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Energetics of Oriented Attachment of Mn-Doped SnO2 Nanoparticles Chi-Hsiu Chang, Sanchita Dey, and Ricardo H. R. Castro* †

Downloaded by RUTGERS UNIV on August 25, 2015 | http://pubs.acs.org Publication Date (Web): August 25, 2015 | doi: 10.1021/acs.jpcc.5b03862

Department of Chemical Engineering and Materials Science & NEAT ORU, University of California, Davis, California 95616, United States ABSTRACT: Growth of nanoparticles by oriented attachment (OA) can occur in electrolyte solutions, in vacuum, or even in air. The energy change in this event is determined by the difference between the excess interface energies of the free nanoparticles and the arrangement with attached grains. Therefore, low energy boundaries (highly coherent) are more likely to attach, and after attachment, atomic rearrangement will allow crystals to effectively grow by coalescing two or more grains. However, if the energy of the boundary formed by attachment is low but the activation energy for coalescence is high, it is possible for the system to enter a metastable state that disables nanocrystals’ growth (enabling design of growth resistant nanocrystals). In this work, we test this hypothesis in manganese-doped SnO2 nanoparticles in the absence of organic agents. We observe that manganese dramatically lowers the energies of (noncoherent) grain boundaries of SnO2, which enhances nanostability and slows grain growth due to the increased activation energy for OA.

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INTRODUCTION Nanoscale materials have been investigated extensively for their exclusive size-dependent properties, such as optics, electricity, and magnetism.1−3 However, grain coarsening due to thermodynamic instability retards the fundamental investigation of quantum effects. That is, the abundant interfaces in nanoparticles bring along remarkable excess energy (i.e., the energy difference between the bulk and the nanosized phases), increasing the driving force for grain coarsening. To maintain the particles with nanosizes, it is important to understand common growth mechanisms to design growth-resistant strategies. Oriented attachment (OA)4−8 is a well described coalescence process where nanoparticles regarded as “building blocks” stack together by colliding and attachment. Used to build 0D, 1D, 2D, or even 3D structures, in OA, the particles orient themselves spontaneously to seek a coherently crystalline facet with neighbor units or induced by particular organic agents.9−11 This orientation, including rotation and alignment, is a rapid and irreversible reaction that can be followed by atomic rearrangement to allow unification of grains (grain growth).12 Comprehensively, OA does not preclude massive atomic transport mechanism but can be triggered easily at low temperatures, occurring even in aqueous solutions. The energetics of OA have been previously discussed in the literature,13 and it was pointed out that interatomic Coulombic interactions are key driving forces for nanoparticles’ approximation and attachment. The energy gain when comparing free nanoparticles and the attached state is the driving force for the process, but after attachment, atomic arrangement must take place for particles to intermix. In the absence of an organic agent, this last step is typically assumed to have low activation energy, as demonstrated for cerium oxide.14 This is because, for the attachment to occur, the energy of the newly formed boundaries must be significantly low, suggesting low angle © XXXX American Chemical Society

boundaries, which are not far from a perfect alignment to the neighbor particle. Avoiding the grain combination stage can allow highly stable nanocrystals. Theoretically, from a thermodynamic perspective, this can be achieved by a very low boundary energy at the “attached state”, leading to a metastable condition resistant to growth. From a kinetic perspective, creating atomic rearrangement barriers in between the grains can also cause similar effects. This can be achieved by using the very same organic agents that are used to cap monomers and then hinder OA, but this is limited to low temperatures because of temperatureinduced degradation. To avoid the use of organic additives for high-temperature nanostability, ionic dopants can be introduced. For instance, Zhang et al. have shown that TiO2 nanoparticles show limited growth upon addition of 0.5 atom % of Fe3+.15 Analogous particle size reduction induced by dopants (Ni, Mn, Mg, and Fe) has been reported in the literature and attributed to the role of dopants in changing interfacial features, such as surface and grain boundary energies.16−19 Recently, we have shown that Mn segregation takes place on SnO2 nanoparticles, and this causes a reduction of both surface and grain boundary energies.20 The reduction is more pronounced in the grain boundaries and is proportional to the concentration of Mn. A preliminary calculation indicates a potential enhancement of particle nanostability due to excess energy of the grain boundaries, but the exact mechanism is still ambiguous. In this work, we discuss the stability of tin dioxide nanoparticles based on the OA model, highlighting the effect of the interfacial energy changes by a dopant (Mn) in each stage Received: April 22, 2015 Revised: August 18, 2015

A

DOI: 10.1021/acs.jpcc.5b03862 J. Phys. Chem. C XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry C

Table 1. Microstructural and Energetic Characteristics of As-Synthesized Mn-Doped SnO2 Nanoparticles Cited from Our Previous Work20,a xT (mol %) S0 S1 S2 S4 S8

0 1.62 2.57 4.07 8.53

± ± ± ±

0.38 0.35 0.42 0.44

G (nm) 10.9 9.3 8.4 6.8 6.1

± ± ± ± ±

0.12 0.07 0.03 0.05 0.03

AS (m2/g) 44.00 49.16 50.72 52.17 79.99

± ± ± ± ±

0.33 0.12 0.07 0.35 0.39

AGB (m2/g) 17.18 21.51 25.86 37.46 31.7

± ± ± ± ±

0.18 0.35 0.20 0.50 0.73

γS (J/m2) 1.20 1.20 1.19 1.17 1.12

± ± ± ± ±

0.02 0.02 0.02 0.02 0.02

γGB (J/m2) 0.70 0.48 0.39 0.38 0.37

± ± ± ± ±

0.08 0.13 0.14 0.08 0.11

a


The parameters include total Mn content (xT), grain size (G), surface area (AS), grain boundary area (AGB), surface energy (γS), and grain boundary energy (γGB).

is important to note that none of the samples had second phases and were indexed as a pure SnO2 tetragonal rutile phase (JCPDF no. 41-1445). Moreover, there are no significant differences on the intensity ratio of the peaks between the samples, regardless of the manganese content, suggesting no effects of the dopant on the present exposed surfaces. The reader is referred to ref 20 for a detailed microstructural analysis of the samples. Table 1 shows a decrease in grain size with increasing manganese content. This is accompanied by a surface area increase and a grain boundary area increase as well. The evolution of interface areas is quite consistent with the interface energies as shown in Table 1, which show a decrease in both surface energy and grain boundary energy with increasing Mn content. That is, as the energy of an interface is decreased, it is thermodynamically more possible to form that particular interface. Since the reduction in the grain boundary energy is much more pronounced, the grain boundary area evolution is also consistent with this idea. Note that the energies (both for surface and grain boundary) shown in Table 1 refer to the respective interfacial areas of the nanoparticles; i.e., as will be discussed later, the effect of dopants on interfacial energies is strongly dependent on its concentration at that interface. Since the area of interface decreases with coarsening, the concentration is not a constant but increases with grain growth (see section 3.4). Parts a−e of Figure 1 show grain growth curves for each sample annealed under different temperatures in air. As expected, coarsening happens in all conditions for all samples, but higher temperatures lead to more pronounced grain enlargement as expected in a thermally activated process. Regardless of the temperature and time though, the trend observed for the as-synthesized powders related to the effect of manganese remains; that is, grain sizes of samples with higher manganese contents are systematically smaller (see Figure 1f for the compiled data for 700 °C annealing). A limit seems to be reached for sample S8, which does not show much difference at 700 °C annealing as compared to S4, but for the first 3 h of growth. As will be discussed in the following sessions, this is a result of a combined kinetic and thermodynamic effect. 3.2. Oriented Attachment Grain Growth Mechanism in Mn−SnO2. Classical Ostwald ripening (OR) is typically regarded as the mechanism of tin dioxide nanoparticles’ coarsening.24 Therefore, the role of dopants in decreasing the particle size is attributed to a surface energy decrease associated with surface segregation.18,25,26 For instance, Ni and Fe ions have been observed to segregate to the surface of SnO2 with an associated increase in surface area of the powders.26 Though evidence of segregation was provided in both cases, surface energy decrease was assumed by describing the growth mechanism as an OR process, creating a circular logic. The

of OA. A geometric model based on OA and cooperating with segregation models was developed, and a series of sizedependent energy equations were derived. The derivations successfully depict the energy evolution during OA grain growth and shows that highly metastable nanocrystals can be achieved by interfacial energy design (without organic additives) in systems growing by OA. Growth curves were studied using current OA kinetic models and showed the coupled effect of Mn in the thermodynamics and kinetics of OA.

2. EXPERIMENTAL SECTION Mn-doped SnO2 nanoparticles were synthesized by a polymeric method.21,22 Tin(II) citrate and manganese(II) carbonate (Alfa Aesar, 99.9%) were added to a mixed aqueous solution prepared with citric acid (Sigma-Aldrich, 99%) and ethylene glycol (Sigma-Aldrich, 99.8%). This solution was continuously stirred, and nitric acid (Sigma-Aldrich, 70%) was concurrently added until the solution was fully transparent. The resulting solution was heated to 140 °C for 30 min to obtain a polyesterified resin. The resin was heated at 450 °C for 4 h, ground as a fine powder in an agate mortar, and calcined again at 500 °C for 15 h. The two-step heat treatment ensures the full combustion of carbon chains and sufficient nucleation and crystallization of nanoparticles. For the grain-coarsening studies, the as-synthesized samples were regarded as the initial conditions (0 h) and then further annealed for additional times at 500, 600, and 700 °C. Although there may be concern about the reliability of the as-synthesized sample as the initial point for the OA study because of its pretreated calcination, heat treatment for such a long time is indeed necessary to eliminate the carbonaceous contaminations from the samples according to previous studies.20,23 All samples were examined by X-ray diffraction (XRD; Bruker AXS Inc., Madison, WI, Model D8 Advance). The XRD patterns were used to analyze crystal phases and estimate the grain sizes upon the full width at half maximum method. The microstructures of selected samples were observed by transmission electron microscopy (HRTEM; JEOL JEM 2100F/Cs, 200 kV). Other cited physical and energetic parameters are listed in Table 1. These parameters and corresponding methodologies of measurement have been described in our previous work.20 3. RESULTS AND DISCUSSION 3.1. Microstructural and Energetic Characterization. The composition, microstructures, and interface energies of the as-synthesized Mn-doped SnO2 nanoparticles have been reported in our previous work and are listed in Table 1 for reference.20 The samples were named S0, S1, S2, S4, and S8 depending on their Mn molar fraction (xT) listed in Table 1. It B


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Figure 1. Experimental grain growth data (open symbol) and its OA fitting curve (solid line).

as-synthesized S0 to S8 were used to identify particular OA microstructural features. Parts a and f of Figure 2 exhibit perfect OA joints for S0 and S8 samples, where two particles are oriented along the [110] direction and share an equivalent fringe in 0.32 nm width. Figure 2b shows a low angle misorientation contact (LA) for S1; parts c, d, and e Figure 2 reveal other coherent twins contacts (T) typical of OA for S1, S2, and S4. In contrast to perfect OA, these widely observed boundaries with minor misorientation are called imperfect OA and are also characteristics of this process. In addition, Figure 2c reveals a multistep attachment where an irregularly shaped

assumption of OR governing SnO2 growth is, however, not strongly supported by evidence. For example, when studying ultrafine SnO2, Leite et al. calculated a growth kinetic exponent too high to have any physical meaning.24 The data reported in Table 1 also works as evidence against OR, since though a dramatic grain size decrease occurs, only a small reduction in surface energy is observed. Oriented attachment (OA) has been comprehensively used in many investigations of nanoceramics growth, including tin dioxide.4,6,7,27 To test if OA is the main mechanism in the samples studied in manganese-doped SnO2, HRTEM images of C


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Figure 2. HRTEM images of as-synthesized Mn-doped SnO2 nanoparticles: (a) S0; (b) and (c) S1; (d) S2; (e) S4; (f) S8. Arrows highlight the joints of particles where idea-oriented attachment (OA), twins (T), or low angle misorientation (LA) contact are exhibited.

grain is built up by three small units denoted as I, II, and III. Each unit shares a twin boundary. These characteristics have been reported elsewhere and are very consistent with OA.4,28,29 The fact that OA growth has the necessary formation of boundaries in between grains as a step for the growth process suggests that the thermodynamics of the grain boundaries must play a significant role in defining the crystal stability. In the next section, the thermodynamics of OA are described in detail and the available energetic data used to test hypothesis on the role of manganese in defining growth paths. 3.3. Thermodynamic and Geometric Model of Oriented Attachment. OA growth can be didactically separated into five distinct configurations: (i) isolated particles; (ii) nonoriented attachment; (iii) imperfect oriented attachment; (iv) perfect oriented attachment; and (v) grain combination (self-integration). Figure 3a shows schematic representations of each configuration. Since the sample is not changing composition or mass while shifting from one state to the other, the energy of each particular state with respect to the bulk phase (coarsened phase) can be singly attributed to the excess energy of interfaces, which can be written as u ΔHexs =

u ∑ ΔHexs,p = ∑ γpuA pu ; p

p = S or GB

u = i−v;

p

(1)

Figure 3. Schematic configuration, energy state, and model for OA grain growth calculation: (a) configurations and corresponding energy states; (b) single building unit/particle with truncated octahedral shape; a is the edge of polyhedron and G is the diameter of midsphere; (c) highly aggregated cluster observed from S8 TEM image; (d) practical model to describe the aggregation; in detail, the center unit is fully surrounded by 14 units and each cluster owns 18 square−square and 32 hexagon−hexagon contacts.

The excess energy (ΔHuexs) is resulted from the combination of interface areas (Aup) and interface energies (γup). The symbol u refers to the respective state (i−v), and p represents the corresponding interface (S or GB). Based on eq 1, we can roughly predict the relative energy of each state during the process. For instance, state i must have the highest excess energy because only surfaces are exposed (no grain boundaries), and surface energies are typically higher than grain boundary energies themselves. State ii shows the formation of nonoriented attachments by randomly colliding between particles. Significant energy lowering is expected when turning from state i to state ii because of the formation of the

lower energy interfaces and because two unit areas of the surface are becoming one unit of grain boundary. Particles’ rotation and alignment can lead to further (but smaller) reduction in energy by lowering the intrinsic energy of the grain boundary by changing misorientation. This may lead D


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Similarly, the grain boundary area of state ii (AiiGB) is written

to a near-zero grain boundary energy state, such as an imperfect (state iii) or a perfect attachment (state iv).30 Note that probabilistically, it is possible for the system to directly move from state i to state iii or iv without rotating or realignment. Regardless of how the system gets there, both these states (iii and iv) can ultimately lead to an effective elimination of grain boundary excess energy by combination of grains (selfintegration): state v. This final stage of the process will only provide a slight energy reduction since the existing boundaries are already of low energy. Excess energy cascade from states i to v is schematically represented in Figure 3a, where the y axis is the energy and the x axis represents the equivalent state of OA. Although Figure 3a gives the rough energy trends of OA states, in order to have a realistic energetic assessment of OA, three-dimensional arrangement of nanoparticles with more realistic shapes (other than spheres) must be considered. A geometric model was then built using truncated octahedron (TO) representing as the nanoparticles. TO is commonly used to represent isotropic ceramic particles in different models.31 Figure 3b shows a single TO unit, where a represents the length of edge and G serves as the diameter of midsphere of TO. It is assumed that G is consistent with the average grain size estimated from XRD. Geometrically, a is equal to G/3. For convenience, other geometric parameters are represented as a function of G. That is, the unit surface area is ∼2.98 G2, the unit volume is ∼0.42 G3, the hexagonal facet is 0.29 G2, and the square facet is 0.11G2. For a gram of isolated particles (TO units), the number of TO units (NTO) can be written as total volume divided by the unit volume NTO =

1 ρT (0.42G3)

as ii A GB =

≅

7.11 ρT G

where CS and CGB are constants only related to the aggregation parameters (k, m, n). Geometrically, states iv and ii have equivalent surface areas (AiiS = AivS ). The grain boundary is absent in state iv (AivGB = 0) because all particles are perfectly oriented. For the purpose of this study, we will only focus on states i, ii, and iv, since state iii is an intermediate state and state v has zero interfacial area. 3.4. Actual Energies of Interfaces in Each Stage. At this point, it is quite tempting to plug in numbers from Table 1 to test the validation of the proposed geometrical model and analyze the energetics of the states. However, the energy values reported in Table 1 are only valid for that particular microstructure (interfacial areas). That is, even if the concentration of manganese is constant in a sample, the amount of manganese segregated at either the grain boundary or the surface is not unique and depends on the respective areas. When particles attach, surfaces become grain boundaries, decreasing surface area and increasing grain boundary area. This will cause redistribution of manganese (according to the respective segregation tendencies). Since the distribution of dopants is correlated to interface energies,20,32,33 the energy of each boundary or surface at each state is not constant but varies as this ef fective concentration of Mn. Actual data can be calculated and is related to the enthalpy of segregation. That is, in a system where an ionic dopant exists, this can distribute itself on three distinct positions: bulk (B), surface (S), and grain boundary (GB). To determine the quantity of dopants in specific region, segregation enthalpy is a reference to infer the segregate tendency. A correlation has been successfully derived in our previous work and written as20

(2)

(3)

xpu 1 − xpu

Meanwhile, all particles are isolated so the grain boundary area is equal to zero (AiGB = 0). To illustrate the configuration of state ii, it is assumed that n particles/units coalesce together to form a cluster. In a straightforward manner, the volume of a cluster is n times of unit volume as the number of clusters is NTO/n of a gram of sample. We will assume cluster aggregation to create m numbers of square−square contacts and k numbers of hexagon−hexagon contacts (faces of TO available for aggregation). To simplify the system, no square−hexagon contacts are considered. Therefore, the surface area of state ii (AiiS) is the product of cluster numbers (NTO/n) and the net surface area of a cluster (in the square bracket), which can be written as

x BuEp 1 − x Bi

;

⎛ −ΔHpseg ⎞ ⎟; Ep = exp⎜ ⎝ RT ⎠

p = S or GB

(6)

To apply the derivation to the Mn-doped SnO2 system, xup represents the Mn molar fraction on respective position p, R is the gas constant, and T is the absolute temperature. The exponential term including segregation enthalpy (ΔHseg p ) is abbreviated as Ep. Equation 6 can further be rearranged as xpu =

Ep 1 x Bu

− 1 + Ep

p = S or GB

≅ Epx Bu ;

u = i, ii, or iv; (7)

This simplification is based on our preliminary reports20 stating that the bulk Mn content (xuB) is extremely small (∼10−9 to 10−6), so its reciprocal is very large. Likewise, ΔHseg p for Mn has been computed as −26.8 kJ/mol for the surface and −51.2 kJ/mol for the grain boundary; thus, Ep is in the range of a few tenths to thousands at temperatures between 500 and 700 °C. Consequently, the terms beside (1/xuB) in the denominator of

⎛ NTO ⎞ ⎜ ⎟[n(unit surface) − 2m(square facet) ⎝ n ⎠ − 2k(hexagonal facet)] ⎛k ⎞ CS ⎛m⎞ , where CS = 7.11 − 0.54⎜ ⎟ − 1.38⎜ ⎟ ⎝n⎠ ⎝n⎠ ρT G

=

u = i, ii, or iv;

ASii =

≅

⎛k ⎞ CGB ⎛m⎞ , where CGB = 0.26⎜ ⎟ + 0.69⎜ ⎟ ⎝ ⎠ ⎝n⎠ n ρT G (5)

where ρT is theoretical density so 1/ρT is the total volume of a gram sample. Thus, the total surface area in state i (AiS) is the product of NTO and the unit surface area: ASi ≅

⎛ NTO ⎞ ⎜ ⎟[m(square facet) + k(hexagonal facet)] ⎝ n ⎠

(4) E


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Table 2. Results of Interface Area (AuS), Interface Energy (γuS), and Excess Energy (ΔHuexs) of Each State along with All Relevant Parameters Used in the Calculationsa

a

Three independent variables G (grain size in nm), xT (Mn content in molar fraction), and T (temperature in K) were used to describe the results. Note that the molecular weight (Mw) of Mn-doped SnO2 (MnxTSn1−xTO2) was also dependent on xT.

eq 7 are negligible ((1/xuB) ≫ EP ≫ 1), and xup can be simplified as EpxuB. To comply with solute conservation, the total Mn content (xT) is the summation of the product of the molar fraction (xup) with the volume fraction (f up). The equation is written as xT =

∑

xpuf pu u

= i, ii, or iv;

boundary area decrease). This factor is quite critical when simulating state ii, which involves grain boundaries. Once the grain boundary is saturated, XuGB is pinned at 0.137 and eq 10 should be modified to xpii ≅

p = S, GB, and B (8)

p

Ω=

Vm ; NA

u = i, ii, or iv;

p = S or GB

x TEp ∑p f pu Ep

(9)

;

u = i, ii, or iv;

;

p = S or B (11)

u γp,doped = γp,undoped + ΓupΔHpseg ;

u = i, ii, or iv;

p = S or GB

where mp is the number of atomic layers, usually assumed as 1 for surface and 3 for grain boundary.34 Ω is the volume of formula unit comes from molar volume (Vm) divided by Avogadro’s number (NA); its cubic root is assumed as the average thickness between atomic layers. Although f Bu is excluded from eq 9, it is easily calculated by (1 − f uS − f uGB). When eqs 7 and 8 are combined, a general form of xup is acquired: xpu ≅

∑p f pii Ep

According to the Gibbs isothermal adsorption modified by Krill et al.,34−36 the determined xup is directly correlated with solute distribution and segregation enthalpy:

The volume fraction is primarily related to interface areas f pu = ρT A pu mpΩ1/3;

ii (x T − f GB xGB,sat)Ep

Γup

=

f pu xpu A pu M w

(12)

= mpV m−2/3N A−1/3xpu

(13)

(Γujp)

The excess Mn concentration is written as eq 13 and simplified by plugging eq 9; Mw is molecular weight. Since the interface energies of undoped SnO2 (γp,undoped) and the Mn segregation enthalpies have been given,20 the interface energies of the doped sample (γj,doped) are dynamically varying with the excess Mn concentration which is a function of G and xT. With the actual energy of interfaces described as a function of Mn concentration and grain size, calculation of the excess energies in each state with actual interfacial energies considering local concentration changes is now feasible. For this purpose, a highly aggregated cluster is used for calculation. The image of the cluster is schematically shown in Figure 3d and is quite consistent with observations from TEM that large clusters are indeed observed in this system (Figure 3c). The cluster is built up by 15 TO units including 18 square−square

p = S, GB, or B (10)

Here, ES and EGB correspond to segregation enthalpy; EB is assumed a constant, 1. Note that the limit of Mn solubility in the grain boundary (xGB,sat) has been already reported for this system.20 This means the grain boundary is not an infinite sink for manganese, but “saturation” occurs whenever the concentration reaches xGB,sat (which can happen by dopant content increase or by grain F


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and 32 hexagon−hexagon contacts. Thus, n, m, and k are determined as 15, 18, and 32, respectively. Since all parameters are well-defined, the interface areas (eq 3−5) and interface energies (eq 12) are substituted into eq 1 to compute the excess energy of each state. The results for each of the states are presented in Table 2, along with all relevant parameters used in the calculations. However, instead of discussing the absolute energy states, for the purpose of understanding the OA energetic dependences, it is more effective to investigate the energy changes in between states which actually define the driving force of reactions and existence of metastable conditions. The energy decrease ̅ between steps is simply denoted as ΔHu−u exs . For example, i i−iv ΔHi−iv exs is ΔHexs minus ΔHexs . This is discussed in the next section. 3.5. Energy Change during Transitions. Figure 4 shows the normalized energy decrease between states i, ii, and iv

(see Figure 3a). To further understand the thermodynamic dependencies in this system, and if the growth behavior is actually following the energetic trends directed by the dopant, it is useful at this point to calculate the stability of state ii, or better ΔHii−iv exs , as a function of microstructure. Figure 5a shows this quantity plotted versus grain size for different Mn contents. As a first observation, ΔHii−iv exs is nearly proportional to the reciprocal of grain size for any Mn content. This is expected since the excess energy scales with the excess surface/grain boundary area. Considering the extremes, i.e., S0 and S8, one can observe very distinct energy profiles, with S0 having at any given grain size. The systematically higher ΔHii−iv exs samples with Mn contents in the middle range (S1, S2, and S4) have energy differences in between, but interestingly, as the grain size increases, all ΔHii−iv exs eventually merge with S8. S4 merges at ∼6 nm, S2 merges ∼9 nm, and S1 merges ∼15 nm, such that after 15 nm, all doped samples have a similar energy difference. This phenomenon has to do with the interfacial saturation conditions, as discussed in a previous session. That is, because the enthalpy of segregation is a fixed quantity, as the interface areas decrease (grain sizes increase) they become enriched in dopant. Since the total number of sites available for the dopants is finite, saturation is inevitable. Saturation leads to leveling of energy, explaining the similar results for all samples at larger grains. In Figure 5b−d, ΔHii−iv exs was plotted as a function of both grain size and Mn content, creating a map graph of actual driving forces for conversion of state ii into state iv. The colors in the map represent the difference of excess energy, with blue being the lowest values and red the maximum, as marked in the legend. The map shows a curved behavior, with highly doped samples never showing ΔHii−iv exs above 4 kJ/mol. Note also that does not change much for relatively high dopant ΔHii−iv exs contents, since the interfaces are expected to be saturated and so are energetically similar. Experimental points of the grain growth curve (Figure 1) were plotted on the top of the energetic map in Figure 5b−d with three different temperatures, respectively. As expected, higher temperatures allow achievement of lower excess energies and energy differences. This is attributed to the thermally activated process of grain growth where kinetics and thermodynamics work in parallel. The trajectory (pink line) in Figure 5b−d shows the linkage of experimental points with equivalent processing factors (i.e., synthesized procedure, annealing time, and temperature). Note that all trajectories are curved, and remarkably, their shapes are very consistent with the energetic trend (contour line). This phenomenon suggests the energy of state ii is a strong contributor for defining grain size in OA and can potentially be used to design nanostability. The imperfect matching between the grain size data as the energy diagram suggests though that kinetic parameters can also be playing a controlling role in the growth profile. Clear evidence of such contribution is that the excited state between state ii and iv for the nanoparticles higher manganese concentration sits on a higher energetic position. This can be attributed to an increase in the activation energy for rearrangement of atoms caused by the built up of a thick layer of manganese in between tin dioxide grains. A more indepth kinetic analysis is discussed in the next session. 3.6. Kinetics of Oriented Attachment Grain Growth. The kinetic OA model proposed by Zhang et al. was used to fit the experimental data obtained in this study (Figure 1) and to

Figure 4. Percentage of normalized energy decrease between states i, ii, and iv during OA of tin dioxide with varying Mn content. The red ii−iv and black colors present percent ΔHi−ii exs and ΔHexs , respectively. A 7% drop of ΔHii−iv exs is observed between S0 and S8, which leads to a thermodynamically more stable intermediate state (state ii).

calculated by using the proposed geometrical model and the interfacial energies corrected for actual manganese distribution. The plot separates the energetic contribution of collision (state i to ii) and reorientation (state ii to iv). Apparently, the overall energy decrease is mainly resulted from the former (ΔHi−ii exs , ∼70%). This is consistent with previous simulations20 and reinforces the fact that particles tend to aggregate by collision, which is in good agreement with many literature reports that mentioned the difficulty of obtaining purely isolated nanoparticles without any organic agent capping.37,20 The next OA step (ΔHii−iv exs ) shows roughly 30% of the total energy decrease during OA. This value suggests only moderate driving force for grain reorientation. Interestingly, Figure 4 highlights a gradual reduction of ΔHii−iv exs with increasing Mn content, reaching a 7% decrease between S0 and S8. This means that the driving force for reorientation decreases with increasing Mn content. This is attributed to the decrease of grain boundary energy due to Mn segregation, which energetically stabilizes state ii. A similar phenomenon has been hypothesized before,19 but this is the first time that direct thermodynamic quantification is provided as a proof of concept. This reduction in driving force is thus responsible for the observed smaller crystallite sizes of the highly doped tin dioxide (Figure 1). The thermodynamic stability and therefore growth resistance is clearly dependent on the stability of the intermediate state ii G


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Figure 5. (a) Plot of ΔHii−iv exs vs grain size at 500 °C; the star symbols mark the position of mergence. (b−d) Map graph with grain size vs Mn content vs ΔHii−iv exs at 500, 600, and 700 °C annealing temperature, respectively. The pink symbols mark the experimental grain results at different annealing times. The pink trajectory linked the symbols at equivalent annealing time but different Mn concentration. The pink arrow guides the time evolution.

of cluster Dx (x ≥ 2) because of its significantly smaller value as compared to D1 of the primary particle. Hence

quantify kinetic constants and activation energies of OA mechanism.5 In the model, coalescence was assumed to be irreversible and to take place only between monomer− monomer and monomer−multimer. The reactions can be described as follows k1

A1 + A1 → A 2

kx = 2πD1(G1 + Gx)

where Gx is the grain size of the particle containing x primary particles, which can be further given according to equivalentvolume relation:

(14)

kx − 1

A1 + Ax − 1 ⎯⎯⎯→ Ax

Gx = x1/3G1

(15)

where A1 is a primary particle, Ax is the cluster containing x primary particles, and kx is the reaction rate constant. Thus, the general reaction rate can be written as

dNx = kx − 1N1Nx − 1 − kxN1Nx dt

(16)

(x ≥ 2)

(19)

Using eqs 16−19, a numerical simulation was used to estimate the grain size distribution changing with time. A firstorder expression of Taylor’s formula was introduced by using Euler’s polygon method to the program39

∞

dN1 = −2k1N12 − N1 ∑ kxNx dt x=2

(18)

N(x , t +Δt ) = N(x , t ) +

∂N(x , t ) ∂t

Δt

(20)

where Δt is the time interval of each step and usually is selected as 1/(ND1) to ensure the accuracy of results. The computed time-dependent grain size distribution (N(x,t)) was further described as the average grain size (Geq) at certain time according to the volume-weighted average particle size estimation:40

(17)

where N1 and Nx are the respective concentration (number per unit volume) in the system corresponding to A1 and Ax. The rate constant kx was defined based on the Smoluchowski theory38 and simplified by neglecting the diffusion coefficients H


Article

The Journal of Physical Chemistry C Geq =

∑ NxGx4 ∑

NxGx3

Table 3 also shows that the activation energy increases from 41 to 60 kJ/mol with increasing manganese content. This suggests an addition kinetic role of the dopant on top of the thermodynamic effects discussed previously. We hypothesize that the dopant-enriched segregated layer shall prevent OA from happening by simple steric effect in a similar way to organic agents which cap nanoparticles and inhibit growth.10 While Mn must be removed from the sites on interfaces before the new Sn−O bonds are forming at state iv, the movement of Mn from the grain boundary to either surface or into the bulk is thermodynamically unfavorable (negative and exothermic enthalpy of segregation for grain boundaries). Therefore, an excited state with an energy higher than that of state ii is expected, as the schematic graph in Figure 6 shows. The energy increase of the excited state causes the observed increase of OA activation energy, and this increment is dependent on the Mn concentration.

(21)

This estimation is used to allow comparison with average grain sizes determined by XRD line broadening in our experiments. The experimental results were fit via the grain growth curve of G eq by adjusting the integral factor D1 N(1,0) . The experimental points (open symbols) and the best fitting results (solid curve) were plotted together in Figure 1. In addition, D1N(1,0) is taken as an apparent kinetic constant K which is varying with temperature; the relation can be written as Arrhenius equation


log K = −

Ea + A0 RT

(22)

where R is gas constant, T is absolute temperature, and A0 is the pre-exponential constant. From the Arrhenius plot of various K, the apparent activation energy of OA (Ea) was estimated. The estimated apparent kinetic constants and apparent activation energy of OA are listed in Table 3. Table 3. Fitting Results by Kinetic OA Modela sample

temp (°C)

K = D1N(1,0)

Ea (kJ/mol)

S0

500 600 700 500 600 700 500 600 700 500 600 700 500 600 700

65 157 1450 48 155 1420 75 180 1320 115 290 3500 70 300 6200

41.28

S1

S2

S4

S8

45.27

38.20

45.37

Figure 6. Scheme of energetic position of states ii and iv and the excited state in between. The Mn distribution of the doped case was also schematically graphed below, where the red dots represent Mn dopants.

59.80

a

K is the apparent kinetic constant, and Ea is the activation energy of OA.

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In Figure 1, all temperatures and compositions showed satisfactory fitting, with the exception of those samples treated at 700 °C, which points at long-term time annealing (as the dash lines in Figure 1), not following the predicted trend by OA. This indicates the concurrence of other growth mechanisms for longer times, such as Ostwald ripening (OR). The two-stage grain growth has been cited elsewhere,4,6,41 and since OR would be happening mostly after OA because of the higher activation energy, the calculation of the activation energy for OA using only short annealing times is still a valid exercise. The activation energy of OA for pure SnO2 was determined as ∼41 kJ/mol (see Table 3). This value is consistent with the work of Zhuang et al.4 for OA of SnO2 nanoparticles, which showed values around 50 kJ/mol. As expected, this activation energy is significantly different compared with those reported for growth of ultrafine SnO2 powders,24 204−222 kJ/mol for grain growth and 310−354 kJ/mol for crystallite growth by surface diffusion, reinforcing that OA is the leading growth mechanism.

CONCLUSION

The energetics of oriented attachment growth of doped and undoped SnO2 were studied. By utilizing recent experimental data on the interface energies (both surface and grain boundaries), the energy evolution during OA was calculated using a geometric model. The results suggest that the stability of the attached cluster before grain realignment is of key importance in defining nanostability. That is, when a dopant such as Mn is introduced into the system and causes a net reduction in the excess energy of the attached cluster, the driving force for further growth by grain rearrangement is decreased, enabling a metastable condition. The net energy in the cluster reduction can be achieved by segregation of dopants to both grain boundaries and surfaces and is dependent on the enthalpy of segregation. The fact that the interfaces are enriched by dopants also introduces a barrier for atomic rearrangement that is responsible for an increase in the activation energy of OA. This creates a combined kinetic− thermodynamic effect. I


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