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Theoretical Study of Cu/Mg Core-Shell Nanocluster Formation Robert J. Buszek, Claron J. Ridge, Samuel B. Emery, Christopher Michael Lindsay, and Jerry A. Boatz J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.6b09772 • Publication Date (Web): 09 Nov 2016 Downloaded from http://pubs.acs.org on November 9, 2016

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The Journal of Physical Chemistry

Theoretical Study of Cu/Mg Core-shell Nanocluster Formation Robert J. Buszek†, Claron J. Ridge‡, Samuel B. Emery§, C. Michael Lindsay‡ and Jerry A. Boatzǁ* †

ERC, Inc. Edwards Air Force Base, California 93524, USA

‡

Air Force Research Laboratory, Munitions Directorate, 2306 Perimeter Rd, Eglin Air Force

Base, Florida, 32542, USA §

Naval Surface Warfare Center Indian Head EOD Technology Division, 3196 Deep Point Court,

Indian Head, Maryland, 20640, USA ǁ

Air Force Research Laboratory, Aerospace Systems Directorate, 10 E. Saturn Blvd, Edwards

Air Force Base, California 93524, USA ABSTRACT In a recently reported helium droplet mediated deposition experiment to produce copper-coated magnesium core-shell nanoclusters, structural inversion was observed which resulted in copper in the nanocluster interior, surrounded by oxidized magnesium on the copper surface. This study utilizes density functional theory methods to model the migration of copper atoms into the interior of a magnesium nanocluster to probe the energetics of this process and to compare it to the complementary process of magnesium atom migration into the interior of a copper nanocluster.

Potential energy surfaces describing the forced migration of copper

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(magnesium) atoms into the interior of a 30-atom magnesium (copper) cluster were generated using the B3PW91 hybrid generalized gradient approximation functional with the augmented correlation consistent core-valence polarized triple-zeta basis set for magnesium (aug-ccpωCVTZ) and a pseudo-potential plus valence-only basis set for copper (aug-cc-pVTZ-PP.) The estimated barrier for atomic copper to penetrate the surface of Mg30 is 0.6 kcal mol-1. In contrast, the migration of atomic magnesium into the interior of Cu30 crosses an estimated barrier of 6 kcal mol-1. These results are qualitatively consistent with the observed structural inversion of coppercoated magnesium nanoclusters and also suggest that inversion of a magnesium-coated copper cluster is less likely to occur.

1. Introduction Metallic nanoparticles are of great interest in the energetics community, due in part to higher energy densities relative to conventional CHNO-based energetic materials.1 Because of higher surface-to-volume ratios and reduced length scales of nanoparticles relative to the bulk, diffusion-limited mass and thermal transport bottlenecks1,2 encountered at the macroscale are circumvented, thereby offering considerable potential as high performance energetic materials for applications in explosives and propellant formulations. Strategies for utilizing nanoparticles in energetic materials applications include, for example, incorporation of aluminum nanoparticles as additives to solid propellant formulations as a way to increase energy density and burn rates.3,4 An additional concept is to use nanoscale metastable intermolecular composites (MICs) and nanolaminates, for which significant improvements in the burn rates relative to bulk thermites has been observed.1,2,5-9


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One type of nanoscale MIC which shows considerable potential in this regard is a coreshell thermite, in which the inner core consisting of a fuel (e.g., Al) is coated with an oxidizer (e.g.,CuO).10 Another related class of promising energetic nanoscale MICs is intermetallic coreshell species such as Cu+Mg.11 These types of novel materials have been made via helium droplet mediated deposition (HDMD) methods in which synthesis occurs via clustering of atoms or molecules within the interior of helium droplets, as described in detail elsewhere.12-21 Briefly, ultracold helium droplets are generated via supersonic expansion of high pressure, low temperature helium gas into a vacuum and are subsequently passed sequentially through multiple pickup cells, each of which contains atomic or molecular species in the vapor phase. Within each pickup cell, the helium droplet traps multiple atoms or molecules, which coalesce within the droplet interior. Thus, the species present in the first pickup cell ultimately comprises the core, with the contents of the subsequent pickup cells forming the intermediate and outer layers ("shells") of the final nanocluster. A surprising discovery involving the formation of the bimetallic Mg/Cu core-shell cluster formation via HDMD was recently reported.11 In this study, it was found that during the production of Mg/Cu core-shell nanoparticles in which a copper shell was deposited upon an initially formed Mg core, the thus-formed core-shell species underwent structural inversion, resulting in copper atoms in the core, surrounded by magnesium on the surface of the copper core. Furthermore, preliminary density functional theory (DFT) calculations were used (a) to probe the formation of these clusters via investigation of the binding energies and structural characteristics of small Cux/Mg6 (x=0-6) bimetallic clusters and (b) to examine the potential energy surface of two Cu atoms initially diffusing into the interior of an Mg30 cluster. The present work includes a more extensive analysis of the potential energy surface (PES) scan of the



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Mg30·Cu2 model system and also provides a comparison to the analogous Cu30·Mg2 system, corresponding to magnesium atoms migrating into the interior of a copper cluster.

2. Computational Methods The structures and harmonic vibrational frequencies of the Mg30·Cu2 and Cu30·Mg2 bimetallic clusters were calculated using DFT with the B3PW91 hybrid generalized gradient approximation (GGA) functional,22 constructed from Becke’s three-parameter hybrid exchange functional23 and the Perdew/Wang 1991 correlation functional,24-27 and a Lebedev quadrature grid containing 96 radial and 302 angular points. This choice of functional has been shown to be appropriate for studies of magnesium clusters.28,29 In previous calculations,30,31 it was found that the magnesium 2s+2p "core" electrons and orbitals should be treated using a basis set which includes core-valence correlation effects. Therefore, the augmented correlation consistent corevalence polarized valence triple zeta basis set (aug-cc-pωCVTZ)31 was used for magnesium. For copper, a comparable valence-only augmented correlation consistent polarized valence triple zeta basis set plus corresponding pseudopotential (aug-cc-pVTZ-PP)32,33 was utilized in order to reduce the computational cost of these large systems. This mixed basis set is henceforth denoted as ωCVT-PP. Closed and open shell species have been calculated using restricted (R-DFT) and restricted open-shell density functional theory (RO-DFT,) respectively. All of the calculations used in this study were performed using the GAMESS quantum chemistry code.34,35 As a benchmark of the B3PW91/ωCVT-PP method, the bond lengths and binding energies of the Mg2, CuMg, and Cu2 diatomics computed at this level were compared to second order perturbation theory (MP2)36-38 and coupled cluster CR-CCL39,40 calculations using the


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same basis set (ωCVT-PP) and to the available experimental data,41,42, with the results summarized in Table 1. For Mg2, the calculated bond energies range from 0.89 to 1.71 kcal mol1

, which bracket the experimental value of 1.65 kcal mol-1.42 Similar variations are also seen in

the Mg2 computed bond lengths, which range from 3.615 to 4.103 Å and also bracket the experimental bond length of 3.890 Å. The large range of predicted bond lengths is not surprising due to the weak Mg-Mg interaction energy and the theoretical challenges inherent in describing the weak binding in Mg2.30 Although the B3PW91/ωCVT-PP predicted bond length of 3.615 Å is significantly shorter than the experimental value, the predicted bond energy of 1.71 kcal mol-1 is in excellent agreement with experiment (1.65 kcal mol-1.) For Cu2, the computed bond energies for all three methods, ranging from 43.4 to 46.3 kcal mol-1, are in excellent agreement with the experimental value of 45.3 kcal mol-1. Similarly, the predicted bond lengths (2.198 to 2.233 Å) agree well with the observed bond length of 2.200 Å. Since experimental data for the MgCu heteronuclear diatomic are unavailable, the coupled cluster CR-CCL/ωCVT-PP results, R(MgCu) = 2.460 Å; D0 = 17.9 kcal mol-1, are used as the baseline for evaluation of the accuracy of the DFT and MP2 predictions. As shown in Table 1, the B3PW91 and MP2 predicted bond energies of 19.4 and 18.6 kcal mol-1 are in good agreement with CR-CCL. The B3PW91 predicted bond length of 2.464 Å agrees well with the CR-CCL result, although the bond length predicted at the MP2 level (2.415 Å) is somewhat smaller than CR-CCL. In summary, the BP3W91/ ωCVT-PP diatomic data are in reasonably good agreement with the experimental data for Mg2 and Cu2, and with CR-CCL/ωCVT-PP predictions for MgCu. An additional set of benchmark calculations of the bond lengths and binding energies of the tetrahedral Mg4 cluster, comparing several basis sets and methods (DFT, MP2, and coupled cluster theory) are included and discussed in the ESI.



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3. Results and Discussion The relative bond energies of Mg2, MgCu, and Cu2 diatomics provide initial insights into the anticipated structures and stabilities of the larger Mg/Cu bimetallic clusters. As discussed above, the experimental Mg2 dimer interaction energy of 1.65 kcal mol-1is quite weak, in sharp contrast to the predicted MgCu interaction energy of 17.9 kcal mol-1 (CR-CCL level) and the Cu2 dimer interaction energy of 45.3 kcal mol-1. These results suggest that the structures of the larger Mg/Cu bimetallic clusters will favor nearest neighbor Cu-Mg and Cu-Cu interactions at the expense of Mg-Mg interactions. More specifically, it seems plausible that migration of a copper atom initially located on the surface of a magnesium cluster into the interior should be an energetically favorable process, ultimately leading to "solvated" interior copper atoms with magnesium displaced to the surface. Of course, the presence of a reaction barrier could inhibit or prevent such a process from occurring, especially in light of the ultracold environment of the helium droplet. In order to probe the energetics of core-shell structural inversion as described above, a model system consisting of a 30-atom magnesium "core" was utilized. This cluster size was chosen since it is sufficiently large to have multiple (three) interior atoms, yet small enough to be computationally tractable. The presence of multiple atoms in the interior of Mg30 enables a probe of the energy required for the Cu atom pair to disrupt the interior bonding rather than simply pushing aside a single core atom. After fully optimizing the structure of the Mg30 cluster and verifying it to be a local minimum, two copper atoms were placed on the surface, on opposite sides of Mg30. The structure of the resulting Cu·Mg30·Cu bimetallic cluster was fully reoptimized and confirmed to be a local minimum and is shown in Figure 1a. At this initial structure, the distance between the two copper atoms is 9.37 Å. The distance between the copper


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atoms was then reduced to 9.25 Å and held fixed, with the remaining structural degrees of freedom reoptimized, subject to the fixed Cu-Cu distance. This procedure was repeated, systematically decreasing the Cu-Cu distance by 0.25 Å at each step. A plot of the total energy versus Cu-Cu distance is shown in Figure 1, which includes images of the constrained Cu·Mg30·Cu cluster at selected Cu-Cu distances. In Figure 1, a local energy maximum (LEM) is seen at R(Cu-Cu) = 9 Å, which is ~0.6 kcal mol-1 higher in energy than the starting local minimum. The corresponding structure (Figure 1b) reveals that the copper on the right side of the Mg30 cluster is beginning to penetrate the surface. It is important to note that this LEM is only an approximation to a true saddle point on the potential energy surface and therefore the corresponding relative energy is only an estimate of the actual energy barrier. Nonetheless, this point has the highest energy along the entire trace in Figure 1 and all constrained configurations at Cu-Cu distances less than 9 Å are more stable than the original, fully optimized Cu·Mg30·Cu cluster. As the Cu-Cu distance is further shortened, another LEM arises at R(Cu-Cu) ≈ 8 Å, at which point the second copper atom, on the left side of the cluster, begins to penetrate the Mg30 surface. This is followed by a steep drop in the energy as the Cu-Cu distance decreases from 6.75Å to 6.50 Å. This rapid change in energy is mainly due to further encapsulation of the copper atoms afforded by rearrangement of the Mg30 cluster, shown in Figures 1c and 1d and in greater detail in Figure S1 in the ESI.

However, as shown in Figure S2 and discussed in the

ESI, this reduction in total energy is not due to simple reconstruction of the underlying Mg30 cluster to a more stable configuration relative to the initial fully optimized Mg30 conformer. Interestingly, the copper atom on the left side reappears on the Mg30 surface as a result of this rearrangement, but this is likely to be an artifact of the small size of the Mg30 cluster. This



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rearrangement is followed by another LEM near R(Cu-Cu) = 6 Å, which corresponds to the copper atom on the left side (re)entering the Mg30 cluster. At the lowest energy point near R(CuCu) = 5.5 Å (Figure 1e,) both copper atoms have migrated through the Mg30 surface into the cluster interior. The next LEM at R(Cu-Cu) = 4.5 (Figure 1f) is due to disruption of the bonding of the three interior Mg atoms. This is illustrated in greater detail in Figure S3, which reveals that one of the interior Mg-Mg bond distances has increased from 3.1 Å in Figure 1e to 3.6 Å in Figure 1f. The following decrease in energy occurs due to partial reformation of the core structure of the three interior Mg atoms. As the Mg3 core further relaxes back to its original structure, the copper atoms are forced between the interior and surface layers of the magnesium cluster, resulting in the LEM at R(Cu-Cu) = 3.0 Å. The final drop in energy at R(Cu-Cu) = 2.75 Å is due to the initial onset of Cu-Cu bond formation. Starting at this point, an unconstrained optimization was performed which resulted in essentially no change in structure or relative energy, denoted by the red triangle in Figure 1. Although the final LEM near R(Cu-Cu) = 3 Å is uphill in energy by ~10 kcal mol-1 relative to the most stable point on the potential energy scan (Figure 1e,) the total energy at this point is still below that of the initial Cu·Mg30·Cu cluster, indicating that this process is energetically accessible. In summary, these results strongly suggest that copper atoms can easily penetrate the surface layer of a magnesium cluster. However, a more thorough investigation of the energetics of copper atom solvation and migration within the cluster interior would necessitate using a substantially bigger cluster and/or large scale molecular dynamics simulations, which is beyond the scope of the present study. In order to obtain a more complete understanding of the interactions present in Mg/Cu bimetallic nanoclusters, the complementary system in which two Mg atoms placed initially on


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the surface of a Cu30 cluster was investigated. This was done in the same way as described above for Mg30·Cu2, beginning with the full optimization of two Mg atoms on the surface of the Cu cluster, followed by constrained optimizations forcing the two Mg atoms closer together at intervals of 0.25 Å, as illustrated in Figure 3. As seen in Figure 2a, the initial structure for the Cu30 structure is markedly different than that of the Mg30 cluster, with a more highly ordered, semi-crystalline atomic arrangement compared to the amorphous structure of Mg30. This difference is not surprising based upon the distinctly stronger Cu-Cu diatomic bond relative to Mg-Mg, as discussed previously. The initial LEM at R(Mg-Mg) = 7.75 Å is ~6 kcal mol-1 above the initial fully optimized structure. However, as can be seen in Figure 2b, the Mg atoms have moved laterally along the Cu30 surface rather than beginning to move into the interior. As the Mg-Mg distance continues to decrease, there is a drop in energy, along with an extensive rearrangement of the Cu30 cluster and the onset of migration of the Mg atoms into the Cu30 surface, at R(Mg-Mg) = 6.75 (Figure 2c.) However, as shown in Figure S4 and discussed in the ESI, the energy stabilization in this region of the potential energy surface is not due to reconstruction of the underlying Cu30 cluster to a more stable configuration relative to the initial Cu30 structure. There is a 30 kcal mol-1 increase in energy as the constraint distance decreases from R(Mg-Mg) = 6.75 Å to R(Mg-Mg) = 4.0 Å(Figure 2d) due to the Mg atom on the left side of the cluster penetrating the Cu cluster. The latter is displayed in greater detail in Figure S5, which shows the formation of a surface cavity in Cu30 as a result of a magnesium atom having been forced into the interior. The relative energy of this point along the PES scan is nearly the same as the initial structure (Figure 2a.) The subsequent steep drop in energy leading to the local energy mininum at R(Mg-Mg) = 3.75 Å, shown in Figure S5, is due to reconstruction of the



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copper cluster surface, resulting in encapsulation of the interior Mg atom. Starting from this point, an optimization was completed with the Mg-Mg distance constraint removed, resulting in relaxation of the Mg-Mg distance to 4.106 Å and denoted by the orange square in Figure 2. In spite of the considerable lengthening of the Mg-Mg distance, one Mg atom remains in the interior and one on the surface of Cu30, as seen in Figure 2e. It should be noted that only a single Mg atom enters the Cu30 cluster, while the other Mg stays on the surface. This is in contrast to Mg30·Cu2, in which both copper atoms entered the interior of Mg30 cluster. This difference in behavior suggests that migration of copper atoms through magnesium is energetically less taxing than magnesium atoms moving through copper. 4. Conclusions In an effort to better understand previously reported results involving the HDMD synthesis and observed structural inversion of Cu/Mg core-shell nanoparticles, the potential energy surfaces of two copper atoms diffusing into an Mg30 cluster, as well as the counterpart system of two Mg atoms diffusing into a Cu30 cluster, were investigated using density functional theory. It was determined that two Cu atoms penetrating the surface of a Mg30 cluster initially encounter a small barrier estimated to be on the order of 0.6 kcal mol-1, followed by exothermic encapsulation of both Cu atoms. Further diffusion into an inner layer of the Mg cluster is more difficult, with an estimated barrier of 10 kcal mol-1, but this process still is exothermic with respect to two Cu atoms on the surface. In the complementary Cu30Mg2 cluster, migration of the Mg atoms through the Cu30 surface is found to be less favorable. An initial barrier of ~6 kcal mol-1 is predicted for lateral motion of the Mg atoms along the copper cluster surface. Although rearrangement of the initial semi crystalline Cu30 cluster to partially solvate the two Mg atoms is


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energetically favorable, full encapsulation of one Mg atom is found to be endothermic by 30 kcal mol-1. The contrasting behavior of these two systems is consistent with the differences in the Mg2 and Cu2 diatomic potential energy curves, with Mg2 having a weak binding energy of 1.65 kcal mol-1 compared to the relatively strong Cu2 binding energy of 45.3 kcal mol-1. Furthermore, these results indicate that structural inversion of a copper-coated magnesium core shell cluster should occur more readily than inversion of a magnesium-coated copper cluster.



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Figure 1. B3PW91/ωCVT-PP potential energy surface scan of the migration of two Cu atoms into a Mg30 cluster as a function of CuCu distance. Energies are in kcal mol-1, relative to the initial fully optimized Mg30·Cu2 cluster. The red triangle near R(Cu-Cu)=2.75Å denotes the fully optimized conformer (see text.)


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Figure 2. B3PW91/ωCVT-PP potential energy surface scan of the migration of two Mg atoms into a Cu30 cluster as a function of MgMg distance. Energies are in kcal mol-1, relative to the initial fully optimized Cu30·Mg2 cluster. The orange square near R(MgMg)=4.1Å denotes the fully optimized conformer (see text.)



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Table 1. Bond lengths (r), vibrational frequencies (λ) and bond energies (B.E.) of Mg, MgCu, and Cu2 diatomic molecules. B3PW91a

MP2a

CR-CCLa

Experiment

3.615

4.103

4.055

3.891b

85

44

43

51

1.71

0.89

1.02

1.65d

2.464

2.415

2.460

n/a

λ (cm-1)

245

271

250

n/a

B.E. (kcal mol-1)c

19.4

18.6

17.9

n/a

2.233

2.198

2.223

2.220b

λ (cm-1)

259

285

266

265

B.E. (kcal mol-1)c

43.4

46.3

44.4

45.3d

Mg2 r (Å) λ (cm-1) B.E. (kcal mol-1)c MgCu r (Å)

Cu2 r (Å)

a b

Using the ωCVT-PP basis set as described in the text.

References 41 and 42

c

Including unscaled zero point energy (ZPE) corrections.

d

Obtained from difference in gas phase standard enthalpies of formation, D0 (M2) = 2∆Hf298 (M) - ∆Hf298 (M2), M=Mg, Cu, from reference 43.


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ASSOCIATED CONTENT Supporting Information. Further supporting information including benchmark data of the Mg4 cluster (bond lengths and binding energies,) enlarged Mg30Cu2 and Cu30Mg2 cluster images, and calculated PESs not including diffusing atoms is supplied. This material is available free of charge via the Internet at http://pubs.acs.org. AUTHOR INFORMATION Corresponding Author *Email: [email protected] Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. †‡These authors contributed equally ACKNOWLEDGMENT The authors gratefully acknowledge funding from the Air Force Office of Scientific Research (grant # 3002NW, Program Officer Dr. Michael Berman.) This work was supported in part by a grant of computer time from the DoD High Performance Computing Modernization Program at the Air Force Research Laboratory, Army Research Laboratory, Engineer Research and Development Center, and the Navy DoD Supercomputing Resource Centers. Funding Sources Air Force Office of Scientific Research (grant # 3002NW, Program Officer Dr. Michael Berman.)



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