Structural Arrangement in Close-Packed Cobalt Polytypes - Crystal

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Structural arrangement in close packed cobalt polytypes Wojciech A. Slawinski, Eirini Zacharaki, Anja Olafsen Sjåstad, and Helmer Fjellvåg Cryst. Growth Des., Just Accepted Manuscript • DOI: 10.1021/acs.cgd.7b01736 • Publication Date (Web): 20 Feb 2018 Downloaded from http://pubs.acs.org on February 25, 2018

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Crystal Growth & Design

Structural arrangement in close packed cobalt polytypes ⇤,†,‡ Eirini Zacharaki,†,¶ Anja Olafsen Sjastad, †,¶ ´ ˚ Wojciech A. Sławinski,

˚ †,¶ and Helmer Fjellvag †Centre for Materials Science and Nanotechnology, Department of Chemistry, University of Oslo, PO Box 1033, N-0315 Oslo, Norway ‡ISIS Facility, Rutherford Appleton Laboratory, Harwell Oxford, Didcot, Oxfordshire, OX11 0QX United Kingdom ¶inGAP Centre of Research based Innovation, Department of Chemistry, University of Oslo, PO Box 1033, N-0315 Oslo, Norway E-mail: [email protected] Abstract In this paper we present a comprehensive study on how stacking faults, crystallite size, crystallite size distribution as well as shape and strain dictate the nature of the X-ray powder diffraction patterns of small (< 20 nm) and large (> 20 nm) cobalt (Co) nanoparticles. We provide a unique library of simulated diffractograms which can be used for fingerprint analysis. Likewise, the simulated data are used as a basis for structural refinements of experimentally obtained X-ray powder diffractograms. We provide examples of using the library for fingerprint analysis and for full structural analysis of synthesised Co nanoparticles. Structural refinements presented in this study allow to reveal fine structural details that directly correlate to different behaviour upon heating in a CO atmosphere relative to H2 or He atmosphere. All calculations were performed using the Discus package and the Debye scattering equation.

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Introduction Cobalt (Co) based nanomaterials are attractive for applications linked to catalysis and magnetic storage. For example, within Fischer-Tropsch (FT) synthesis, Co-based catalysts are extensively used in industrial scale. 1,2 The design of a FT-catalyst depends strongly on the type of feedstock and the targeted hydrocarbon product to be synthesised; hence there is no universal code on how to rationally include all beneficial features to the catalyst. More specifically, the particle size, polytype and stacking faults, promoters, type and nature of support are critical ingredients to control when optimizing a catalyst for a set of pre-fixed FT-process conditions. 1,3,4 At ambient pressure metallic cobalt is reported to crystallize with hexagonal close packed (hcp) AB-packing or cubic close packed (ccp) ABC-packing, where the hcp variant is the thermodynamic stable polytype below 420 °C. 5 Due to particle size effects, Co may be also stabilized in the ccp form below 420 °C. 6 In addition, metastable cobalt modifications taking the b -Mn-type structure and a body centre cubic (bcc) structure are known. 7–9 Metallic cobalt is also reported to exist in various high pressure modifications. 10 As shown by Longo and co-workers, 11 the polytypism of most nanostructured metals possessing close packed crystal structures are complicated in the sense that hcp and ccp sequences can be present at the same time in the individual particles at the nanometre scale depending on particle size and shape as well as on applied synthesis route. This implies that the long range three-dimensional (3D) translational symmetry becomes broken. Any structure that exhibits some level of disruption of the perfect layer sequence is referred to as a stacking faulted structure. Figure 1 shows three examples of structures built from 2D-hexagonal close packed layers; ccp, fully disordered structure with stacking faults (intergrowth) and hcp. In the literature few efforts are reported on how to describe hcp-ccp stacking disorder in cobalt beyond the situation of identifying the concurrent appearance of both stacking sequences in X-ray powder diffractograms. The first approach to model cobalt structural disorder was performed through whole pattern integration using the Debye scattering equation. 11–13 This allowed modelling of local disorder and short range ordering in single nanoparticles, but the method cannot describe average powder patterns as experimentally obtained 2


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for bulk samples (or large nanoparticles). Whole X-ray powder diffraction (XRPD) patterns may be modelled by using the DiFFAX program. 14 This approach allow one to calculate XRPD patterns for structures with stacking faults, but neither refinement, nor multiple phase analysis can be performed. More recently the Discus software 15,16 has proved highly suited for refining stacking faulted structure of two dimensional (2D) flakes and 3D bulk structure of layered double hydroxides. 17 The methodology described in details in the present paper, has recently been used by us to demonstrate modelling of Co-based Fischer-Tropsch catalysts at operando conditions. 2 In this study we simulate X-ray powder diffractograms of large (> 20 nm) and small (< 20 nm) hcp-ccp Co nanoparticles using total scattering analysis and the Debye scattering equation, respectively. For large nanoparticles we focus on stacking faults, while for small particles the modelled patterns include also the additional effects of crystallite size, shape, strain and size distribution. The obtained library of simulated diffractograms pave the way for identifying signatures in experimental diffractograms of large and small Co nanoparticles, either by refining experimentally obtained X-ray powder diffractograms or by solely comparing simulated diffractograms with real diffractograms for facile fingerprint analysis. In the current work we provide examples where we refine experimental diffractograms and apply the fingerprint approach to explain the fine nanostructuring in complex Co nanoparticles.

Simulations and experimental Crystal structure of cubic, stacking faulted and hexagonal close packed cobalt Cobalt nanoparticles crystallize both in ccp and hcp structures. Figure 2 shows single crystallographic unit cells for both cases. For the ccp structure (left), the unit cell is rotated in order to make the [111] layer stacking direction parallel to [001] in the hcp structure (right). This projection reveal the close similarities between the two structures. Both ccp and hcp structures are formed by stacking identical hexagonal close packed layers. Each layer is a triangular lattice, described in hexagonal setting with the angle between [100] and [010] equal to 120°. In a hexagonal setting, we 3



Figure 1: Three examples of ccp, stacking faulted (intergrowth) and hcp crystal structures represented in terms of stacked layers. The ccp and hcp structures are built with sequences of ABC... and AB..., respectively. The stacking faulted intergrowth structure is built with a fully random sequence. set the first layer in (0, 0, 0). The next layer is translated by [1/3, 2/3, 1/2] in both packing variants. The difference occurs when the third layer is to be placed. In the ccp structure, the translation between 2nd and 3rd layer is [1/3, 2/3, 1/2] again, whereas in the hcp structures the 3rd layer is translated by [2/3, 1/3, 1/2]. This is why we describe the ccp structure as ABC-type and hcp as AB-type where A, B and C indicate layers translated with respect to the origin by [0 0 0], [1/3, 2/3, 0] and [2/3, 1/3, 0]. Stacking faulted structures are obtained when a disruption of the perfect ABC- or AB-layer sequence occurs. In order to quantify the level of stacking faults in a structure we introduce a probability of stacking faults pABC defined as the probability of the next layer being translated by [1/3, 2/3, 1/2]. Using this notation, the ccp structure has pABC = 1.0 and the hcp structure has pABC = 0.0. For 0.0 < pABC < 1.0 the structure will have stacking faults. The most disordered structure occurs for pABC = 0.5, which means that there is no preference between ccp and hcp layer sequences (i.e. randomly stacked layers).

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Figure 2: Unit cells of ccp (left) and hcp (right) crystal structures. The ccp unit cell is rotated to make [111] parallel to [001] in the hcp unit cell. The connected atoms show the hexagonal close packed planes, which are here considered as the key building units.

X-ray powder diffraction simulations of large and small nanoparticles The atomic arrangement of large nanoparticles (> 20 nm) is typically investigated by standard crystallographic methods, for instance by the classic Rietveld method. In such cases, additional peak broadening is frequently added to the instrumental resolution function as a parameter. This is to attempt modelling effects of small crystallite size or strain. In the case of anisotropic particle shape, the anisotropic peak broadening should be considered. However, Rietveld analysis cannot be used for particles with significant level of structural disorder like stacking faults. In order to demonstrate the ability of quantitative analysis of stacking faulted structures ccp-hcp based large metal nanoparticles (> 20 nm; large particle approach), a series of powder diffraction patterns has been calculated using the Discus package. 15 The calculations were performed using the following values: ˚ and chex = • Unit cell parameters of the hexagonal (hcp) unit cell were set to ahex = 2.5055 A ˚ 4.0914 A. • The z-translation between the layers was equal to 0.5 ⇥ chex for ccp and hexz (hexz

shi f t

shi f t

⇥ chex

= 0.4966) for hcp structures. This means that the interlayer distance in the ccp

structure is slightly larger than for the hcp variant. • The peak profile was modelled by a pseudo-Voigt function with the h parameter equal to 0.5 and peak width parameters UVW of 0.6367, -0.1230 and 0.0084 (i.e. typical values in the 5



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case of Co nanoparticle refinements). • Each partial pattern was calculated assuming 2000 layers in the model in order to obtain better averaging. The final patterns were calculated as an average of 200 partial patterns in order to obtain proper integration over different possible stacking sequences and thereby mimic experimentally obtained bulk samples. For small nanoparticles (< 20 nm; small particle approach) the Debye scattering equation 18 is adopted to analyse structural details. The diffracted intensity I(Q) for the given scattering vector Q is equal to

I(Q) =

N

N

ÂÂ

i=1 j=1

fi (Q) f j (Q)

sin(Qri j ) Qri j

where i, j changes from 1 to the number of atoms N in the crystal, fi (Q) is the atomic scattering factor of atom i, and ri j is the distance between atoms i and j. Since the formula requires double summation over all atoms, the computing time scales with N 2 and since the number of atoms N scales with the particle volume by ⇠ R3 it is therefore proportional to D6 , where D is the diam-

eter of a spherical particle. 19 For this reason the formula can only be used for relatively small nanoparticles. In our study we set the limit at D < 20 nm for the use of the Debye formula. For the case study of the influence of crystallite size distribution the final pattern was calculated as an average of 1000 individual patterns. Each individual pattern was calculated using the Debye scattering equation assuming Log-Normal crystallite size (radius r) distribution 20,21 defined as 1 P(r, r0 , s ) = p exp 2prs

✓

(ln(r)

ln(r0 ))2 2s 2

◆

where r0 = 5 nm is a median of the distribution and s is the parameter describing its width which is varied from 0.05 to 0.5. For the case with uniform crystallite size the calculated diffraction pattern will be denoted as s = 0.0.

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Sample preparation Cobalt nanoparticles (NPs) with different stacking fault probabilities were obtained under inert conditions via thermal reduction of bis(2,4-pentanedionato)cobalt(II) [Co(acac)2 , 97 %] in benzyl alcohol (BA, 99.8 % anhydrous) in the presence of oleic acid (OA, 99 %). For some syntheses 1,2-dodecanediol (90 %) was used in addition as the reducing agent. All synthesis preparations were carried out using standard Schlenk line- and glove box techniques in Ar (5.0, Aga). All listed chemical were purchased from Sigma-Aldrich. Co nanoparticles enriched in intergrowth phase (denoted as Sample 1) were produced as follows: 0.45 g Co(acac)2 (1.75 mmol) were dissolved in 18 mL BA containing 175 µL OA (0.55 mmol) in a 50 mL round bottom flask. The reaction mixture was heated to 100 °C and stirred for 15 min before transferring to a Teflon-lined stainless steel autoclave for solvothermal treatment at 200 °C for 48 h. After cooling to room temperature, the resulting suspension was centrifuged, and the precipitate was thoroughly washed with ethanol and stored under an inert atmosphere. Co nanoparticles enriched in hcp (denoted as Sample 2) were synthesised at ambient pressure via 1,2-dodecanediol assisted thermal reduction of Co(acac)2 in BA. A reaction mixture of 0.45 g Co(acac)2 (1.75 mmol), 175 µL OA (0.55 mmol) and 18 mL BA was heated to refluxing conditions under continuous stirring in a 250 mL round bottom flask. When the reaction mixture reached 200 °C, a solution of 1,2-dodecanediol (7.2 mmol) in 5 mL BA, preheated inertly at ⇡ 120 °C, was rapidly injected to the BA/OA/Co(acac)2 hot solution. The reaction was allowed to run to completion at refluxing conditions for 2 h and subsequently ice quenched. The obtained particles were isolated by ethanol flocculation and centrifugation, washed in ethanol and stored as described above. Scanning electron microscopy (SEM) images document that both samples have irregular particle morphologies with particle sizes ranging from ⇠ 10 - 100 nm (see Figure S1 in Supplementary Information).

Synchrotron X-ray powder diffraction data collection Powder diffraction data were collected using the high-resolution powder diffractometer at the Swiss-Norwegian Beamlines (SNBL, station BM01B) at the European Synchrotron Radiation Fa7



cility (ESRF). A quartz capillary-based in situ cell was used, as described by Tsakoumis et al., 22 for variable temperature measurements in controlled gas atmosphere. The samples were loaded in 0.7 mm diameter quartz capillaries, with a bed length of ⇡ 10 mm, and kept in place by quartz wool plugs to avoid sample loss during gas flow. The capillaries (open at both ends) were subsequently mounted and sealed by gluing on stainless steel brackets. Sample heating (temperature range 20 550 °C, heating rate 5 °C/min) was provided by a vertical hot air blower. Gas flows were supplied by a set of mass flow controllers calibrated for the relative small flows (⇡ 5 mL/min). 5 vol % CO/He and 4 vol % H2 /He gas mixtures (Messer Schweiz AG, Switzerland), and He (Air Products, France) were used with purity of 99.2 % or higher. The wavelength, calibrated by means of ˚ and the scattering vector length used in all the refinements a NIST Si standard, was l = 0.50486 A ˚ for real samples was 2.38 A

1

1

˚ . The data were collected by a high resolution < Q < 7.59 A

6-channel detector equipped with Si[111] analyser crystals. The measured XRPD patterns were analysed using the Discus 15 package. The refinement was done using the evolutionary algorithm implemented in the Diffev program. 15 The estimated errors of the refined parameters are calculated as a standard deviation of the last generation of parameters from the evolutionary algorithm.

Results and discussion Simulation of X-ray powder diffraction patterns of large particles (> 20 nm) Large metallic cobalt nanoparticles (> 20 nm) with ccp and hcp close packed structures frequently suffer from stacking faults. Stacking faults give rise to specific signatures in the X-ray powder diffraction patterns, which cannot be refined with classic Rietveld type analysis. By applying the large particle approach using the Discus software we have simulated diffraction patterns of Co nanoparticles for different stacking fault probabilities, pABC . The simulation results are reported in Figure 3. Diffraction patterns for both pABC = 1.0 (ccp structure) and pABC = 0.0 (hcp structure) show sharp Bragg reflections as they possess perfect packing. When pABC differs from 0.0 and 1.0, selected Bragg reflections (200)ccp , (101)hcp , (102)hcp , (103)hcp become significantly 8


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broader, before they finally disappear for pABC = 0.5. On the other hand, there is a group of Bragg reflections (220)ccp /(110)hcp , (311)ccp /(112)hcp which remains unaffected by stacking faults. Further, as a consequence of hexz

shi f t

< 0.5 the (111)ccp /(002)hcp and (200)ccp Bragg peaks become

shifted in 2q position when introducing stacking disorder. With reference to the simulations, one can conclude that even for relatively low probabilities of stacking faults (pABC ⇡ 0.05 or pABC ⇡ 0.95) major changes become evident in the powder diffraction patterns. The practical implication of this observation is that even minor quantities of stacking faults must be taken into account when modelling real metal nanoparticles in detail.

Figure 3: Series of simulated X-ray powder diffraction patterns for ccp-hcp stacking faulted Co nanoparticles by means of the large particle approach. Patterns are calculated for several stacking faults probabilities pABC from 0.00 to 1.00. The two sets of Miller indices are shown for hcp and ˚ ccp structures. l = 0.50486 A.

Simulation of X-ray powder diffraction patterns of small particles (< 20 nm) Structural irregularities as stacking faults are also prominent in smaller Co nanoparticles (< 20 nm). In addition, parameters such as crystallite size, shape and strain may influence the diffraction pattern to a large extent. Some of these effects lead to anisotropic Bragg peak broadening and/or peak position shift. It is difficult to deconvolute these effects since a combination typically occurs simultaneously. In the following we simulate X-ray powder diffractograms by means of the Debye 9



scattering equation, bringing each of the effects systematically into account. In our study we also limit ourselves to the case with a single direction of stacking faults (more complex models are not considered here). Effect of stacking disorder: In Figure 4 we present a series of X-ray powder diffractograms for spherical 5 nm sized nanoparticle for different levels of stacking faults. Again, pABC = 1.0 and 0.0 leads to ideal ccp and hcp stacking, respectively. All values between 0.0 and 1.0 provide structures with stacking faults. The current simulations corroborate with those for larger NPs (> 20 nm) (Figure 3); giving similar trends with respect to peak broadening, shift in certain peak positions and disappearance of Bragg reflections as a function of pABC . The more significant peak broadening observed for the 5 nm particles relative to the larger particles is the signature of the size effect.

Figure 4: Series of simulated X-ray powder diffraction patterns using Debye scattering equation for 5 nm spherical nanoparticles, pABC = 1.0 (ccp) through different levels of stacking faults to ˚ pABC = 0.0 (hcp). l = 0.50486 A. Effect of crystallite size: To explore the effect of peak broadening in more detail for 1 to 20 nm spherical nanoparticles, three series of diffractograms were simulated; ccp and hcp nanoparticles without stacking faults (pABC = 1.0 and 0.0) and fully disordered ccp-hcp intergrowth nanoparticles (pABC = 0.5), Figure 5. The smaller crystallite sizes give rise to significant peak broadening in all scenarios. In addition, the ccp-hcp intergrowth (Figure 5b) shows strong anisotropic peak 10


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broadening. Based on the conclusions from the study of large Co NPs (> 20 nm; Figure 3), which showed that the (220)ccp /(110)hcp and (311)ccp /(112)hcp Bragg peaks are not affected by stacking disorder, we claim that these peaks are well suited for rough crystallite size estimates based on the Scherrer equation [see section for full width at half maximum (FWHM) analysis]. At this point it is worth noticing that the simulation of powder diffraction patterns using the Debye scattering equation produces a number of ripples for crystallite sizes larger than 10 nm. The ripples could not be eliminated by simply integrating a large number of simulated patterns as long as the no crystallite size distribution is concerned. Effect of crystallite size distribution: In order to investigate the influence of crystallite size distribution three series of diffractograms were simulated for ccp and hcp nanoparticles without stacking faults (pABC = 1.0 and 0.0) and fully disordered ccp-hcp intergrowth nanoparticles (pABC = 0.5). We assumed spherical particle with the median r0 = 5 nm varying the width of the LogNormal distribution s = 0.00, 0.05, 0.10, 0.20 and 0.50 where s = 0.00 denotes fixed crystallite size at r0 . Figure 6 shows the results of the calculations for pABC = 0.0, 0.5 and 1.0 on panels a,b and c, respectively. Figure S2 in Supplementary Information shows the Log-Normal crystallite size distribution used for the calculation. The comparison of the diffractograms shown on Figure 6 calculated for nanoparticles without stacking faults (panel a and c) shows significant increase of total intensity and also isotropic line sharpening for increasing value of s . This is due to the fact that even thought all Log-Normal distributions have identical median value r0 = 5 nm the average crystallite size seen by diffraction experiment is the so-called volume weighted average crystallite size < r0 >VOL = r0 exp( 72 s 2 ). 20 The tickmarks below patterns on Figure S2 show < r0 >VOL for each distribution. Figure S3 in Supplementary Information shows a comparison of X-ray powder diffraction pattern calculated on bcc nanoparticle using Debye equation for the case of Log-Normal crystallite size distribution with median value r0 = 5 nm and s = 0.5 in comparison to a uniform crystallite size of < r0 >VOL = 12 nm (normalised to the total scattered intensity). One can observe that the Full Width at Half Maximum (FWHM) is equal for both cases but the Log-Normal based case gives different peak

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Figure 5: Series of simulated X-ray powder diffraction patterns using the Debye scattering equation for spherical nanoparticles with diameter 1 to 20 nm; a) ccp stacking (pABC = 1.0), b) fully ˚ intergrowth ccp-hcp (pABC = 0.5), c) hcp stacking (pABC = 0.0). l = 0.50486 A.

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Figure 6: Series of simulated X-ray powder diffraction patterns using the Debye scattering equation for spherical nanoparticles with the radius following Log-Normal distribution with r0 = 5 nm and width parameter s = 0.00, 0.05, 0.10, 0.20 and 0.50 where s = 0.00 denotes fixed crystallite size at r0 : a) ccp stacking (pABC = 1.0), b) fully intergrowth ccp-hcp (pABC = 0.5), c) hcp stacking ˚ (pABC = 0.0). l = 0.50486 A.

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shape which can be recognised as Lorentzian function. The similar isotropic line broadening can be observed for intergrowth particles, as shown on Figure 6 (panel b). Although it affects all the reflections, the broadening due to stacking faults is significantly stronger and independent to the crystallite size. Anisotropic particle shape: Anisotropic particle shape may give rise to anisotropic Bragg peak broadening. Different extensions of the particle along different crystallographic directions lead to (hkl)-dependent Bragg peak broadening. Figure 7 shows a few examples of ellipsoidal shaped nanoparticles with intergrowth crystal structure. The projection along b-direction allows to see stacking faults along c-direction and the anisotropic particle shape. The ellipsoids shown have equal dimensions along the a- and b-directions. For all considered particle shapes the total particle volume is conserved.

Figure 7: Different Co nanoparticle shapes used for calculations: spherical (top left) and various ellipsoidal anisotropic shapes. Projection along b-direction visualises the stacking faults along c-direction. Figure 8 presents a set of X-ray powder diffraction patterns simulated for differently shaped stacking faulted nanoparticles. For both series [small (panel a); larger (panel b)], the relevant pattern for spherical particles is specified. The results show that there are two distinct sources to an observed anisotropic peak broadening; stacking faults and anisotropic particle shape. These two effects cannot be separated and only full pattern refinement which incorporates both shape and stacking faults as parameters can lead to a correct structure description. For real Co samples 14


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falling into this category, it is advised not to extract information on size based on peak broadening and the Scherrer equation.

Figure 8: Series of simulated X-ray powder diffraction patterns using the Debye scattering equation for ellipsoidal small (panel a) and large (panel b) nanoparticles. The relevant pattern for spherical particles is labelled in the middle of each set. All considered particles are fully intergrowth ccp-hcp ˚ (pABC = 0.5). l = 0.50486 A. Effect of strain: As the last parameter considered in the simulations of small Co nanoparticles we evaluate strain along the c-direction. We will clarify the effect of strain as if the nanoparticle shrinks or expands along the c-direction; i.e. for a c-axis multiplied by 0.96 - 1.04. The unstrained particle has a strain parameter equal to 1.0. Figure 9 shows a series of simulated powder diffraction patterns varying the strain of a spherical 5 nm sized nanoparticle with pABC = 0.5. The simulations clearly reveal significant shifts in Bragg diffraction peaks when tuning the strain, but no sign of any additional significant peak broadening is observed. This finding is of importance when extracting exact unit cell dimensions of nanometre sized particles. 15



Figure 9: Series of simulated X-ray powder diffraction patterns using the Debye scattering equation for spherical 5 nm nanoparticles with different strain along the c-direction. The unstrained particle is indicated in the middle of the series. All particles are fully intergrowth ccp-hcp (pABC = 0.5). ˚ l = 0.50486 A.

Modelling of Co nanoparticles with stacking faults As-synthesised Co NPs explored at room temperature: X-ray powder diffractograms of the two assynthesised Co nanoparticle samples denoted Sample 1 and Sample 2 are reported in Figures 10 and 11, respectively. By visually inspecting the measured X-ray powder diffractograms, it is clear that both samples show complex behaviour with respect to polymorphism. Furthermore, SEM imaging document the particle size to be in the range of ⇠ 10 - 100 nm for both samples. For this reason, in order to describe the atomic arrangement of the two samples in a satisfactory manner the large particle approach using the Discus software is pursued. By carefully inspecting the diffractograms, we recognize (hkl)-dependent Bragg peak broadening as well as anisotropic and asymmetric peak shape. Also a Lorentzian type peak shape is observed. To describe the two diffraction patterns we assumed that both samples consist of three different crystalline cobalt phases/stacking sequences; ccp-enriched (pABC > 0.8), intergrowth (pABC ⇡ 0.5) and hcp-enriched (pABC < 0.2). The only difference between these three constituents is the level of stacking faults, as quantified by different pABC . However, note that this model does not incorporate other aspects such as broad distribution of crystallite sizes and strain. The results of the refinements are included to Figures 10 and 11. It is concluded that both samples are heavily faulted and that the intergrowth constituent (pABC ⇡ 0.5) 16


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contributes as much as ⇡ 50 % to the scattered intensity of Sample 1. The simulations further clearly show that the two samples are quite different with respect to stacking sequences; Sample 1 and Sample 2 have, respectively, intergrowth (50 %) and hcp-enriched (67 %) components as their main constituents. Identifying such fine details in the structural arrangement of bulk samples would indeed not be possible by means of traditional Rietveld refinements. This clearly documents the strength of applying total scattering analysis.

Figure 10: Whole pattern refinement of Sample 1 exposed to He at room temperature. In addition to the observed (points) and calculated patterns (solid, black line), the difference curve is shown below. The insert shows an enlarged view of the low angle part of the measured and calculated patterns, deconvoluted into the contributions from the three constituents; ccp-enriched, intergrowth ˚ and hcp-enriched. l = 0.50486 A. Influence of temperature and atmosphere on Sample 1 and Sample 2: In order to explore and understand the fine details in the atomic arrangement of Co NPs applied for catalysis the particles should be studied when exposed to temperature-gas atmosphere conditions that mimic the living environment in the catalytic process unit. Therefore we have heated Sample 1 and Sample 2 between room temperature and 550 °C in He, H2 and CO containing atmosphere with the purpose to follow the propagation of the ratio between the different stacking sequences, possible changes in stacking probabilities (pABC ) for the different constituents as well as particle sintering. Diffrac17



Figure 11: Whole pattern refinement of Sample 2 exposed to He at room temperature. In addition to the observed (points) and calculated patterns (solid, black line), the difference curve is shown below. The insert shows an enlarged view of the low angle part of the measured and calculated patterns, deconvoluted into the contributions from the three constituents; ccp-enriched, intergrowth ˚ and hcp-enriched. l = 0.50486 A. tograms obtained at selected conditions were analysed in detail using the same approach as for the as-synthesised counterparts (see above). In Figure 12 we present as example the experimental X-ray powder diffraction pattern for Sample 1 heated to 550 °C in He together with the calculated pattern. Figure 13 presents an overview of the evolution of the relative ratio between the three phases (ccp-enriched, intergrowth, hcp-enriched) as a function of temperature and atmosphere (He, H2 and CO) for Sample 1 and Sample 2. One can see two distinct temperature regions for both samples and all atmospheres. For the temperature range between 20 °C and 450 °C, there is no significant change (within uncertainty obtained from the refinements) of relative phase fractions nor the probability of stacking faults pABC . The corresponding average values are for Sample 1: 20 %, 50 % and 30 % for ccp-enriched, intergrowth and hcp-enriched relative phase fractions and pABC equal to 0.93, 0.45 and 0.12, respectively. For Sample 2: 8 %, 25 % and 67 % for ccp-enriched, intergrowth and

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hcp-enriched relative phase fractions and pABC equal to 0.93, 0.51 and 0.05, respectively. Observing no change in pABC with temperature is inline with corresponding observations for the heavily stacking distorted layer double hydroxides (LDH) for which Radha et al. report that there are not any changes in the stacking disorder upon thermal treatment. 23 Between 450 °C and 550 °C a significant structural rearrangement is taking place. In most cases the ccp-enriched phase is becoming the majority of both sample volume. This is indeed in line with thermodynamic considerations, which predict that the ccp variant is stable above 420 °C. 5 For both Sample 1 and Sample 2 exposed to He and H2 over 70 % of the sample volume transforms into ccp-enriched phase. Also the amount of intergrowth phase is highly reduced and the hcp-enriched phase transforms completely in most cases (see Figure 12). A significantly slowed down transformation process takes place in CO atmosphere. For Sample 1 the intergrowth phase is still present, overtaking nearly 50 % of sample volume. The most extraordinary behaviour is observed for Sample 2 exposed to CO atmosphere where no structural reorganisation has been observed. We have currently no explanation to this, but elaborate more on the issue below. It should be mentioned that the Co nanoparticles sinter upon heating, as manifested through the sharpening of the Bragg reflections, see Figure 10 and Figure 12 (Sample 1 at 25 °C and 550 °C in He). In order to evaluate the effect of crystal growth with temperature, the (220)ccp /(110)hcp peak can be used since this reflection is not sensitive to stacking faults (see above and Figure 3). In Figure 14 we report the temperature dependency of the full width at half maximum (FWHM) of the (220)ccp /(110)hcp Bragg peaks for Sample 1 and Sample 2 in He, H2 and CO atmospheres. For all scenarios but Sample 2 in CO atmosphere, we see a significant reduction in the FWHM upon heating, indicating particle sintering. Sample 2 in CO does not follow the expected trend above ⇡ 300 °C. Instead it appears as the FWHM maximum is broadened between 300 - 450 °C before it again decreases. This implies that either the particles do not sinter to the same extent in CO as compared to other conditions, or that some other competing phenomena take place. We further noticed that Sample 2 in CO does not undergo the expected phase transformation into a ccpenriched form at evaluated temperatures [see Figure 13 (bottom right panel)]. To further analyse

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Figure 12: Whole patterns refinement of Sample 1 heated in He to 550 °C. In addition to the observed (points) and calculated patterns (solid, black line), the difference curve is shown below. The insert shows an enlarged view of the low angle part of the measured and calculated patterns, deconvoluted into the contributions from two constituents; ccp-enriched and intergrowth phase. ˚ l = 0.50486 A. the situation, we inspected ahex for the two samples as a function of the temperature (Figure 15) as it is well known that CO in presence of metallic Co facilitates carbon formation via the Boudouard reaction [2CO(g) * ) CO2 (g) +C(s)]. 24 From Figure 15 it appears as Sample 2 in CO atmosphere does not show any anomalies in ahex at elevated temperatures. This together with that no extra reflections appear in the patterns leads us to believe that carbide formation does not take place. The findings on Sample 2 in CO atmosphere with respect to suppression of phase transformation to ccp, maintaining large FWHM as well as showing no anomalies for ahex remains puzzling. As the current scope was to demonstrate how total scattering analysis can be used to elaborate fine details in nanostructured ill-defined Co nanoparticles, we suggest the interesting issue for Sample 2 in CO atmosphere as a fruitful topic for further investigations. Evaluation of small Co nanoparticles (< 20 nm): With application in mind, Co nanoparticles smaller than 20 nm are of particular technological importance. In the following we will evaluate an experimental X-ray powder diffractogram of Co nanoparticles, reported by Murray and co-

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Figure 13: Evolution of ccp-enriched, intergrowth and hcp-enriched fractions with temperature and atmosphere (He, H2 , CO) for Sample 1 (left panel) and Sample 2 (right panel).

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Figure 14: Evolution of FWHM of (220)ccp /(110)hcp with temperature and atmosphere (He, H2 , CO) for Sample 1 (panel a) and Sample 2 (panel b). FWHM according to instrumental resolution is indicated by the dotted line.

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Figure 15: Evolution of unit cell ahex with temperature and atmosphere (He, H2 , CO) for Sample 1 (panel a) and Sample 2 (panel b).

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workers 25 to demonstrate that our library of simulated X-ray powder diffractograms can act as a guideline for identifying sample nature by a fingerprint approach. Murray et al. report a wide-angle X-ray scattering pattern (WAXS) of 10 nm spherical Co NPs, which is analysed to consist of hcp Co with some stacking disorder due to broadening of the hcp Bragg reflections (100), (102) and (103). 25 The paper does not provide any clear explanation to how they arrived at this conclusion. By carefully inspecting the published diffractogram of Murray et al. 25 (see Figure 3 in Murray et al. 25 ), it can be seen that the hcp Bragg peak (102) is more or less completely absent whereas the hcp (103) still is visible. Comparing these observations with our simulated diffractograms of 5 nm spherical Co NPs for pABC = 0.5 and 0.3 (Figure 4) and 10 nm spherical Co NPs for pABC = 0.5 (Figure 5b) we see many similarities. The fact that the experimental diffractogram shows some intensity in the (102) and (103) peaks indicate that the stacking disorder is less than pABC = 0.5, and from the profiles of (100), (002) and (101) peaks it appears that pABC is larger than 0.3. From the visual fingerprint inspection it is tempting to conclude that the 10 nm Co hcp NPs is a hcp-enriched sample with pABC in the range 0.3 - 0.5.

Concluding remarks Polymorphism of cobalt has attracted substantial attention the last decades. Efforts in describing the ccp-hcp nanostructuring in Co nanoparticles by means of X-ray powder diffraction are plentiful, however only some very limited studies are tackling the challenge of moving beyond reporting on the co-existence of ccp-hcp stacking. Ducreux et al., Longo et al. and Price et al. are three excellent examples where detailed structural models including stacking probabilities are taken into account. 2,11,12 These studies reveal essential new insight, and Price et al. 2 document existence of a heavily intergrowth Co phase. In the current work we provide a unique library of simulated X-ray powder diffractograms of Co nanoparticles, bringing the effects of stacking faults, size, size distribution, shape and strain into play one by one with the purpose to identify signatures linked to each of these effects. We

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document in detail how these parameters affect the XRPD for small and large Co nanoparticles. The developed library is intended for fingerprint characterization of Co nanoparticles when simulation tools are not at hand. Alternatively, the library can be used to develop a solid starting model for full structural analysis of Co nanoparticles. In this study we have demonstrated the strength of the Discus software in developing models that allow refining the ratio between involved polytypes. Without this option it would not be possible to identify that the investigated as-synthesised Co samples consist of three constituents, ccp- and hcp-enriched as well as a heavily intergrowth phase. Furthermore, the simulations document that it is just the ratio between these three constituents that is altered upon heating; not the stacking fault probability pABC of any of them. Such fine structural details are not possible to extract by classic approaches. The intergrowth phase reported by Price et al. 2 is also present in our samples, and it remains still open to explain the role of this intergrowth phase in relation to e.g. Fischer-Tropsch catalysis. Our study documents that different nanostructuring of the Co nanoparticles in terms of stacking faults give rise to different thermal behaviour in CO atmosphere. Further systematic studies may provide answers to underlying reasons, and then also the role of this unusual behaviour with respect to catalytic applications. The prospective is clear; applying this careful structural analysis approach to functional Co based nanoparticles will help us in understanding fine details, which in next step allow us to properly design ultimate functionality of Co-based nanoparticles for catalysis. We foresee this simulation approach also to be applicable to other industrial relevant metals with close packed structures.

Acknowledgement The authors are grateful for receiving beam time and assistance from the research team at the Swiss-Norwegian Beam Lines, ESRF, Grenoble, France. Erwan Y. Rauwel is acknowledged for his guiding in nanoparticle synthesis. This work is part of activities at the inGAP Centre of Researchbased Innovation, funded by the Research Council of Norway, Grant no. 174893. We also acknowledge the Research Council of Norway for providing the computer time (under the project

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number NN2875k) at the Norwegian supercomputer.

Supporting Information Available Scanning electron microscopy (SEM) images of both samples with particle sizes ranging from ⇠ 10 - 100 nm are presented on Figure S1. Figure S2 shows the Log-Normal crystallite size distribution used for the calculation. A comparison of X-ray powder diffraction pattern calculated on bcc nanoparticle using Debye equation for the case of Log-Normal crystallite size distribution with median value r0 = 5 nm and s = 0.5 in comparison to a uniform crystallite size of < r0 >VOL = 12 nm (normalised to the total scattered intensity) is shown in Figure S3. This material is available free of charge via the Internet at http://pubs.acs.org/.

References (1) Rytter, E.; Holmen, A. Deactivation and regeneration of commercial type fischer-tropsch cocatalystse - A mini-review. Catalysts 2015, 5, 478–499. (2) Price, S. W. T.; Martin, D. J.; Parsons, A. D.; Sławiński, W. A.; Vamvakeros, A.; Keylock, S. J.; Beale, A. M.; Mosselmans, J. F. W. Chemical imaging of Fischer-Tropsch catalysts under operating conditions. Science Advances 2017, 3, e1602838. (3) Jahangiri, H.; Bennett, J.; Mahjoubi, P.; Wilson, K.; Gu, S. A review of advanced catalyst development for Fischer-Tropsch synthesis of hydrocarbons from biomass derived syn-gas. Catalysis Science and Technology 2014, 4, 2210–2229. (4) Mirzaei, A. A.; Arsalanfar, M.; Bozorgzadeh, H. R.; Samimi, A. A review of Fischer-Tropsch synthesis on the cobalt based catalysts. Physical Chemistry Research 2014, 179–201.

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(5) Cavalier, M.; Walls, M.; Lisiecki, I.; Pileni, M.-P. How can the nanocrystallinity of 7 nm spherical Co nanoparticles dispersed in solution be improved? Langmuir 2011, 27, 5014– 5020. (6) Kitakami, O.; Sato, H.; Shimada, Y.; Sato, F.; Tanaka, M. Size effect on the crystal phase of cobalt fine particles. Physical Review B - Condensed Matter and Materials Physics 1997, 56, 13849–13854. (7) Dinega, D.; Bawendi, M. A solution-phase chemical approach to a new crystal structure of cobalt. Angewandte Chemie - International Edition 1999, 38, 1788–1791. (8) Zacharaki, E.; Kalyva, M.; Fjellv˚ag, H.; Sj˚astad, A. O. Burst nucleation by hot injection for size controlled synthesis of epsilon-cobalt nanoparticles. Chemistry Central Journal 2016, 10, 10. (9) Ram, S. Allotrophic phase transformations in HCP, FCC and BCC metastable structures in Co-nanoparticles. Materials Science and Engineering A 2001, 304-306, 923–927. (10) Torchio, R.; Marini, C.; Kvashnin, Y.; Kantor, I.; Mathon, O.; Garbarino, G.; Meneghini, C.; Anzellini, S.; Occelli, F.; Bruno, P.; Dewaele, A.; Pascarelli, S. Structure and magnetism of cobalt at high pressure and low temperature. Physical Review B 2016, 94, 024429. (11) Longo, A.; Sciortino, L.; Giannici, F.; Martorana, A. Crossing the boundary between facecentred cubic and hexagonal close packed: the structure of nanosized cobalt is unraveled by a model accounting for shape, size distribution and stacking faults, allowing simulation of XRD, XANES and EXAFS. Journal of Applied Crystallography 2014, 47, 1562–1568. (12) Ducreux, O.; Rebours, B.; Lynch, J.; Roy-Auberger, M.; Bazin, D. Microstructure of supported cobalt Fischer-Tropsch catalysts. Oil and Gas Science and Technology - Rev. IFP 2009, 64, 49–62.

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(13) Makinson, J.; Lee, J.; Manger, S.; De Angelis, R. X-Ray Diffraction Signatures of Defects in Nanocrystalline Materials. Advances in X-ray Analyis 2000, 42, 407–411. (14) Treacy, M. M. J.; Newsam, J. M.; Deem, M. W. A general recursion method for calculating diffracted intensities from crystals containing planar faults. Proceedings - Royal Society of London, A 1991, 433, 499–520. (15) Proffen, T.; Neder, R. B. DISCUS: A program for diffuse scattering and defect-structure simulation. Journal of Applied Crystallography 1997, 30, 171–175. (16) Neder, R. B.; Proffen, T. Diffuse Scattering and Defect Structure Simulations; Oxford University Press, 2008. (17) Sławiński, W.; Sj˚astad, A. O.; Fjellv˚ag, H. Stacking Faults and Polytypes for Layered Double Hydroxides: What Can We Learn from Simulated and Experimental X-ray Powder Diffraction Data? Inorganic Chemistry 2016, 55, 12881–12889. (18) Debye, P. Zerstreuung von Rntgenstrahlen. Annalen der Physik 1915, 351, 809–823. (19) Beyerlein, K. A review of Debye Function Analysis. Powder Diffraction 2013, 28, S2–S10. (20) Krill, C. E.; Birringer, R. Estimating grain-size distributions in nanocrystalline materials from X-ray diffraction profile analysis. Philosophical Magazine A: Physics of Condensed Matter, Structure, Defects and Mechanical Properties 1998, 77, 621–640. (21) Wardecki, D.; Przeniosło, R.; Bukowski, M.; Hempelmann, R.; Fitch, A. N.; Convert, P. Influence of the crystalline microstructure on the magnetic ordering of nanocrystalline chromium. Phys. Rev. B 2012, 86, 064410. (22) Tsakoumis, N.; Voronov, A.; Røonning, M.; Beek, W.; Borg, O.; Rytter, E.; Holmen, A. Fischer-Tropsch synthesis: An XAS/XRPD combined in situ study from catalyst activation to deactivation. Journal of Catalysis 2012, 291, 138–148.

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(23) Radha, A.; Kamath, P.; Shivakumara, C. Order and disorder among the layered double hydroxides: combined Rietveld and DIFFaX approach. Acta Crystallographica Section B: Structural Science 2007, 63, 243–250. (24) Bremmer, G. M.; Zacharaki, E.; Sj˚astad, A. O.; Navarro, V.; Frenken, J. W. M.; Kooyman, P. J. In situ TEM observation of the Boudouard reaction: multi-layered graphene formation from CO on cobalt nanoparticles at atmospheric pressure. Faraday Discuss. 2017, 197, 337–351. (25) Murray, C. B.; Sun, S.; Gaschler, W.; Doyle, H.; Betley, T. A.; Kagan, C. R. Colloidal synthesis of nanocrystals and nanocrystal superlattices. IBM Journal of Research and Development 2001, 45, 47–56.

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For Table of Contents Use Only Structural arrangement in close packed cobalt polytypes Wojciech A. Sławiński, Eirini Zacharaki, Anja Olafsen Sj˚astad and Helmer Fjellv˚ag

Synopsis X-ray Powder Diffraction (XRPD) is a powerful tool to study nano-sized materials. Here we present a comprehensive study on how stacking faults, crystallite size, crystallite size distribution, shape and strain dictate the nature of the XRPD patterns of small (< 20 nm) and large (> 20 nm) cobalt (Co) nanoparticles. This knowledge is then applied to study nano-Co particles structure evolution upon heating in different atmospheres.

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Structural Arrangement in Close-Packed Cobalt Polytypes - Crystal

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