1 High Temperature Physical and Chemical Stability and Oxidation2 Reaction Kinetics of Ni−Cr Nanoparticles3 Md Taibur Rahman,† Kathryn Mireles,† Juan J. Gomez Chavez,‡ Pui Ching Wo,† Jose Marcial,†

4 M. R. Kessler,† John McCloy,† C. V. Ramana,*,‡ and Rahul Panat*,†

5†School of Mechanical and Materials Engineering, Washington State University, Pullman, Washington 99163, United States

6‡Department of Mechanical Engineering, University of Texas at El Paso, El Paso, Texas 79968, United States

7 *S Supporting Information

8 ABSTRACT: We report on the high temperature oxidation behavior and stability of9 nickel−chromium (Ni:Cr at 80:20 wt %) alloy nanoparticles (NPs) at temperatures10 up to 973 K. Structural characterization of the oxidized Ni−Cr NPs provides11 evidence for the inhomogeneous oxide formation with the presence of NiO,12 NiCr2O4, and Cr2O3 phases, indicating a degradation in the oxidation resistance of13 Ni−Cr NPs compared to comparable bulk compositions. Chemical identification14 coupled with thermogravimetric analysis indicates an increase in the activation15 energy for oxidation reaction from 1.69 to 2.98 eV for conversion ratios of 0.1 to16 0.56, respectively. The higher activation energy values compared to those reported17 for Ni NPs at similar conversion ratios demonstrate the superior oxidation resistance18 of Ni−Cr NPs compared to Ni NPs. Theoretical modeling of the experimental data19 suggests that the reaction kinetics were diffusion dominated and could be described20 by the classical Jander 3D diffusion model. The implications of these experimental data and modeling aspects are discussed to21 demonstrate the potential of these Ni−Cr NPs for high temperature applications.

I. INTRODUCTION

22 Nickel−chromium (Ni−Cr) alloys have found widespread use23 in high temperature applications due to their high melting point24 (∼1400 °C), high electrical stability with temperature (e.g., low25 temperature coefficient of resistance, i.e., TCR, of ∼85 ppm/26 K),1−4 and a high oxidation resistance.5−9 For example, the27 Ni−Cr alloys are one of the oldest known materials used as28 resistive heating elements.10 In addition, the bulk Ni−Cr alloys29 have also been used under ambient conditions when the30 electrical stability under temperature drifts is important.11−13

31 Recently, environmentally sustainable fabrication methods such32 as additive manufacturing and printed electronics have33 necessitated the use of materials in the nanoparticle (NP)34 form rather than the bulk for device manufacturing. For35 example, NP-based additive methods have been used to36 fabricate electronic devices such as biosensors,14 capacitive37 touch sensors,15,16 antennas,17 and flexible conductive net-38 works.18 However, utilization of Ni−Cr NPs in these emerging39 technologies requires a detailed, fundamental understanding of40 their oxidation behavior and high-temperature chemical41 stability. Furthermore, a fundamental understanding of the42 oxidation behavior of Ni−Cr at the nanoscale is also of interest43 for their potential applications in catalysis,19 semiconductor44 metallization,20 and the passivation of alloys.21

45 The oxidation behavior of alloys is highly complicated, and46 the process depends upon the compositions and diffusivities of47 different species at a given temperature.9,22 In the case of bulk48 Ni−Cr alloys, it is generally recognized that in order to support49 a predominantly Cr oxide layer at the alloy-scale interface, a

50minimum Cr content of about 10 wt % is required.23 The oxide51scale in such cases is stable with no evidence of undesirable52spinel (NiCr2O4) and only a thin NiO layer present from the53time of oxide nucleation.23 For bulk Ni−Cr alloys with Cr54content ≤10 wt %, however, the oxide scale is unstable and55consists of micrometer-length-scale layers of an outer zone of56NiO, an intermediate zone of NiO containing spinel particles57(i.e., NiCr2O4), and an inner region containing Cr2O3 particles58embedded in nearly pure Ni.24,25 As would be expected, the59bulk Ni−Cr alloys with 20 wt % Cr (i.e., the alloy composition60chosen for the current study) form a highly stable oxide up to61800−1200 °C.23,26,27

62It is known that at nanoscales the high surface-to-volume63ratio of the oxidizing species promotes the inward diffusion of64oxygen and outward diffusion of metal ions through the oxide65layer, required for the continued oxidation reaction.28−33

66Although the details of Ni−Cr NP oxidation, and hence its67stability, are largely unknown, several recent in situ TEM68observations have shed some light on oxidation initiation in Ni−69Cr alloys.34,35 Initial stages of Ni−9 wt % Cr oxidation using70environmental TEM showed a step-by-step adatom growth71mechanism in 3D with a nonuniform oxidation due to local72surface kinetic variations.35 Further, it was reported that for73Ni−Cr alloys with Cr content lower than about 14 wt % the Cr74based oxides could not be detected in the initial oxidation stage,

Received: November 17, 2016Revised: January 26, 2017Published: January 27, 2017

Article

pubs.acs.org/JPCC

© XXXX American Chemical Society A DOI: 10.1021/acs.jpcc.6b11560J. Phys. Chem. C XXXX, XXX, XXX−XXX

cxs00 | ACSJCA | JCA10.0.1465/W Unicode | research.3f (R3.6.i12 HF01:4457 | 2.0 alpha 39) 2016/10/28 09:46:00 | PROD-JCAVA | rq_8031540 | 2/03/2017 08:53:28 | 11 | JCA-DEFAULT

75 while the Cr2O3 phase is always present when Cr concentration76 is >30 wt %. In other words, the initial oxidation was dominated77 by the epitaxial growth of NiO rather than Cr oxide. At lower78 Cr concentration (5 at. %), in situ TEM at 573 K showed79 different oxidation rates for Ni and Cr, with outward Ni80 diffusion, giving rise to voids in the alloy NPs.34 A similar81 phenomenon consisting of void formation in nanoparticles82 during oxidation has also been reported for Fe.36 Note that the83 oxidation kinetics of nanoparticles can be studied by measuring84 their precise weight gain as a function of heating rate by85 standard thermogravimetric analysis (TGA).37,38 This data can86 be used to obtain the activation energies at different conversion87 ratios. The oxidation mechanisms/kinetics are then identified88 by comparing the results with standard rate kinetic89 models.29,31−33,39 In this context, the fundamental mechanisms90 of oxide formation and the physical stability of the nano-91 particles in the Ni−Cr alloy system are scientifically quite92 important. In particular, the oxidation kinetics at nanoscales will93 determine the applicability of the Ni−Cr nanoparticles in94 various high temperature applications and has not been95 investigated before. The ultimate goal for the present work,96 therefore, was to carry out a detailed study of the high97 temperature oxidation of a commonly used Ni−Cr alloy (with98 20 at. % Cr) NPs and determine the structural changes, phases99 formed, and the oxidation kinetics. Spherical Ni−Cr nano-100 particles were subjected to oxidation for up to 973 K in a TGA101 apparatus to identify the precise weight gain and the oxidation102 conversion ratio. Transmission electron microscopy (TEM)103 and selective area electron diffraction (SAED) were used to104 directly observe the nanoparticles and gain insight into the105 resultant phases of the formed oxides. The nanoparticles were

106further analyzed using X-ray diffraction (XRD) for amorphous/107crystalline phase identification and to characterize particle108coalescence, crystallite sizes, and lattice strain. The activation109energies of the oxidation reaction were then calculated at110different oxide conversion ratios. Finally, we used this111information to identify the active oxidation mechanisms for112this alloy.

II. EXPERIMENTS113The Ni−Cr alloy NPs had a composition of Ni:Cr, 80:20 wt %,114a spherical shape, an average diameter of about 70 nm, and an115oxygen passivation layer around the particles (oxygen content116of 3 wt %) from manufacturer specifications. TheNPs were117subjected to TGA analysis in a Discovery Series thermogravi-118metric analyzer (TA Instruments, New Castle, DE). The weight119of the Ni−Cr alloy NPs used for TGA was ∼8.75 ± 0.15 mg.120The Ni−Cr nanoparticles were placed on a platinum TGA pan121with a diameter of 10 mm. All experiments were performed122under atmospheric pressure conditions using air as the oxidant.123The gas flow rate was set as 20 mL min−1 for all the124experiments. The experiments were started at room temper-125ature and performed at five different heating rates varying from1265 to 25 K min−1 (both included) in steps of 5 K min−1. The127measurements were stopped upon reaching a temperature of128973 K (set by the TGA pan capability). This temperature was129well exceeding the temperature range of interest where130electronic chips can survive in high temperature sensor circuits131(∼723 K for the current state-of-the-art wide-band-gap132semiconductors such as SiC40) but was not enough to133complete the nanoparticle oxidation process as confirmed by134XRD studies afterward.

Figure 1. TEM micrographs of (a) as-received NiCr nanoparticles and (b) oxidized NiCr nanoparticles (post-TGA, heated at 5 K min−1).

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135 The morphology and crystal structures of the samples pre-136 and post-TGA were examined through imaging and SAED137 analysis in a TEM (Philips CM200, operating at 200 kV and138 equipped with a LaB6 filament and a Gatan CCD camera). The139 TEM samples were prepared by immersing the Ni−Cr140 nanoparticles (as-received or oxidized) in ethanol and141 sonicating for 2 min before deposition onto a carbon-coated142 TEM copper grid. The XRD study on nanoparticles (as-143 received and oxidized) was carried out at room temperature144 with a PANalytical X’Pert Pro MPD X-ray diffractometer145 (PANalytical Inc., EA Almelo, Lelyweg, Netherlands). The146 XRD used Cu Kα radiation (λ = 1.5406 Å) at 45 kV and 40147 mA. Scans were taken in Bragg−Brentano geometry with a148 0.05° step size and a 10 s dwell. One scan was taken for a bulk149 powder sample of the precursor material. For the oxidized150 samples, 12 scans were summed together in order to increase151 the signal-to-noise ratio. Lattice parameters and phase ratios152 were least-squares fit using Rietveld refinement with HighScore153 Plus software (PANalytical, EA Almelo, Lelyweg, The Nether-154 lands).

III. RESULTS AND DISCUSSION155 A. High Temperature Structural and Phase Stability of156 Ni−Cr Nanoparticles. Transmission Electron Microscopy157 (TEM). The representative TEM images of the as-received and

f1 158 post-TGA Ni−Cr NPs are shown in Figures 1a and 1b,159 respectively. The as-received Ni−Cr nanoparticles had a size160 distribution of ∼77 ± 31 nm. Some outliers (large particles) are161 also observed. The particle size range was reasonably close to162 the supplier specification of the mean diameter of 70 nm. The163 higher magnification image in Figure 1a confirmed the spherical164 shape of the as-received particles. The particles had a core−165 shell structure, with the core showing the Ni−Cr alloy and the166 shell with the oxide passivation (thickness of 3.85 ± 0.48 nm)167 which was used to prevent NP agglomeration during dispersion168 according to the supplier. Note that similar oxide passivation (a169 few nanometers thick shell layer) is observed in other NP170 systems (e.g., Fe41,42) and prevents agglomeration. The Ni−Cr171 NPs exposed to 973 K and removed from the TGA (Figure 1b)172 were approximately equiaxed but not spherical and had Feret173 diameters (i.e., distance between the two parallel planes174 restricting an object perpendicular to that direction) ranging175 from ∼80 to ∼120 nm. These particles also showed a high176 degree of oxidation (as confirmed by TEM-SAED and XRD).177 The irregular shape of the oxidized nanoparticles is likely to be178 the result of a nonuniform oxidation process that occurred179 along the spherical surface of the as-received NPs as observed180 from other Ni−Cr systems in the literature.35 This oxidation181 behavior is completely different compared to bulk Ni−Cr alloys182 with same composition that show a near ideal Cr2O3 scale183 formation.27

184 The SAED patterns of the oxidized and as-received185 (nonoxidized) nanoparticles obtained in the TEM are shown

f2 186 in Figure 2a and Figures 2b,c, respectively (see Figure S1 for187 images without annotations). The ring-shaped diffraction188 patterns in both cases suggest the presence of randomly189 oriented nanocrystals, which is in agreement with the TEM190 images shown in Figure 1. The SAED pattern obtained from191 the nonoxidized sample (Figure 2a) shows strong reflections192 close to Ni and Ni3Cr. We note that Ni and Ni3Cr share similar193 crystal structures and lattice parameters, making it difficult to194 unambiguously differentiate between them. It is, however, very195 likely that both phases are present given that Ni3Cr has 22.8 wt

196% of Cr, which is very close, but not equal, to the manufacturer197specification on the overall Cr concentration. Half of the SAED198pattern obtained from the oxidized sample (Figure 2b) is199shown adjacent to that obtained from the nonoxidized sample200(Figure 2a) for comparison. In the SAED for the oxidized

Figure 2. (a) Typical SAED patterns obtained from the nonoxidizedsample. (b) SAED pattern for the oxidized sample at one locationindicating the presence of NiO. (c) SAED pattern of oxidized sampleat another location (area encircled with dotted line in (d), and (d)bright-field image of a particle cluster in the oxidized sample. Inset isan enlarged image of a particle showing dislocation structures(arrowed). The dotted circle indicates the approximate size andlocation of the SAED aperture used to obtain the diffraction pattern in(c).

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201 sample, strong reflections close to NiO, in addition to Ni and/202 or Ni3Cr, were observed. Comparing the two SAED patterns203 obtained from the two samples, there are some stronger204 reflections along most of the diffraction rings in the oxidized205 sample. In addition, there are only a few spots for a certain206 crystal orientation (e.g., only one or two strong reflection spots207 corresponding to the (002) planes for Ni and Ni3Cr),208 indicating that the particles are favorably oriented in a certain209 orientation. The spherical crystals of the as-received NPs210 (Figure 1a), however, are more likely to be randomly oriented211 leading to a diffraction pattern that consists of complete212 reflection rings (Figure 2a). A close examination on the SAED213 patterns obtained from as-received and oxidized NPs reveals214 that the diffraction rings exhibit a finite width. This finite width215 indicates that the lattice parameters have a range of values,216 which is often observed in nanoparticles due to the relatively217 larger volume of crystal surface (distortion). Of note, the SAED218 in Figure 2b did not show any Cr oxides, indicating a219 dominance of the oxidation of Ni over that of Cr in the220 nanoparticle system.35 This behavior is closer to that shown by221 bulk NiCr alloys with <10 wt % Cr,24,25 indicating that the222 benefit of adding Cr to improve the oxidation resistance of Ni is223 diminished at nanoscale. In order to further investigate if Cr224 was oxidized, we obtained SAED patterns from several225 locations in the oxidized nanoparticles. Figure 2c shows the226 SAED pattern obtained from an area on an oxidized227 nanoparticle cluster indicated with a dotted circle in Figure228 2d (different location compared to that used to obtain the

229SAED shown in Figure 2b). Only a small number of diffraction230spots are visible in this SAED pattern, suggesting that there are231only a small number of crystals within the encircled area. In232addition to NiO, this area shows the presence of NiCr2O4 and233Cr2O3, indicating that the Ni−Cr oxidation process consists of234reactions involving both of the species and occurs in a235nonhomogeneous manner. Nonhomogeneous oxidation (in-236dicated by the segregation of Cr oxide from Ni oxide) was also237observed in Ni−5% Cr at nanoscale recently.34 Interestingly,238dislocations (indicated by arrows in the inset of Figure 2d) can239be observed from this cluster of particles. The volume of240material that contains the dislocation must be a single crystal241that is large enough to allow the dislocation structures. Large242particles as such are likely to be outliers as observed in Figure2431a or a result of particle agglomeration that formed during high244temperature exposure.245X-ray Diffraction (XRD). The XRD patterns of the as-246received Ni−Cr NPs and those post-TGA (subjected to the247four heating rates of 5, 15, 20, and 25 K min−1) are shown in248 f3Figure 3. The multiple peaks observed in Figure 3a indicate that249the as-received Ni−Cr NPs had a polycrystalline structure and250that no oxide phases were detected. For the oxidized samples,251the Ni oxide phases appeared for all the heating rates, along252with a distortion of the most intense (111) peak as shown in253Figure 3b. The database entries used for Rietveld refinement254were Ni3Cr (98-010-2820)43 and NiO (98-024-6910).44 The255XRD was not able to detect any Cr oxide phase, likely due to256low concentration of Cr or due to inhomogeneous oxidation, as

Figure 3. X-ray diffraction (XRD) results for the NiCr nanoparticles at different conditions. (b) High resolution scan of the maximum intense peak.(c) Lattice constant from the XRD data for as-received and post-TGA samples heated at different rates. (d) Crystallite size from the XRD data for as-received and post-TGA samples heated at different rates.

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257 discussed in section A. The lattice constant for pure Ni−Cr258 NPs from the d-spacing of the most intense peak was 3.5446 Å,259 in good agreement with that reported previously.45 Note that260 the lattice constant is expected to increase due to the sintering/261 melting of the NPs and the resulting agglomeration during heat262 treatment. The lattice parameter may also increase due to the263 ionic radius mismatch between Ni (0.69 Å) and Cr (0.61 Å)264 along with the diffusion process occurring at high temperature.265 Figure 3c shows lattice constants for NPs heated at different266 heating rates along with the as-received NPs. The lattice267 constant for post-TGA samples is high compared to that in the268 as-received condition, with the highest value for the NPs heated269 at the highest rate (25 K min−1). Figure 3d shows crystallite270 size (D) for NPs heated at different heating rates along with the271 as-received NPs. The crystallite size (D) of the films was272 evaluated based on Scherer’s formula46

λβ θ

=D0.9cos273 (1)

274 where λ is the X-ray wavelength (λ = 1.5046 Å), β is the full275 width at half-maximum (fwhm), and θ is the Bragg diffraction276 angle. The crystallite size increased for the heat treated samples277 by about 24% (Figure 3d).278 B. Thermal Analysis of the Ni−Cr Nanoparticles’279 Oxidation Behavior. The weight gain of the NPs due to280 oxidation was then measured by the TGA technique. These281 results were combined with the phases identification described282 in Sections A and B to obtain the oxidation conversion ratio for283 the Ni−Cr NPs at different temperatures. Note that the284 conversion ratio, α, is the ratio of converted/oxidized fraction, x285 of the alloy NPs, to the maximum possible conversion fraction286 xmax. This can be obtained only by knowing the components of287 the alloys that have undergone oxidation. The rate of the solid-288 state reaction, dα/dt, is a linear function of temperature289 dependent rate constant k(T) and a temperature-independent290 function, f(α), as29,32,47

α α=t

k T fdd

( ) ( )291 (2)

292 The conversion ratio for the TGA measurements is given by293 the formula

α =−−

W WW W

t i

f i294 (3)

295 where Wt is the weight at any time, t, Wi is the initial weight of296 the specimen, and Wf is the final weight of the specimen. For297 nonisothermal/constant heating rate process,33 eq 2, can be298 further modified as

αβ

α= −

Tk

fdd

( )e E k T0 /a B

299 (4)

300 where heating rate, β = dT/dt, is a constant, kB is the301 Boltzmann constant, and k0 is the pre-exponential factor.302 Rearranging the terms of eq 4 and integrating from the initial303 temperature T = T0, where oxidation ratio α0 = 0 to T = Tp,304 gives29

∫ ∫

∫

αα β

β

βα

=

=−

= =

α−

∝

fk

T

k Ek

yy

y

k Ek

p y g

d( )

e d

exp( )d

( ) ( )

TE k T

y

p

0

0

0

/

0 a

B2

0 a

B

p p

p

a B

305(5)

306where y = Ea/kBT and yp = Ea/kBTp. The solution of eq 5 can307give the activation energy, Ea, at a given conversion ratio, α.308Since eq 5 is not solvable analytically, we use three established309approaches, namely, the Kissinger method,48 the Flynn−Wall−310Ozawa (FWO) method,49 and the Starink method.50

311In the Kissinger method,48 the integral function can be

312simplified as ∫=

∝ −p y y( ) dy

yy

exp( )

p2 , and eq 5 can be expressed

313as

∫ αα β

= + −α ⎛

⎝⎜⎞⎠⎟

⎛

⎝⎜⎜

⎞

⎠⎟⎟f

k EE y

yd( )

ln ln1

pp0

0 a

a2

p

314(6)

315For a constant fraction transformed, eq 6 simplifies to

β = − +⎛⎝⎜⎜

⎞⎠⎟⎟T

Ek T

Cln1

p p2

a

B1

316(7)

317where C1 is the integral constant

∫ αα

= −α

Ck k

E fln ln

d( )1

0 B

a 0

p

318A plot of ln β⎜ ⎟⎛

⎝⎞⎠Tp

2 vs ⎜ ⎟⎛⎝

⎞⎠T

1

pfor different heating rates can give a

319straight line having a slope equal to (Ea/Kb), giving the320activation energy.321In the FWO method,51 the integral function is taken as log322p(y) = −2.315 + 0.4567y, which simplifies eq 5 to

β = − +⎛⎝⎜⎜

⎞⎠⎟⎟

Ek T

Clog( )0.457 1

p

a

B2

323(8)

324where C2, an integral constant, is

∫ αα

= − −α⎛

⎝⎜⎞⎠⎟C

k kE f

log lnd( )

2.31520 B

a 0

p

325(9)

326The activation energy can then be obtained by plotting

β ⎜ ⎟⎛⎝

⎞⎠log( ) vs

T1

pfor different conversion ratios.

327Starink50 has developed a more general expression of f(α) as

α αα

= −−

⎜ ⎟⎛⎝

⎞⎠f ( ) (1 ) ln

11

pq

328(10)

329where p and q are constants which vary depending upon330different reaction kinetics. Considering q = 0 for any331homogeneous kinetic reactions, eq 10 can be used to get

β = − +⎛⎝⎜⎜

⎞⎠⎟⎟

⎛⎝⎜⎜

⎞⎠⎟⎟T

AEk T

Cln1

p p1.8

a

B3

332(11)

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333 where C3 is the integral constant, A = 1.007−1.2 × 10−5Ea, with334 Ea expressed in kJ/mol. The activation energy can be obtained

335by plotting β⎜ ⎟ ⎜ ⎟

⎛⎝

⎞⎠

⎛⎝

⎞⎠ln vs

T T1

p p1.8 for different conversion ratios.

f4 336 Figure 4 shows the TGA data (weight of the nanoparticles vs337 temperature) for different heating rates for the Ni−Cr

338 nanoparticles used in this study. The data show an increase339 in weight of the samples starting at about 275 °C and a total340 weight gain of about 18−22%, with higher gain for lower341 heating rates. The start of the oxidation for Ni−Cr nano-342 particles is at lower temperatures, whereas bulk Ni−Cr is stable343 up to 1000 °C.9 Note that while plotting the data in Figure 4,344 we have assumed a transition of Ni to NiO and Cr to Cr2O3.345 The oxidation of Ni to NiO was confirmed by TEM/SAED and346 XRD in the current work. Oxidation of Cr to sesquioxide Cr2O3347 was confirmed in the TEM/SAED study (section A). This gives348 a theoretical maximum weight gain of ∼30.8 wt % and was used349 to calculate the conversion ratio using the actual weight gain at350 that temperature. The effect of the thin initial oxygen351 passivation over the nanoparticle was deducted from the352 experimental value by modifying eq 3 as described by Song et353 al.29

f5 354 Figure 5 shows the activation energies as a function of the355 conversion ratio calculated by the three methods mentioned356 above. The parameters to estimate the activation energies were

357taken from the thermogravimetric data (Figure 4). The358activation energies increased from about 1.7 eV to about 2.9359eV for the conversion ratios of 0.1 and 0.56, respectively. The360activation energy profile is similar for all the three approximate361methods (within ∼1.7%) and is only a function of the362conversion ratio. The increasing trend for the activation energy363shown in Figure 4 is similar to that seen for the oxidation of the364Ni nanoparticles.29 Activation energy for Ni−Cr is higher than365that for Ni by about 20−30% for identical respective conversion366ratios.29,31−33,39 This data are consistent with the fact that Ni−367Cr is known to have higher oxidation resistance in the bulk368form when compared to Ni due to a more stable oxide formed369by Cr that can impede further oxidation. The increase in the370activation energy observed with the conversion ratio seen in371Figure 5 can be explained from the fact that the reactants are372seen to undergo continuous modifications during oxidation due373to factors such as crystal defect formation (dislocations in374Figure 2d), particle agglomeration (and hence the surface to375volume ratio) (Figures 1b and 2d), and an increase in the376crystalline strain (Figure 3c). Also, the particle boundary faces377can change to different crystallographic indices during the378reaction, and hence the initial reactivity may be different than379that for the agglomerated nanoparticles as the reaction380progresses.381C. Reaction Kinetics and Mechanism. Direct TEM382observation and SAED analysis in conjunction with the XRD383analysis as described above allow us to identify the reactant384phases and gain unprecedented detailed understanding of the385oxidation process. In order to determine the reaction kinetics,386we fit the experimental data with existing kinetic models.29 The387TGA data for 5 K/min heating rate were fitted with different388models and plotted in a kinetic “master plot”. The master plot389is obtained by plotting g(α)/g(α0.5) as a function α, i.e., by390using half-conversion ratio (α = 0.5) as a reference. The master391plots for different solid-state reaction models are summarized392 t1by Khawam47 (see Table 1). For half-conversion ratio, eq 5 can393be written as

αβ

=gk E

kp y( ) ( )0.5

0 a

B0.5

394(12)

395where y0.5 = Ea/kBT0.5. Dividing eq 5 by eq 12

αα

=g

gp y

p y( )

( )( )

( )0.5 0.5 396(13)

397Next, we plotted g(α)/g(α0.5) as a function of α for the398different oxidation models/mechanisms such as the nucleation399model, geometrical contraction model, reaction order models,400and diffusion models and compared that with the TGA data401shown in Figure 4. Since all the approximations used to solve402eq 5 give the activation energies within 1.7%, we will use the403FWO method to get g(α)/g(α0.5) and plot the conversion ratio404for 5 K min−1 heating rate (the results are the same for other405heating rates).406First, we compare our experimental data with the nucleation407models, i.e., the solid-state reactions dominated by the408nucleation processes such as crystallization,52 crystallographic409transition,53 decomposition, etc. The nucleation model assumes410constant growth of nucleus without any consideration to411growth restrictions which generally expressed as g(α) = α1/n,412with n = 1, 2, 3, ... (see Table 1). In real situations, nucleation413dominated reactions will encounter two restrictions, namely,414ingestion (i.e., existing nucleus growth eliminates nearby

Figure 4. TGA curves at different heating rates. TGA profiles show thestart of gain in the weight at about 250 °C for all heating rates and asimilar profile for all the heating rates. The maximum weight gain forthe samples is about 18−22% at a conversion ratio of 0.6.

Figure 5. Activation energies (Ea) as a function of conversion ratios.Activation (Ea) is a strong function of conversion ratio.

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415 potential nucleation sites) and coalescence (i.e., loss of interface416 between the reactant and product during the coalescence of the417 two or more growing nuclei). Avrami54 and Erofeyev55

418 incorporated these restrictions into the nucleation models419 and predicted g(α) = [−ln(1 − α)]1/n, where n = 1, 2, 3, ... (see

f6 420 Table 1). Figure 6a compares g(α)/g(α0.5) of the TGA data in

421the current study with that predicted by the nucleation models.422It is clear that the nucleation models cannot predict the423observed oxidation behavior of the Ni−Cr nanoparticles. We424thus conclude that neither ingestion nor coalescence of nuclei425are the dominant factors during the oxidation reaction/kinetics426and that the large surface-to-volume ratio of fered by the

Table 1. Solid-State Reaction Models47

model symbol f(α) g(α)

nucleation modelssecond-order power law P2 2α1/2 α1/2

third-order power law P3 3α2/3 α1/3

fourth-order power law P4 4α3/4 α1/4

Avrami−Erofeyev A2 2(1 − α)[−ln(1 − α)]1/2 [−ln(1 − α)]1/2

Avrami−Erofeyev A3 3(1 − α)[−ln(1 − α)]2/3 [−ln(1 − α)]2/3

Avrami−Erofeyev A4 4(1 − α)[−ln(1 − α)]3/4 [−ln(1 − α)]3/4

geometrical contraction modelscontracting area R2 2(1 − α)1/2 1 − (1 − α)1//2

contracting volume R3 3(1 − α)2/3 1 − (1 − α)1//3

reaction order models3rd homogeneous n = 3 (1 − α)3 1/2[(1 − α)−2 − 1]4th homogeneous n = 4 (1 − α)4 1/3[(1 − α)−3 − 1]5th homogeneous n = 5 (1 − α)5 1/4[(1 − α)−4 − 1]6th homogeneous n = 6 (1 − α)6 1/5[(1 − α)−5 − 1]

diffusion modelsone dimension 1-D 1/2α α1/2

two dimension 2-D [−ln(1 − α)]−1 (1 − α)[ln(1 − α)] + α

three dimension Jander 3/2(1 − α)2/3[1 − (1 − α)1/3]−1 [1 − (1 − α)1//3] 2

3-D, accounts changing particle size during reaction Guintling 3/2[(1 − α)1/3 − 1] −1 (1 − 2α/3) − (1 − α) 2/3

Figure 6. Kinetic model fitting for NiCr nanoparticles: (a) nucleation models (A2, A3, A4 represent different Avrami−Erofeyev nucleation modelsand P2, P3, P4 represent different power law nucleation models), (b) geometry contracting models, (c) reaction order models (n = 3−6 representsthe order of homogeneous reaction), and (d) diffusion models. Diffusion based 3D classical Jander model fits well with the experimental data.

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427 nanoparticles can make the nucleation process a noncritical factor428 in determining the oxidation reaction.429 Second, we compare the experimental data with different430 geometry contraction models. These models consider nuclea-431 tion on the surface of the crystal where the resulting reaction432 interface progresses toward the crystal center, which controls433 the rate of the reaction. Depending on crystal shape, geometric434 contraction models can be two types: (a) contracting area435 model expressed as g(α) = [1 − (1 − α)1/2]; (b) contracting436 volume model expressed as g(α) = [1 − (1 − α)1/3].56

437 However, comparing the experimental data in Figure 6b with438 the geometry contraction models suggests that these models439 are not appropriate to describe the reaction kinetics of Ni−Cr440 nanoparticles. This is not surprising since the oxidation process441 involves both the ingress of oxygen species and the diffusion of442 alloy species through the oxide scale.443 Next, we consider the homogeneous reaction order models.444 These models consider reaction rate as proportional to the445 reactants fraction remaining raised to a particular power (n = 1,446 2, 3, ...), which is the reaction order. It is clear from Figure 6c447 that all the homogeneous reaction models do not fit the448 experimental data particularly well with any nth-order449 homogeneous reaction models. There is significant mismatch450 between the theoretical and experimental curves. The reason451 could be that in the case of the current solid-state oxidation452 reactions the atoms need to permeate the oxide layer to453 continue the oxidation reaction.35

454 Lastly, we compare the experimental data with surface455 diffusion models (see Table 1), where the rate of product456 formation decreases proportionally with the thickness of the457 product barrier layer. Figure 6d shows that unlike all the458 previous models, the trends of the master plot for diffusion-459 based models matches that of the experimental data. For 1-D460 and 2-D diffusive reaction models,47 Figure 6d shows only a461 reasonable fit to the experimental data. The poor agreement is462 expected considering that the Ni−Cr nanoparticle oxidation463 process is likely to be 3-dimensional as suggested from TEM464 images (e.g., Figure 1). We now compare the 3-D diffusion465 models with the experimental data. Jander57 developed a 3-D466 solid-state reaction model, where for a number of particles, n,

f7 467 each with a radius r, and a reaction zone thickness x (see Figuref7 468 7), which will have the conversion ratio as

αρπ ρπ

ρπ=

− −n r n r x

n r

( )43

3 43

3

43

3469 (14)

470 This equation reduces to47

α α= − −g( ) [1 (1 ) ]1/3 2471(15)

472From Figure 6d, the 3-D Jander diffusive reaction model473provides an excellent fit to the experimental data and is likely to474be the dominant reaction kinetic for the oxidation process. This475is in spite of the fact that inhomogeneous oxide layer formation476was observed, which likely precludes an idealized uniform oxide477formation assumed in this model. A second 3-D diffusion-based478solid-state reaction model by Ginstling−Brounshtein58 shows a479fit better than the 1-D or 2-D diffusion models but not as good480as the Jander model. The Ginstling−Brounshtein model is481considered to be important only at high conversion ratios. It is482still not clear whether the Ginstling−Brounshtein model will483provide the best fit at high conversion ratios (>0.5) or whether484some other mechanisms are operative at that level. Because of485the distortion in particle shape observed in the current study486(Figure 1b and lattice parameters/strain in Figure 3c), there is a487question of applicability of the model itself.488On the basis of the results from Figure 6 and the discussions489above, we now postulate that microscopic diffusion mecha-490nisms (including transport) to be operating during the Ni−Cr491nanoparticle oxidation, while the Jander model does not take492into account the diffusion of two species of the alloy. Note that493metal oxides generally have ionic bonding, and therefore the494oxidation reaction involves the transport of both ions and495electrons (ambipolar diffusion in the oxide layer), giving rise to496an electric field during oxidation59 which influences the497diffusion process.60 A schematic of the possible reaction498processes involving the diffusion of Ni and Cr ions and499 f8electrons is shown in Figure 8a. If the metal ions have more500mobility than oxygen ions, new oxide will form at the oxide501interface, while higher mobility oxygen results in new oxide on502the oxygen interface. For Ni−Cr alloys, either a monolayer of503nichromate (NiCr2O4), separate layers of NiO and Cr2O3, or all504three phases NiCr2O4, NiO, and Cr2O3 can form during505oxidation. The TEM SAED patterns clearly show that NiO,506NiCr2O4, and Cr2O3 were formed due to the thermal oxidation,507but in an inhomogeneous manner, with possible epitaxial508growth of each of the oxides. The schematic in Figure 8b509illustrates the possible evolution of the Ni−Cr alloy nano-510particles during the oxidation processes. We believe that the511oxidation reaction progresses with a combined inward diffusion512of oxygen and outward diffusion of metal ions through the513oxide layer. It is likely that the Cr oxide and Ni oxide form514separately and grow epitaxially with metal ions diffusing515through the newly formed oxide to reach the surface. The516lattice mismatch between the oxides and the alloys can be517accommodated by misfit dislocations. As this process continues,518the metallic structure eventually converts to metal oxide519structure having well-defined grains, with possible agglomer-520ation of adjacent particles.521From the above results, we conclude that the Ni−Cr alloy522nanoparticles are stable up to 275 °C, which is significantly523lower than the stability temperature for bulk Ni−Cr alloys. For524example, at 800 °C, bulk Ni−Cr (80:20) shows a weight gain of525only 2.5%,26 while the equivalent weight gain occurs at ∼400−526500 °C for the nanoparticles in Figure 5. Thus, the527improvement in the oxidation resistance offered by the addition528of Cr to Ni is reduced at nanoscale when compared to bulk529alloys. We believe that the minimum Cr proportion in the Ni−530Cr alloy nanoparticles required to form a stable oxide layer is531higher for nanoparticles than that required for bulk. The532degradation of oxidation resistance at nanoscale, however, can

Figure 7. Schematic representation of a spherical particle with reactionzone considered for 3-D Jander diffusion-based reaction model.

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533 be overcome by sintering the nanoparticles in an inert534 environment using heat61 or by photonic flash sintering.62

535 Once partly sintered, the nanoparticles will rearrange to reduce536 the surface to volume ratio and surface curvatures at the537 nanoscale, and this may result in stable Cr oxides which further538 retard the oxidation process. Other methods such as promoting539 the nucleation of a stable oxide layer observed in alumina540 forming alloys (e.g., NiAl−Cr)63 needs further work. Addition-541 ally, it may be possible to increase the Cr content in the Ni−Cr542 alloys so that a stable Cr2O3 layer is preferentially formed. A543 detailed consideration of this phenomenon from the application544 perspective will be part of a future investigation.

IV. SUMMARY AND CONCLUSIONS

545 A detailed study of the high temperature physical and chemical546 stability of Ni−Cr (80:20 wt %) nanoparticles up to 973 K has547 been performed, and the oxidation mechanisms governing their548 behavior at nanoscale are reported in this paper. The TEM and549 SAED analyses showed that the Ni−Cr alloy nanoparticles are550 heavily oxidized upon exposure to 973 K and form NiO, Cr2O3,551 and NiCr2O4 as the oxide phases. The oxide formation is552 inhomogeneous and accompanied by particle agglomeration.553 The inhomogeneous oxidation behavior of Ni−Cr NPs is554 different compared to that reported for bulk alloys in the555 literature where a uniform stable chromium oxide layer is556 formed. The results suggest a significant degradation of557 oxidation resistance for these alloys at nanoscale dimension558 due to the short length scale and high surface-to-volume ratio.559 XRD analysis of the oxidized nanoparticles showed a 20%

560increase in the crystallite size and an increase in the lattice561constant, suggesting crystal distortion during oxidation. The562activation energy increase from 1.69 to 2.98 eV for a conversion563ratio of 0.1 to 0.56 suggests the formation of a kinetic barrier to564thermal oxidation as the reaction progressed. Comparison of565experimental results with existing solid-state reaction models566demonstrate that the Ni−Cr oxidation kinetics at nanoscale was5673-D surface diffusion-dominated (rather than nucleation-568dominated) and could be described by the classical Jander 3-569D diffusion model.

570■ ASSOCIATED CONTENT

571*S Supporting Information572The Supporting Information is available free of charge on the573ACS Publications website at DOI: 10.1021/acs.jpcc.6b11560.

574Original (unannotated) images of the SAED patterns of575the NiCr nanoparticles before and after oxidation (PDF)

576■ AUTHOR INFORMATION

577Corresponding Authors578*E-mail rahul.panat@wsu.edu (R.P.).579*E-mail rvchintalapalle@utep.edu (C.V.R.).

580ORCID581John McCloy: 0000-0001-7476-7771582Rahul Panat: 0000-0002-4824-2936583Notes584The authors declare no competing financial interest.

Figure 8. (a) Transport of ions and electron across the growing oxide layer on NiCr nanoparticle. (b) Schematic illustrating the postulated structuralevolution of the NiCr alloy nanoparticles to oxide phase due to high temperature.

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585 ■ ACKNOWLEDGMENTS586 This work was supported by the U.S. Department of Energy,587 National Energy Technology Laboratory (NETL), under Grant588 DE-FE0026170. We thank Mr. M. Sadeq Saleh at WSU for his589 help in obtaining some of the TEM images.

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