution showed partially sintered, aspherical agglomerates. Larger particles obviously required higher sintering temperatures, so that 803 K was too low at the given dwell time of 2 s in the furnace to enable grain growth and obtain fully dense, monocrystalline particles. In the micrograph of the 29.7 nm sample one can see some nonspherical particles composed of small primary crystallites. Apparently such agglomerates have the same mobility as the spherical particles with 30 nm diameter. The structure was analyzed by diffraction with X-ray radiation from the Synchrotron source PETRA III (DESY, Hamburg). Figure 5 shows a diffractogram together with the results from the Rietveld refinement. The structure of the analyzed 30 and 14 nm particles was clearly the metastable βBi2O3 structure with a = b = 0.775 nm and c = 0.567 nm. From line broadening (calibrated with a LaB6 standard) the isotropic crystallite size was determined to be 13.9 nm for the sample with nominal size of 15 nm. As this accords well, the particles had to be monocrystalline. As the particle volume and thus the diffracting volume decrease with r3, the measured signal decreases drastically with the decreasing size, and the
Figure 4. Representative micrographs and corresponding histograms from five selected particle sizes which were also used in the in situ TEM experiments (part II9). The samples up to 16.0 nm consist of primary particles only. In the two biggest sizes coagulation and agglomeration lead to less spherical, polycrystalline particles. Size calibration was performed with NIST reference materials RM 8011− RM 8013.
coherently diffracting regions become too small for conventional Rietveld analysis. This is why smaller particle sizes could not be measured with XRD. However, in the TEM such particles had the same appearance in the HR micrographs (Figure 6) and SAED patterns. The HR images also showed a faceted shape and lattice fringes whose d-spacing could usually 27014
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In summary, pure, monodisperse, monocrystalline β-Bi2O3 nanoparticles were synthesized in five sizes and used for the size-dependent evaporation experiments (part I) and the sizedependent melting experiments (part II9). 3.2. Size-Dependent Evaporation. The working principle and theoretical base of this measurement and evaluation method is described in part 2.2: in short the thermodynamic properties γlv and ΔvH were fitted by applying a dynamic evaporation model to the measured size changes in the evaporation chamber. The experiments took place in an atmosphere of 90% N2 and 10% O2 at 105 Pa. Different initial particle sizes were used, and the temperature was raised in steps. As an example Figure 3 shows the measured mode of the particle size distribution in an experiment with 47 nm particles and another experiment with 17 nm particles. Above a certain temperature the particle size starts to decrease due to evaporation from the surface. In addition to these experiments, calculations of the dynamic evaporation of particles over time were performed at constant temperature. This was done by numerically solving the differential eq 9. Examples of a 6 and a 47 nm particle are shown in Figure 7: owing to the smaller volume the smaller particle has fully evaporated at lower temperatures. Furthermore, the Kelvin effect (eq 2 or 3) leads to higher vapor pressures and self-reinforcing evaporation at small sizes, hence bending the curve downward. This model was applied to calculate the final sizes (marked as squares in Figure 7) depending on γlv and ΔvH. The shrinkage rate at a certain
Figure 5. X-ray diffractograms and Rietveld refinements measured for 14 nm bismuth oxide nanoparticles on a MgO single crystal at PETRA III synchrotron, beamline P02.1 (λ = 0.207309 Å) in air. The structure is β-Bi2O3, and no additional phases could be detected.
be attributed to the 201 and 220 planes of β-Bi2O3. No amorphous surface region could be observed. The purity of the particles was validated with an XPS measurement (DAISY-MAT, TU Darmstadt) which only showed Bi and O peaks as well as C peaks from the exposure to ambient. Further details can be found in the Supporting Information.
Figure 6. High-resolution (phase contrast) TEM micrographs of the synthesized Bi2O3 nanoparticles. Lattice fringes and faceting are proof of their (mono)crystalline character. The identifiable d-spacings were from the 201 or 220 planes of β-Bi2O3. 27015
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Figure 7. Simulated shrinking of a 47 nm (a) and 6 nm (b) nanoparticle during the time in the heating chamber. The total dwell time was 2 s. Each line shows the size change at a constant temperature. The higher the temperature, the higher is the shrinkage by evaporation. The size effect becomes measurable when the bending of the curves is visible (colored lines). As the effect is self-accelerating the relevant temperature range before complete evaporation is very narrow for small nanoparticles, like in (b). The squares indicate the initial and final time/size. These points are experimentally measurable (see Figure 2) and were used to match the simulation to the experiment in Figure 8.
Figure 8. Fit of the model parameters to the experimental values: (a) Shows the size-dependent evaporation rate (here rate of diameter change) as a function of temperature. Different colors are different initial particle sizes. The black lines indicate the simultaneous fit to extract γlv as the only unknown parameter that causes size-dependent changes. The fit gave an average γlv = 0.13 (eq 2) or 0.09 (eq 3) ± 0.04 J/m2. (b) Deduced vapor pressure curve of bulk Bi2O3 determined from dynamic evaporation calculation of Bi2O3 nanoparticles. It serves as a visualization to show how ΔvH was fitted to the slope: it was averaged over all species and over the temperature region. The dashed line is a function for the total vapor pressure deduced from Knudsencell MS measurements from the literature.22
temperature was calculated and compared to the experimental values. This can be seen in Figure 8a for all five initial particle sizes: the surface energy is responsible for the differences in curving upward between the five initial sizes. Therefore, γlv could be determined by fitting the model (black lines) to the measurement values (see also part 2.2). The average value of γlv = 0.13 J/m2 according to eq 2 or γlv = 0.09 J/m2 according to eq 3 fitted within ±0.04 J/m2 to the curves. Inaccuracies in the measurement as well as changes in the material properties could be responsible for the misfit to the five curves. On the other hand, the onset method by Nanda et al. yielded γlv = 2.08 J/m2 which is unrealistically high. With this γlv the fit parameter ΔvH was determined by a fit to the slope of the vapor pressure curve in Figure 8(b), resulting in 185 ± 15 kJ/mol. The small size changes in the 6 and 8 nm samples lead to uncertainties during fitting. The dashed line from Sidorov et al.22 comes from a mass spectrometry (MS) study in 1980 and will be a subject of the discussion.
4. DISCUSSION Two important points are treated in this discussion: (i) if the measurement and analysis method is suitable to probe the evaporation behavior of inorganic nanoparticles and (ii) if the common 1/D dependence with constant γlv can be applied to the evaporation of (bismuth) oxide nanoparticles. Therefore, the discussion is split up in two parts. 4.1. Measurement and Analysis Method. In Figure 3 evaporation sets in at around 1000 K. As temperature has a e−1/T influence on the evaporation rate, the size changes ever faster at increasing temperature until the particles fully evaporate within the dwell time in the heated region. The determined value of γlv from the evaluation method of Nanda et al.4 was very high compared to literature values.44 This generally seems to be the case for this onset method.45 In the present work the evaluation of the data via a fit of the dynamic evaporation process gave more realistic values. The 27016
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that due to lack of better knowledge or ambiguous nomenclature they are commonly but erroneously described by the same term. Another aspect of γlv can be seen by close inspection of Figure 8(a): it shows that γlv = 0.13 J/m2 underestimates the curvature for large particles and overestimates the curvature of small particles. Within the evaporation model this is explained by a variable γlv. A temperature dependence as well as a size dependence of γlv would be possible to explain this variation. According to the Eötvös rule for the temperature dependence of γlv, it increases with decreasing temperature. This would cause a trend opposite to the observed direction. So temperature dependence can be excluded as cause for a variable γlv. A size dependence of γlv with the correct trend was predicted by Tolman.48 However, the uncertainty of the present measurement with the unknown vapor-pressure function of Bi2O3 does not allow definite statements. Instead, the differences of the values are included in the error of ±0.04 J/m2. Within this uncertainty the 1/D dependence with constant γlv is valid for the evaporation of bismuth oxide nanoparticles. The determined values of γlv and ΔvH were used to calculate the size-dependent normal vapor pressure function. From eqs 2 or 3 and 8 Tv was calculated as follows
theory requires the particles to be much smaller than the mean free path in the aerosol which was fulfilled for the tested aerosol. An advantage of this evaluation is that the surface energy can be determined for each size separately, if the vapor pressure function of a material is known exactly. Thus, sizedependent changes of γlv could be measured which is a unique feature. Unfortunately this was not possible in this work because the bismuth oxide vapor pressure is not known. It had to be approximated by the Clausius−Clapeyron equation with ΔvH as an additional fit parameter. For enabling the fitting procedure γlv had to be assumed constant for all sizes. Independent of the evaluation method, the size measurement of evaporating liquid droplets has some advantages. First, free particles without influence of a substrate or a matrix are measured. Second, different atmospheres can be usedmost important for oxides: also high oxygen partial pressures. The measurement sensitively depends on an accurate determination of the initial and final particle size. In this work the sizes measured by SMPS were calibrated with reference materials from NIST (RM 8011−RM 8013). The fact that the temperature distribution in the heating chamber is only approximated by the maximum value constitutes some deviation from the real temperature distribution. All in all our new measurement and analysis method has proven to be suitable. Accuracy and measurement range could be improved with a specifically designed heating chamber which warrants a homogeneous temperature and adjustable dwell times. 4.2. Size Dependence of Evaporating Bi2O3. The size dependence of the evaporation behavior of bismuth oxide at the nanoscale will be discussed now. Under constant molar volume it results solely from the surface energy γlv in eq 2 or 3. This is in contrast to the size-dependent melting (part II9) where the difference Δγ between the solid and liquid phase is relevant. The measured average value of 0.13 (eq 2) or 0.09 (eq 3) ± 0.04 J/m2 is lower than the only reported bulk value of 0.217 J/ m2 at 1123 K. This was measured by Fujino et al. with the ring method.46 They also reported a linear temperature dependence of dγ/dT = −2.1 × 10−5 J m−2 K−1. Using this dependence to extrapolate to 1023 K γlv would be 0.215 J/m2. This is still much higher than the value of this work. The discussed measurement errors could be responsible for one part of such a difference. A further contribution to the large difference could be that different properties are probed by the two methods: 1. The ring method measures the maximum force when a platinum ring detaches from the surface of liquid bismuth oxide. It probes the surface stress which is a purely mechanical property. 2. Surface energy is defined as the excess energy occurring due to the existence of a surface. Surface energy and surface stress are related via the Shuttleworth equation.47 The molecules of a liquid are free to move and therefore cannot sustain a bond stress. So generally, surface stress and surface energy are said to be the same in a liquid. 3. The experimental way of determining γlv with the presented method comes directly from the evaporation of gas components on the nanoparticles’ surface. Thus, it is a measure of how hard it is to remove these molecules or atoms from the surface. Hence, an evaporating surface is a different process than the above definition of an excess state or a stress. Ouyang et al. treat this topic with their own model for γsv and γlv.45 In this light the measured values of our study and the other one by Fujino et al. could differ because different surface-related properties are probed with the different methods. It is possible
Tv =
Δv H − 4γlvvm/D Δv H /T1 − R ln(pv /p1 )
(10)
Tv and pv belong to the boiling point, and T1 and p1 come from a known P−T point in Figure 8(b). The Tv−1/D plot (boiling curve) can be seen in Figure 9. The lines are isobares for
Figure 9. Normalized, size-dependent boiling-point curve showing isobar lines of the normal pressure plotted over the reciprocal diameter to show the 1/D size dependence. Different vapor pressure functions lead to different slopes and different normal boiling temperatures.
normal pressure. Because small differences in ΔvH strongly affect the extrapolated value Tv, the functions of Sidorov et al.22 and this work were normalized to the respective bulk value. In both cases γlv = 0.13 J/m2 was used with the factor 4 in eq 2. The slope of the straight line depends on γlv. Because of the low value of γlv the size effect of boiling point reduction is measurable but small. This statement holds, independent of the questionable vapor pressure function. Since metals usually have a higher γlv they show a stronger change of the boiling temperature with size.4,45 27017
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5. CONCLUSIONS A comprehensive study was conducted to investigate the size dependence of phase transformations in binary oxide materials in general and bismuth oxide in particular because previous publications were restricted to metallic materials. The study is published in two parts. In this first part the synthesis of the sizeselected particles, a method for analyzing the evaporation behavior, and the size-dependent boiling temperature were described. The synthesized particles were pure, monodisperse, monocrystalline β-Bi2O3 nanoparticles produced with an aerosolbased evaporation−condensation process with a size-fractioning apparatus. Five sizes were synthesized and used for the sizedependent evaporation experiments (this part) and the sizedependent melting experiments (part II9). The evaporation of Bi2O3 nanoparticles was investigated by a new, custom method based on mass loss caused by evaporation. The respective shrinkage decreases the size (diameter) of the nanoparticles. Hence, the thermodynamic properties γlv and ΔvH could be determined by applying a dynamic evaporation model to the measured size changes in an evaporation chamber. This method has proven to be suitable. Yet, a specifically developed setup could further enhance the results considerably. Problematic was the unknown and complicated vapor pressure function of the multiphase Bi−O system. With accurate information about all phases thermodynamical simulation software would be able to calculate such a system. Because it is not known yet, it had to be approximated by the Clausius− Clapeyron equation with ΔvH as an additional fit parameter. A value of 185 ± 15 kJ/mol was determined. Still, the Kelvin equation itself is valid, and an average value of 0.13 (eq 2) or 0.09 (eq 3) ± 0.04 J/m2 was determined for the surface energy, γlv, of liquid Bi2O3 between 6 and 47 nm. Due to the low value the determined boiling point depression is weak compared to the melting point depression (part II9).
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ASSOCIATED CONTENT
* Supporting Information S
Details on the collection and analysis of XPS spectra for bismuth oxide nanoparticles. This material is available free of charge via the Internet at http://pubs.acs.org.
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AUTHOR INFORMATION
Corresponding Author
*Tel.: +49 2461 615181. Fax: +49 2461 619866. E-mail o.
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS We acknowledge financial support of the Deutsche Forschungsgemeinschaft (DFG) within the frame of the Emmy Noether program (GU 993/1-1). We are also very grateful to R. Schmechel, G. Schierning, R. Theissmann, M. Stein, and the whole NST group for the possibility to produce the nanoparticles and perform evaporation experiments. Great thanks go to M. Hinterstein for the Synchrotron measurement and C. Hein for the XPS measurement.
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