The new dimension of silver.

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Physical Chemistry Chemical Physics View Article Online

DOI: 10.1039/C5CP03465E

Li-Ming Yang*,1 Thomas Frauenheim,1 and Eric Ganz2

Published on 06 July 2015. Downloaded by Mount Allison University on 07/07/2015 15:16:39.

1

Bremen Center for Computational Materials Science, University of Bremen, Am Falturm 1, 28359, Bremen, Germany; 2Department of Physics, University of Minnesota, 116 Church St., SE, Minneapolis, Minnesota 55416, USA. (email: [email protected])

Abstract: Although significant progress in the fabrication and applications of graphene-like materials has been made, free-standing metal monolayers are extremely rare due to the challenges in fabrication. Furthermore, such structures are often unstable versus 3D close-packed forms. Silver is an important noble metal with many unique properties, and has wide applications in daily life and industry. Here, we display a new dimension of silver, i.e., a 2D Ag monolayer, with reduced dimensionality and quantum confinement. We observe that the Ag monolayer is stable in ab initio molecular dynamics simulations up to 800 K for 10 ps. The bond strength per atom actually increases from 0.21 eV for the bulk with twelve bonds to 0.33 eV for the 2D layer with six bonds. This increase in bond strength contributes to the stability of the free-standing 2D layer. Detailed density functional theory calculations are used to predict the properties of this material. The 2D Ag monolayer is the global minimum structure. One electron is delocalized into the whole sheet and is donated into a nearly free 2D electron gas.

Physical Chemistry Chemical Physics Accepted Manuscript

The New Dimension of Silver

Physical Chemistry Chemical Physics

Page 2 of 14 View Article Online

DOI: 10.1039/C5CP03465E

Ultrathin materials including graphene, translation metal dichalcogenides, and boron nitride have aroused great interest and exhibit fascinating properties such as high carrier mobility,[1] quantum Hall effects,[2] extraordinary thermal conduction,[3] magnetic resonant mode and Published on 06 July 2015. Downloaded by Mount Allison University on 07/07/2015 15:16:39.

superconductivity.[4] So far, the preparation of ultrathin materials with few atomic layers mainly relies on the material itself having a lamellar structure, a feature that ensures the stability of their few- or even single-layer structures, because of the strong intra-layer chemical bonding and weak inter-layer interaction.[5] By contrast, metal atoms have a strong preference for three-dimensional (3D) close-packed structures. Therefore, ultrathin freestanding metallic structures with numerous unsaturated atoms are difficult to stabilize and their synthesis remains challenging. In standard chemistry textbook, silver (Ag) is a very ductile, malleable, univalent coinage metal, with a brilliant white metallic luster that can take a high degree of polish. Protected silver has higher optical reflectivity than aluminum at all wavelengths longer than ~ 450 nm, and so is desirable for telescope and other mirrors. Dimensionality is an important material parameter, the same chemical compounds can exhibit dramatically different properties depending on whether it is arranged in a 0D, 1D, 2D, or 3D crystal structure. This is exemplified by the different carbon allotropes, such as, fullerene (0D),[6] carbon nanotube (1D),[7] graphene (2D),[8] and diamond (3D) which have completely different properties. Silver clusters have demonstrated size-dependent properties completely different from the bulk phase.[9] Silver clusters and small particles have practical importance because of their role in photography,[10] catalysis,[11] and their potential use in new electronic materials. Recently, ultra-small thiolated silver nanoclusters are emerging as a new class of promising theranostic agents for a wide spectrum of biomedical applications (such as bioimaging, antimicrobial agents, disease diagnostics).[12] This further demonstrated how the dimensionality, quantum confinement, and size/shape effect have a fundamental impact on the properties, function, and application of materials. Adsorption of molecules such as azobenzene can be used to create molecular switches on the Ag(111) surface.[13] We note that various experiments have used copper foils or single crystal Ag(111) surfaces as substrates to fabricate various 2D materials (including porous graphene,[14] silicene,[15] boron nitride,[16]). These experiments take advantage of the attractive properties of silver (high purity, weak bonding energies to over layers, and etchability). We note that various experiments have used copper foils or single crystal


I. Introduction

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DOI: 10.1039/C5CP03465E

silicene,[15] boron nitride,[16]). These experiments take advantage of the attractive properties of silver (high purity, weak bonding energies to over layers, and etchability). In an exciting new development, free-standing atomically thick iron membranes suspended Published on 06 July 2015. Downloaded by Mount Allison University on 07/07/2015 15:16:39.

in graphene pores have been fabricated experimentally.[17] These iron layers were small with up to ten atoms inside the pores. This demonstrates the potential of perforated graphene as a support for small free-standing 2D membranes, and paves the way for novel 2D structures to be formed experimentally. Zhao et al. also used DFT calculations to study these systems, and predicted that the largest thermodynamically stable patch would be twelve atoms across.[17] This method could potentially be used to fabricate a small free-standing Ag monolayer. There have been ab initio studies of gold patches. Koskinen and Korhonena have studied the solid and liquid phases of a small monolayer gold patch in a graphene hole.[18] This 49 atom gold patch stayed solid up to 700 K, and then at 900 K formed an unusual 2D liquid layer. We are motivated by these experimental and theoretical results on Fe and Au patches. We are also motivated by recent DFT calculations that we have performed on similar Cu and Au free-standing 2D monolayers.[19] In this paper, we will use DFT calculations to study the properties of a free standing 2D silver monolayer sheet. We wanted to see how the 2D monolayer compares to the bulk, and whether its properties are closer to those of bulk silver or nanoscale Ag materials. Silver is a unique element with a special position in the periodic table (in the same column as important noble metals Cu and Au) and is essential for life. A fundamental understanding of the chemistry and relevant physiochemical properties might pave the way towards practical applications. Here, we add a new dimension to the chemistry of silver by proposing planar hexacoordinate motifs (hexagonal close packing) in a 2D monolayer sheet via systematic first principles calculations and molecular dynamics simulations. To our knowledge, no free-standing 2D silver monolayer has been reported to date. We hope that our results will inspire experimental fabrication of these free-standing monolayers.

II. Computational methodologies The electronic structure and total energy were calculated using DFT via the plane-wave pseudopotential (PWPP) technique implemented in the Vienna ab initio simulation package


Ag(111) surfaces as substrates to fabricate various 2D materials (including porous graphene,[14]



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electron interaction. The generalized gradient approximation (GGA) expressed by the PBE functional[22] and a 500 eV cutoff for the plane-wave basis set were adopted in all calculations. The convergence threshold was set as 10−6 eV in energy and 10−2 eV/Å in force. We put the Published on 06 July 2015. Downloaded by Mount Allison University on 07/07/2015 15:16:39.

monolayer Ag sheet on the xy plane and the z direction perpendicular to the layer plane, and the vacuum space of 20 Å in the z direction was used to avoid the interactions between adjacent layers. For geometry optimization and electronic structure calculations, the Brillouin zone was sampled with a 21×21×1 Γ-centered Monkhorst-Pack (MP)[23] K-points grid, respectively. Lattice dynamics was evaluated using finite displacement method[24] implemented in the CASTEP package[25] in Materials Studio 7.0. This was done at “ultrafine” level within the localdensity approximation (LDA) CA-PZ and using ultrasoft pseudopotentials. The energy cutoff was set as 330 eV and SCF tolerance was set as 5×10−7 eV/atom, force tolerance was set as 10−3 eV/Å. The Brillouin zone was sampled with a 21×21×1 Monkhorst-Pack (MP) grid for both phonon dispersion and phonon density of states. The supercell defined by cutoff radius was set to 7.0 Å for the finite displacement method. The supercell volume is 36 times that of the current cell. The separation of dispersion in the Brillouin zone was set as 0.003 Å−1, which represents the average distance between Monkhorst-Pack mesh q-points used in the real space dynamical matrix calculations. Ab initio Born-Oppenheimer molecular dynamics (BOMD) simulations were performed to assess the thermal stability of Ag monolayer. The scalar-relativistic DFT+D and Tkatchenko and Scheffler method were used in CASTEP[25] in Materials Studio 7.0. MD simulation in NVT ensemble were carried out for 10 ps with a time step of 1.0 fs (parameters: accuracy fine, SCF = 3 × 10−6, smearing = 0.04, DIIS = 20, Nosé-Hoover method,[26] Nosé Q = 2, Nosé chain length = 2). We fixed the center of mass. Materials Studio was also used to create the initial structures and visualize the results. Crystal structure predictions were performed using the evolutionary algorithm as implemented in the USPEX code.[27] In these calculations, initial structures are randomly produced using planar group symmetry. All newly produced structures are relaxed and relaxed energies area used for selecting structures as parents for the new generation of structures (produced by carefully designed variation operators, such as heredity and soft mutation). We considered systems with up to 18 atoms in the unit cell, and used 30 structures in each generation,


(VASP).[20] The projector-augmented wave (PAW)[21] method was used to represent the ion-

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heredity (60%), lattice mutation (30%), and atomic permutation (10%). In addition, two lowestenthalpy structures were allowed to survive into the next generation. The structure relaxations during the evolutionary algorithm were performed using the PBE functional as implemented in Published on 06 July 2015. Downloaded by Mount Allison University on 07/07/2015 15:16:39.

VASP. The Visualization for Electronic and Structural Analysis software (VESTA, series 3)[28] was used for visualization and plotting.

III. Results and discussion We have performed a comprehensive crystal structure search for the global minimum and low-lying polymorphs for Ag in 2D space using USPEX code.[27] The ground state structure (0 meV/atom) of the free-standing Ag monolayer is shown in Figure 1a. Other motifs, such as (Fig.1b) square (216 meV/atom), (Fig.1c) honeycomb (536 meV/atom), (Fig.1d) tetracoordinate (544 meV/atom) configurations, are all have higher energies than 1a. The uniform and highly symmetric distribution of the hexagonal close packed Ag atoms is the global minimum in 2D space. This close packed structure maximizes the number of bonds in the plane. These bonds act to stabilize and maintain the planar configuration of the sheet. It is noteworthy that this freestanding 2D Ag monolayer holds potential to be realized experimentally based on our results in this paper. We now focus on an analysis of various properties of the 2D Ag monolayer. We use periodic boundary conditions. The sheet has P6/mmm (#191) space group symmetry (Figure 1a). One unit cell includes a single Ag atom, and has lattice constants a = b = 2.8 Å. The calculated Ag-Ag bond length is 2.8 Å.


with 60% of the lowest-enthalpy structures allowed to produce the next generation through



Figure 1. Different motifs of Ag-monolayer: (a) hexagonal close packed, (b) square, (c) honeycomb, (d) tetracoordinate. The electron charge density is used to evaluate the chemical bonding between silver atoms of the monolayer. From the charge density plots and from the charge density analysis below Published on 06 July 2015. Downloaded by Mount Allison University on 07/07/2015 15:16:39.

(upper panel in Fig. 2), one can see that one electron from each atom is completely delocalized and participates in a nearly free homogeneous electron gas. The level of the charge density ranges between 0 and 7.2 units. In the 2D case, between the atoms, the value goes down to approximately 0.2 for the 2D case. This can be compared to a lower value of approximately 0.15 for the 3D case. Therefore, there is somewhat more delocalized charge between the atoms in the 2D case. Further insight into the bonding interaction comes from the analysis of the electron localization function (ELF), which provides a good description of electron delocalization in molecules[29] and solids,[30] and is a useful tool for chemical bond classification.[31] The ELF values are very low. From the ELF (lower panel in Fig. 2), one can see that the valence electron is delocalized into the whole 2D sheet. In conclusion, the distribution of electrons in the 2D Ag monolayer is similar to that for the 3D Ag(111) surface. From the chemical bonding analysis, we see that the bonding in the 2D silver monolayer is completely different from that of graphene[32] where 2c-2e σ bonds constitute the rigid honeycomb framework and one 6c-2e π bond is located over every hexagon. It is also different than the all-boron α-sheet[33] where the σ framework is formed by 3c-2e and 4c-2e σ-bonds and the π bonding involves 6c-2e or 7c-2e π-bonds. Furthermore, it is different from the BC3 honeycomb epitaxial sheet[34] with 2c-2e B-C and C-C σ-bonds and six π electrons (three 6c-2e π bonds) located over every carbon hexagon. As a 2D metal, we expect more similarity to other 2D metal layers such as the free-standing Au film.[19] Next, we evaluated the cohesive energy, which is defined as Ecoh = (xEAg-atom − EAgmonolayer)/x.

Ecoh = (xEAg-atom − EAg-bulk)/x. EAg-atom, EAg-monolayer and EAg-bulk are the total energies of

a single Ag atom, one unit cell of the Ag monolayer, and one unit cell of 3D bulk Ag (fcc phase) respectively. Based on our results, the 2D Ag monolayer and the 3D bulk have cohesive energies of 2.01 and 2.49 eV/atom, respectively. For comparison, using the same computational method, the cohesive energies of graphene, silicene, and germanene are 7.85, 3.98, and 3.26 eV/atom, respectively. We can also compare to the cohesive energy of free-standing 2D Au monolayer, which is 2.82 eV.[19] We note that although the cohesive energy of Ag monolayer is slightly


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0.21 eV for the bulk with twelve bonds to 0.33 eV for the 2D layer with six bonds. This increase in bond strength contributes to the stability of the free-standing 2D layer. We observed a similar increase in the bond strength in the free-standing gold 2D layer.[35] The cohesive energy of the Published on 06 July 2015. Downloaded by Mount Allison University on 07/07/2015 15:16:39.

Ag monolayer is lower than the others, but the bond strengths are still large enough to support experimental fabrication.


lower than that of the Ag 3D bulk phases, the bond strength per atom actually increases from



Figure 2. a) Charge density (upper panel) and b) ELF (lower panel) of the 2D Ag monolayer and 3D bulk Ag.

The dynamic stability of the Ag monolayer was confirmed by calculating the phonon dispersion along the high-symmetry lines using the finite displacement method.[24] All the frequencies are real, indicating kinetic stability. No imaginary phonon modes were found in the whole Brillouin zone. In particular, the highest frequency reaches up to 230 cm−1.



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Figure 3. Phonon dispersion and phonon density of states of the 2D Ag monolayer. Γ (0, 0, 0), M (0, 1/2, 0), K (1/3, 2/3, 0) refer to special points in the first Brillouin zone in the reciprocal space.

To verify the thermal stability of this new material at both ambient conditions and also at elevated temperatures, we have performed ab initio Born-Oppenheimer molecular dynamics simulations.[36] A periodic 4 × 4 supercell was used in the MD simulations. A series of individual 4 − 10 ps simulations were carried out to evaluate the thermal stability of the 2D silver monolayer at temperatures of 500, 800, and 1200 K. Snapshots taken at the end of each simulation are shown in Figure 4. The structure survives a 10 ps anneal up to 800 K. A survey of bond length extensions shows an increase of up to 29% and 36% during last 1 ps of the 500 and 800 K runs. These results demonstrate that the Ag monolayer has good thermal stability and can maintain its structural integrity during brief 10 ps annealing up to 800 K. At 1200K, the system



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bulk Ag. We can compare these results to free-standing Cu or Au monolayers. The 2D Cu monolayer was able to be annealed up to 1200 K, while the 2D Au layer survived 10 ps anneal


up to 1400 K.[19]

Figure 4. Snapshots of the final frame of each molecular dynamics simulation from 500 to 1200 K (top and side views). Bonds to atoms outside this section exist but are not shown.

To get insight into the electronic properties, we have computed the band structure as well as its density of states (DOS). As shown in Figure 5, the material shows a band structure typical for metals. The metallic character of Ag monolayer is demonstrated by the Fermi level (E = 0) being located inside the bands, and no observation of a band gap at this energy. We performed a separate spin dependent DFT calculation to test for magnetism in this material. We find that the 2D Ag monolayer is non-magnetic. The partial density of states (PDOS) was plotted (Fig. 5 right) in order to visualize the contributions of individual orbitals. There is a sharp peak under the Fermi level mainly contributed by Ag d-states. The states at the Fermi level have major contributions from Ag-p and -s states, with p > s > d (right). There is apparent hybridization between the Ag-p and -s states. This is consistent with the chemical bonding analysis of the Ag monolayer.


is clearly starting to melt. These numbers can be compared to the melting point of 1235 K for

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Figure 5. Electronic structure of the Ag monolayer. The band structure (left), total density of states (TDOS) and the partial density of states (PDOS) (right). The Fermi level is at 0 eV. Finally, we have analyzed the mechanical properties for practical applications of the Ag sheet. The in-plane Young modulus, (or in-plane stiffness), is commonly used to evaluate the mechanical stability of 2D layered materials. We compared the calculated value of our new material to reported experimental values[37] and previous theoretical results[38] for several commonly known 2D materials, including graphene, silicone, and germanene. For the Ag monolayer, the in-plane stiffness was computed to be 31 N/m, which is much lower than graphene (295 N/m). However, it is comparable to the value for germanene (42 N/m) computed at the same theoretical levels. This in-plane stiffness is appropriate for a 2D metal layer.

IV. Conclusions



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simulations show that the framework is maintained during short 10 ps annealing runs up to 800 K. The bond strength is substantially increased in comparison to the bulk due to the smaller number of bonds per atom. It is hexagonal close packed with planar hexacoordinate bonding. Published on 06 July 2015. Downloaded by Mount Allison University on 07/07/2015 15:16:39.

One valence electron is delocalized, and is donated to a nearly free electron gas. This material is metallic. Many properties are similar to 3D bulk Ag. Local structural stability is predicted by the absence of any imaginary phonon modes. A general search using an evolutionary algorithm confirmed that the Ag monolayer is the global minimum structure in the 2D space. Considering the rapid development of experimental techniques for fabrication of low-dimensional materials in recent years, we hope that this work will inspire the experimental realization of these new 2D Ag monolayers.

Acknowledgements Support in Germany by the Fellowship of Hanse-Wissenschafts-Kolleg (HWK) and Research Scholarship of University of Bremen (to L.-M.Y) are gratefully acknowledged. L.M.Y and E.G thank Matthew Dornfeld for his assistance. We thank the Minnesota supercomputer Institute, HLRN & JULICH supercomputers for support.


In summary, we have studied the free-standing 2D Ag monolayer. Molecular dynamics

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References



DOI: 10.1039/C5CP03465E

We predict a novel and highly stable 2D Ag monolayer featuring planar hexacoordinate silver.



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