Transformation of the Anion Sublattice in the Cation-Exchange

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Transformation of the Anion Sublattice in the CationExchange Synthesis of AuS from Cu S Nanocrystals 2

2-x

Emil A. Hernández-Pagán, Andrew O'Hara, Summer L. Arrowood, James R. McBride, Jordan M. Rhodes, Sokrates T. Pantelides, and Janet E. Macdonald Chem. Mater., Just Accepted Manuscript • DOI: 10.1021/acs.chemmater.8b03814 • Publication Date (Web): 13 Nov 2018 Downloaded from http://pubs.acs.org on November 19, 2018

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Chemistry of Materials

Transformation of the Anion Sublattice in the Cation-Exchange Synthesis of Au2S from Cu2-xS Nanocrystals Emil A. Hernández-Pagán,†,‖ Andrew O’Hara,‡ Summer L. Arrowood,†,‖ James R. McBride,

†,‖

Jordan M. Rhodes,

†,‖

Sokrates T. Pantelides,

Macdonald*,

†Department

‡,§,‖

Janet E.

†,#,‖

of Chemistry, ‡Department of Physics and Astronomy, §Department

of Electrical Engineering and Computer Science, #Interdisciplinary Materials Science, and ‖The Vanderbilt Institute of Nanoscale Science and Engineering, Vanderbilt University, Nashville, Tennessee 37235, United States

* Email: [email protected]

ABSTRACT

ACS Paragon Plus Environment

Chemistry of Materials 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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Cation exchange is a versatile post-synthetic technique that has been exploited in the synthesis of metastable nanocrystals through preservation of the anion sublattice. Here we report on the mechanistic details of the synthesis of metastable Au2S via cation exchange with Cu2-xS nanocrystals. This conversion requires a transformation of the anion sublattice, from hcp in Cu2-xS to bcc Au2S accompanied by an expansion of the unit cell. The ligand environment plays a key role in the driving force of the reaction as the presence of oleylamine allows the conversion to proceed at room temperature while the addition of trioctylphosphine hinders the reaction. By employing transmission electron microscopy (TEM) on faceted nanocrystals and partial cation exchange of nanocrystals, it was demonstrated that the reaction proceeds in a highly directional

manner

through

the

pyramidal

facets.

Since

cation

exchange

produces high quality nanocrystals as seen through XRD and TEM, UV-Vis and Raman spectroscopy were used to characterize the optoelectronic properties of the metastable Au2S nanocrsytals. A Tauc plot analysis revealed a band gap of 2.6 eV, while two intrinsic Raman modes were identified at 265 cm-1 and 329


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cm-1. Density functional theory (DFT) calculations of structures, energy bands, optical spectra, and phonon spectra were performed and combined with the experimental data to provide additional insights into the characterization of Au2S nanocrystals.

The impact of nanomaterials in the discovery of new phenomena and the development of applications that exploit them has led to intense research efforts to expand the library of synthesized materials. While such efforts have led to an ever-growing synthetic toolbox, the fundamental understanding and study of many synthetic mechanisms has not always been rigorous and as result the rational design of nanomaterials still remains a challenge. Among the different strategies, cation exchange is a versatile post-synthetic technique that facilitates the transformation of a host nanomaterial through exchange of its constituent

cations.

In

addition

to

complete

cation

exchange

to

a

new

nanomaterial, partial cation exchange can lead to core-shell, Janus, striped, and other hybrid nanostructures or to the doping of the host material.1,2 In both



cases, the starting size and shape is closely retained after exchange, with the exception of reactions leading to a significant change in the unit cell volume, when formation of voids and defects has been observed.3 Along with retention of the size and shape, a predominant feature that has been investigated in cation-exchange reactions is the preservation of the anion sublattice during the exchange. The anions typically possess a larger size and lower mobility relative to those of the cations.4–6 Retention of the anion sublattice has been extensively used to obtain metastable phases that would be challenging to obtain via direct synthesis. Most recently, the Schaak group has presented preservation of both anion and cation sublattice in the cationexchange synthesis of wurtzite CoS and MnS.7 While there are cases involving a change in the anion sub-lattice, these have received considerably less attention. Alivisatos et al. demonstrated the transformation of ~4 nm wurtzite CdSe quantum dots to cubic Ag2Se at room temperature, which requires a concerted transformation of both the anion and cation sublattices.8 It is notable that, in this work, slightly larger quantum dots were found to adopt an


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orthorhombic Ag2Se structure, indicating conservation of the anion sublattice. This observation was rationalized by employing a reaction-zone model where the diameter of the smaller quantum dots was close to the reaction-zone width, allowing the reordering of both cations and anions. Jeong and coworkers reported on the formation of tetragonal CuInSe2 nanocrystals from the layered trigonal form of In2Se3, which requires cleavage of neighboring sheets bonded through Se-Se van der Waals interactions and a unit-cell-volume change of 5 %.9 Moreels et al. showed the conversion of hexagonal Cu2Te to wurtzite CdTe and, while both structures were hexagonal in nature with comparable lattice constants,

rearrangement

of

the

Te

anions

is

required

due

to

different

orientations of the c-axis.10 This process only occurs at temperatures > 150 C, suggesting

that

the

anion

rearrangement

has

a

large

activation

energy.

Therefore, to achieve a rational synthesis of nanomaterials via cation exchange it is important to understand all the different variants. Copper chalcogenides have emerged as preferred host materials as the high Cu mobility and inherent vacancies facilitate cation-exchange reactions.11 There



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have been numerous reports of exchanges with Ni2+, Mn2+, Zn2+, Cd2+, Co2+, and Hg2+. However, there have only been two reports employing Au+ and the underlying mechanisms were not investigated.12,13 Au2S crystallizes in the same cubic structure as Cu2O (space group 𝑃𝑛3𝑚) with Au forming a face-centered cubic sublattice and sulfur forming a body-centered cubic sublattice.14,15 In this paper, we report the synthesis of high-crystalline-quality and high-purity Au2S nanocrystals from Cu2-xS via cation exchange and deduce the atomicscale mechanism that underlies the transformation from Cu2-xS to Au2S, aided by extensive scanning transmission electron microscopy data that systematically tracked

the

changes.

We

also

report

UV-VIS

and

Raman-spectroscopy

characterization of the resulting nanoparticles and combine the experimental data with density-functional-theory (DFT) calculations of the band structure, optical absorbance, and vibrational spectra of Au2S to further elucidate its properties. In comparison to other reactions, the Cu2-xS-to-Au2S system presents four unique features. First, the ionic radius of Au+ (137 ppm) is ca. 1.8 times the


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size of that of Cu+ (77 pm). This is a significant difference relative to the cations commonly employed (see above) in cation-exchange reactions which have smaller or similar radii to that of Cu+. Second, Au+ is a softer acid than the cations listed above and Cu+. Third, while the Cu2-xS host has a pseudohexagonal crystal structure, Au2S only forms with the previously mentioned cubic structure. Therefore, in order for this reaction to proceed a substantial transformation of the anion sublattice from hcp to bcc must occur. Last, accompanied with the crystal-structure transformation is a large change in the unit cell volume (∆V/V 38 %). Considering these factors, it is quite impressive that this reaction occurs at room temperature with preservation of size and shape of the nanocrystals. RESULTS AND DISCUSSION

The Cu2-xS nanoparticles that served as seeds for the cation exchange (Figure 1A) were synthesized following a previously reported method. Briefly, Cu(acac)2, DDT, and DOE were combined in a flask and heated to 215 C. Figure 1B shows a TEM image of the Cu2-xS seeds. The seeds were single



crystalline and monodisperse. XRD analysis (Figure 1F) revealed the Cu2-xS seeds had the djurleite phase (Cu1.94S, ICDD-023-0959). The particles had an average size of 10.2 ± 1.2 nm (n = 130). The size was obtained by treating the particles as spheres and measuring the diameter. However, previous work has shown that particles synthesized under similar conditions are in fact highly faceted (truncated hexagonal biprisms).16 The cation-exchange reaction was carried out at room temperature by mixing the Cu2-xS seeds with the gold precursor, HAuCl4·nH2O dissolved in oleylamine (OLAM) and chloroform. Upon dissolution of HAuCl4·nH2O, OLAM reduces the Au3+ to Au+ forming an orange colored [OLAM-AuCl] complex.17 A similar approach was reported in the work by Swihart et al. and Park et al.12,13 However, in the former, the seeds were of mixed phase (predominately CuS covellite) and in the latter the authors only performed partial exchange to render hybrid nanorings. We used this approach to understand the fundamental mechanistic details associated with this cationexchange reaction.


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Figure 1C shows a TEM image of the resulting nanoparticles after exchange. The average size of the exchange product increased to 11.2 ± 1.2 nm (n = 130). The XRD pattern in the top panel of Figure 1D shows conversion of the Cu2-xS seeds to Au2S (ICSD-78718), with a minor Cu2-xS impurity. The valency, and thus the size of the entering cation, plays a role in the mechanism and product of the exchange. For example, the exchange of Cu+ with Sn4+ in Cu2xSe

proceeds through a ternary alloy to form Cu2SnSe3.18 Conversely, with Sn2+

the product is SnSe and the exchange progresses via Cu2-xSe/SnSe Janus heterostructures. Therefore, to validate that the Au3+ is reduced and the exchange is between Au+ and Cu+, the reaction was carried out with AuCl in place of HAuCl4·nH2O under otherwise identical conditions. XRD analysis showed that Au2S is also formed (Figure S1) when using AuCl, confirming that the exchange is between Au+ and Cu+. Au2S is a metastable phase and as a result metallic Au is commonly found as an impurity in the direct synthesis of Au2S.19 In contrast, peaks corresponding to metallic Au were not observed in the diffraction pattern of the product obtained via cation exchange. However,



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exposure of the particles to the electron beam during TEM imaging does lead to the formation of metallic Au (Figure S2), in agreement with previous reports.12,20 Therefore, low current STEM-HAADF imaging was employed to mitigate the formation of Au. STEM-HAADF images (Figures 1E-F) show two distinct shapes based on the particle orientation. From the top view, four crystalline domains are observed with lattice spacings of 2.9 Å corresponding to the (111)Au2S plane. Conversely, a single crystalline domain is observed when the particles are oriented on their side. The lattice spacing for this domain is also 2.9 Å, corresponding to the (111)Au2S

plane.

To

elucidate

the

reaction

pathway

that

leads

to

these

morphologies, partially exchanged nanocrystals were examined. The STEMHAADF (Figure 2A-C and Figure S3) images of partially exchanged product show that the nucleation of Au2S occurs through multiple entry points. However, these entry points are highly directional and facet-specific as the exchange proceeds via the pyramidal facets and not the basal or prismatic facets (Figure 3A). The STEM-EDS elemental maps (Figure 2D-G) further confirm this


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observation. It is notable that the same directionality and facet dependence was also observed when the exchange was carried out with hexagonal Cu2-xS platelets and faceted CuS discs (Figure S4). In the case of the Cu2-xS platelets, the reaction begins exclusively at the tips of the hexagonal platelets, and not the basal or prismatic facets. For faceted CuS discs, the exchange also proceeds from the side facets. It should be noted that the presence of disulfide bonds in CuS limits the rearrangement of the anion sublattice required for the exchange,21 resulting only in a core-shell structure. The highly directional nature of the cation exchange can be rationalized from three standpoints: the ionic radii, the facets, and the required transformation of the sulfur sublattice. The first factor contributing to the directionality is the large ionic radii (r= 137 pm), and thus coordination number of Au+. Djurleite has a large orthorhombic unit cell (Z=8) with a distorted hexagonal packing of the anions in the crystallographic a direction. The small copper cations (ionic radii, r= 77 pm) occupy trigonal and tetrahedral coordination sites.22 The octahedral sites are vacant, which allows diffusion of the much larger Au+ cation requiring



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an octahedral coordination. Access of the Au+ to the octahedral sites occurs through the (b,c) planes perpendicular to the close packed direction, as evidenced by STEM-HAADF and HRTEM images. This observation aligns with what has been observed in other systems. For example, in the exchange of hexagonal Cu2-XSe with Pb2+ it was shown experimentally and theoretically that Pb2+ preferentially diffuses through the panes perpendicular to the close packed direction, in order to fulfill the octahedral coordination.23 Other reports have shown that these crystallographic planes play a key role in exchange reactions involving cations with tetragonal coordination as well.6 It

has

been

nanoparticles

demonstrated

contain

that

the

low-coordination

surfaces atoms,

of

steps,

highly and

faceted

metal

edges.24

Facet

dependent and directionally specific cation exchanges have been reported by Alivisatos et al.25 In their work, they observed asymmetric cation exchange when reacting CdS nanorods with Cu+. This asymmetry was attributed in part to the lower stability of the (0001) end facet due to lower-coordination Cd leading to preferential reaction at this end of the nanorods. Therefore, we


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posited that the pyramidal facets of the truncated hexagonal Cu2-xS biprism and CuS discs and the corners of the hexagonal Cu2-xS platelets possess similar defects, making them higher-energy surfaces. As a result, these surfaces become preferential nucleation sites for Au2S. We examined the atomic arrangement of the sulfur anions on the facets of Cu2-xS hexagonal biprisms, assuming there is no major surface reconstruction compared to the bulk materials. The basal {400}dj/{001}hex facets and the prismatic {042}dj/{010}hex and {002}dj/{110}hex facets present trigonal channels (~37 pm) between the sulfur anions to solution (Figure 3A). In stark contrast, the pyramidal {442}dj/{011}hex and {404}dj/{111}hex facets present two layers of trigonal channels alternating with large truncated octahedral channels (~99 pm). These large channels are the likely point of entry for Au+ and the nucleation of the Au2S phase and explain why cation exchange preferentially occurs on the prismatic facets. The third factor is the sulfur sublattice. The sulfur anions in the djurleite structure conform to a pseudo hcp lattice.22 Consequently, in addition to the change in the cation coordination, the exchange requires a transformation of



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the anion sublattice from hcp in Cu2-xS to bcc in Au2S. The hcp and bcc structures are closely related. HCP has hexagonally arranged atoms in the (001)hcp plane, and follows an ABAB stacking pattern. Similarly, the (110)bcc contains sulfur atoms arranged in distorted hexagons. The anion stacking pattern is also ABAB. As illustrated in Figure 3B, the transformation in the anion sublattice from hcp to bcc requires: i) a shift of every other {001}hcp plane in the [110]hcp direction and ii) a lattice expansion in [110]hcp direction. In the transformation from Cu2-xS to Au2S, this expansion is 27% and is coupled to smaller 3-4% expansions in the other two perpendicular [110]hcp and [101]hcp directions, which correspond to the [001]bcc, [110]bcc and [110]bcc, respectively. This significant expansion is due to the large lattice mismatch between Cu2-xS to Au2S. Since this transformation can occur in three symmetry equivalent directions of the HCP lattice, Au2S crystals that nucleate at different parts of the host Cu2xS,

will

not

always

crystallographically

align,

polycrystalline Au2S projects (Figure 2).


as

was

observed

in

the

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The direct conversion from hcp to bcc sublattice seen here in a cation exchange is in direct contrast to the work by Robinson et al.26 who saw a retention of the hcp anion sublattice in cation exchange from roxbyite Cu1.8S (distorted hcp anion lattice) to wurtzite-ZnS, and Schaak et al.7 who also showed a retention of the anion sublattice in cation exchanges from roxbyite Cu1.8S to notably metastable wurtzite phases of CoS and MnS. The ionic radius of Cu+(77pm), Zn2+ (74 pm), Co2+ (88.5pm) and Mn2+ (81-97 pm) are similar, whereas the ionic radius of Au+ is almost twice the size at 137 pm. It is likely that the expansion of the lattice to accommodate the large gold ions facilitates the hcp-bcc transformation, as one of the key requirements is a distortion and expansion of the lattice. A bcc to hcp transition is known for CuBr at 742K, and is facilitated by the high ionic mobility of the Cu in that structure.27 Rearrangement in the anion sublattice has also been observed in other copper chalcogenide based exchange reactions. Teranishi, et al. observed the reverse transformation

from

bcc

to

distorted

hcp.28

However,

this

transformation

occurred through anion exchange from cuprite Cu2O to roxybite Cu1.8S. In the



conversion of Cu2Te to CdTe, both with hexagonal structure, Te anions had to rearrange due to different orientation of the c-axis.10 Moreover, Manna and coworkers showed the reaction of Cu2-XSe with Sn2+ to form SnSe was accompanied by a change in the Se sublattice from cubic to orthorhombic.18 It is notable that, when they replaced Sn2+ (118 pm) with Sn4+ (69 pm) the cubic lattice was retained. However, in both systems (Cu2Te/CdTe and Cu2-XSe/SnSe) temperatures ≥ 100 C were required to drive the exchange despite the small lattice mismatch (∆V≤ 7%) between the reactant and product. Conversely, the transformation of Cu2-xS to Au2S involves a large volume change of ∆V≤ 30% and occurs at room temperature. It is remarkable that such a large volume change does not cause voids or fragmentation of the particles as observed in other work3 and suggests a high stress tolerance. This result prompts the question; what provides the driving force for this reaction? The fact that the reaction proceeds at room temperature suggests that formation of Au2S is thermodynamically favorable with minimal activation energy. The reaction’s Gibbs Free Energy change (G) was calculated following two


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different simplified calculations reported elsewhere (see SI) that employ the standard free energy of formation of the bulk solids.20,29 Both calculations resulted in a negative G. Yet an important factor, which is not accounted for in these calculations, is the solvation energies of the entering and exiting cations in the reaction. The hard-and-soft-acids-and-bases (HSAB) theory has been extensively employed to design and explain cation exchange reactions. In the myriad of exchange reactions involving copper chalcogenides found in the literature (including those discussed above), Cu+, a soft acid (= 6.28 eV), is replaced with harder acids such as Pb2+, Zn2+, and Co2+. Consequently, the soft base trioctylphosphine (TOP,  6 eV) is required to drive the reaction, solvating the exiting soft Cu+. In this work, only the gold precursor and OLAM are present in solution. Au+ is softer (= 5.6 eV) than Cu+, and the hard base OLAM ( 8 eV) is used to drive the solvation of the harder Cu+ relative to the soft Au+. Given that like interactions are favored, one can expect the binding of Cu+ to OLAM to be more favorable than that of Au+ to OLAM, thus promoting cation exchange. This is analogous to the CdSe  Ag2Se system, where



methanol is employed as a hard base to drive the replacement of hard Cd2+ with soft Ag+. If this is the case, addition of TOP to the reaction should hinder cation exchange due to the stronger TOP:Au+ binding. To test this, a control reaction was carried out where the gold precursor was first mixed with OLAM followed by addition of TOP. As mentioned earlier, the mixture of OLAM with HAuCl4 in chloroform results in an orange solution. Upon addition of TOP, the solution became colorless indicating the formation of a TOP-AuCl complex.30 The Cu2-xS seeds were then added and the reaction was allowed to proceed for 5 min. XRD analysis showed that cation exchange did not occur under these reaction conditions (Figure S5). Interestingly, exposure of the obtained Au2S to TOP and CuCl at room temperature did not result in conversion to the starting Cu2-xS, but rather the nanocrystals remained as Au2S (Figure S6). These results strongly support the interplay between cation solvation during the reactions and the G of the systems involved, both must be considered in designing and rationalizing the driving force of the exchange process.


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Since the present cation exchange process produces both highly crystalline and

relatively

clean

stoichiometric

nanoparticles

in

comparison

to

direct

synthesis techniques, further characterization of the nanoparticles will help shed light

on

long

standing

questions

about

the

band

gap19,31

and

Raman

features32,33 of Au2S. To this end, we have performed additional experimental characterization and combined it with corresponding DFT calculations. We start with DFT calculations aimed at understanding the electronic structure and optical excitations of Au2S. The optimized LDA lattice constant of Au2S is 5.18 Å. While this is an overestimation of the experimental lattice constant, it is better than that obtained with the PBE functional (5.31 Å). At this level of theory, we find that Au2S has a direct gap of 1.34 eV located at the Γ-point of the first Brillouin zone as shown in the band structure of Figure 4A. Although neglected in a previously reported study of the electronic structure of Au2S,34 there is a strong spin-orbit splitting effect in both the valence and conduction bands. The ordinarily threefold-degenerate spatial orbitals split so that the valence band maximum (VBM) comprises a split-off band while the other two



bands are doubly-degenerate heavy- and light-hole bands sitting 0.42 eV below the VBM. In the conduction band, the bottom of the conduction band comprises a heavy- and light-electron band with a split-off band 0.72 eV higher in energy. While the band splitting in the valence band is due entirely to spin-orbit coupling, the observed conduction band splitting is due primarily to differences in orbital characteristics, with only 0.17 eV of the splitting arising from spin-orbit coupling. The heavy- and light-electron bands comprise primarily Au p-orbital character while the split-off conduction band consists primarily of S s-orbital character. Conversely, all three of the previously mentioned valence bands are hybridization of the Au s- and d-orbitals. To improve the accuracy of our calculated band gap, which is underestimated by the LDA exchange-correlation functional, we perform LDA+G0W0 perturbative calculations and Bethe-Salpeter excitonic calculation of the optical absorbance. These techniques have been shown, generally, to provide a much more accurate description of both the fundamental and optical gaps of semiconductors.35 The LDA+G0W0 method introduces a perturbative correction to


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the electronic structure by effectively replacing the LDA exchange-correlation energy with the electron self-energy calculated from the LDA wave functions. Within this approach, the fundamental band gap of Au2S is 2.48 eV. The dispersion of the bands remains relatively unaffected and can be considered, in the present case, to be an approximately rigid shift of the bands. The dielectric response functions of Au2S were calculated using the Beth-Salpeter equation. The absorbance is calculated from the real and imaginary parts of the dielectric function via:

𝛼 = 4𝜋

(|𝜀| ― 𝜀1) 2 𝜆

where 𝜀 = 𝜀1 +𝑖𝜀2 is the complex dielectric function and 𝜆 is the respective wavelength of light. The calculation is performed both explicitly excluding and including e-h exciton effects shown in Figure 4B. Explicitly excluding these effects provides the ability to understand how the oscillator strengths are altered by the e-h interaction as well as provide a determination of the exciton binding

energy

(i.e.

the

role

of

excitonic

effects

in

differentiating

the

fundamental gap and the optical gap). As expected from the band structure



analysis, there are a series of well-defined peaks arising from the direct gap excitations. The binding energy of the lowest exciton is 164 meV indicating that the optical gap is reduced to ~2.32 eV. Unlike in the isostructural and isovalent Cu2O where the first exciton is dark,36 the first exciton in Au2S is bright. The difference can be attributed to differences in the orbital nature of the conduction band. In Cu2O, the lowest conduction-band state is composed of Cu 4s characteristic and hence the optical excitation is parity forbidden from the Cu 3d derived VBM. As previously mentioned, the CBM in Au2S has predominantly p-orbital characteristic and as such the transition is parity allowed. Although the first exciton is bright, room temperature photoluminescence of the nanocrystals was not observed indicating the main decay pathways were non radiative. Using the effective masses extracted from the band structure calculation and the calculated dielectric constant (see SI), the exciton Bohr radii can be approximated via: ℏ2ℰ∞ 1 1 𝑎0 = 2 + . 𝑒 𝑚𝑒 𝑚ℎ

(

)


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Since the dispersion of the effective masses is not generally constant across ∗ ∗ ∗ cubic high-symmetry points (e.g. 𝑚Γ→𝑋 ), we perform an effective ≠ 𝑚Γ→𝑀 ≠ 𝑚Γ→𝑅

cubic average for the various exciton mass combinations. The degeneracy of the heavy and light holes is treated via a geometric mean. This treatment indicates approximate Bohr radii for the four excitons as 0.27 nm, 0.23 nm, 0.16 nm, and 0.13 nm. The largest Bohr radius is slightly less than half the Bohr exciton radius reported for Cu2O37 and can be mostly attributed to the larger dielectric constant of Cu2O and heavier effective masses of Au2S. Therefore, the synthesis of high-quality quantum confined nanoparticles of Au2S may prove challenging as in the case of Cu2O. For comparison of the calculated absorbance spectrum to the experimentally obtained UV-VIS spectrum, additional broadening was applied to the calculated spectrum via Gaussian convolution to yield an effective broadening width of 0.8 eV as a best match to the slopes of the two absorbance spectra. The experimental and broadened calculated spectra are overlaid in Figure 4C. This additional broadening effectively accounts for systematic issues, temperature



Page 24 of 48

effects, and colloidal scattering. A Tauc plot (Figure S7) for the experimental absorbance indicates a gap of ~2.6 eV. Due to ambiguity on where to place the Tauc tangent, this method provides a reasonable but somewhat error-prone extraction of the band gap. The broadened calculated absorbance spectrum, however, shows that the theoretical optical gap (fundamental gap minus exciton binding energy) of ~2.32 eV is satisfactory. The additional broad, low intensity peak in the experimental absorbance centered around 1,400 nm is most likely due to remaining Cu2-xS impurities. Literature comparisons for the band gap of Au2S show that disagreement between experiments is widespread. Early theoretical results indicated that Au2S had a direct gap between 1.3 and 2.6 eV;38 however, no details of these calculations were published. We note that this range is similar to the values for the

present

LDA

calculation

and

G0W0

calculation.

Recent

theoretical

calculations using PBE and hybrid functional estimated the fundamental gap to be 1.94 eV and 3.00 eV, respectively.34 A Tauc-like Scanlon analysis by Morris, et al.19 on colloidal nanoparticles indicated a direct gap of 1.8 ± 0.2 eV and an


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indirect gap of 0.5 ± 0.2 eV; while a Tauc analysis by Kuo, et al.31 found a direct gap of ~2.5 eV and an indirect gap of ~1.77 eV. These experimental results along with our own indicate that the size and quality of the particles has a strong impact on the value of the extracted band gap. Furthermore, it illustrates that the use of Tauc plots in nanoparticle absorbance can provide misleading results (i.e. whether the material is a direct gap or indirect gap semiconductor). The direct gap obtained by Kuo, et al. does agree with our experimental and calculated band gap. Additional characterization of Au2S is provided by vibrational spectra analysis. Like isostructural Cu2O, Au2S belongs to the space group 𝑂4ℎ with two formula units per cell, which implies that the 15 optical phonon modes can be classified according to the irreducible representation as: Γopt = A2u + Eu + T2u + T2g + 2T1u where the T2g mode is Raman active and the 2 T1u modes are IR active. Experimental Raman spectroscopy was performed for large nanoparticles (d ~ 14 nm) and small nanoparticles (d ~ 10 nm). In order to extract the phonon



Page 26 of 48

frequencies from the experimental data, a series of Gaussian functions was fit to the data. The best fit was obtained using 5 Gaussian functions and their peak centers are shown in Figure 5 for the large nanoparticles. Raman spectra for the other samples are available in the supplemental information. The peaks at 474 cm-1, 467 cm-1, and 428 cm-1 are consistent with S-S bonds which occur on the surface due to oxidation of the particles.32,33,39 Due to the closeness of the 474 cm-1 and 467 cm-1 peaks, they are often reported as a single peak in the literature, but the peak often contains an asymmetry.39 The peak at 428 cm-1, while difficult to see in the current results without the Gaussian fits, has been observed clearly with surface enhanced Raman spectroscopy.33 The presence of these defect related Raman peaks provides further confirmation that non-radiative recombination pathways may exist to prevent observation of photoluminescence. The peaks at 265 cm-1 and 329 cm-1 are, however, intrinsic to the Au2S nanoparticles. The 265 cm-1 peak has been previously

reported

as

being

due

to

surface

or

interface

Au-S

bond

stretches.32,33,40 The 329 cm-1 mode has been observed in other works [as a


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broad peak around 340 cm-1, analogous to a peak at 515 cm-1 in Cu2O (Ref. 32); a shoulder peak at 325 cm-1 in the data of Ref. 32]. DFT phonon calculations (see discussion below) find that this mode is a bulk bond stretch mode. Further confirmation that the 329 cm-1 peak is the bulk peak while the 265 cm-1 peak is due to the surface can be obtained by comparing Figure 5 with the corresponding figure for the smaller particles (Figure S8). As expected, the 329 cm-1 peak is enhanced relative to the 265 cm-1 peak for the nanocrystals with larger volume. The identification of the 329 cm-1 Raman mode as the intrinsic Au2S peak can be corroborated by a detailed examination of the DFT calculations of the optical phonon modes. As it turns out, the LDA functional for DFT significantly overestimates the phonon modes in the present case, therefore the modes were also calculated using the PBE functional. Both sets of calculated phonon frequencies are reported in Table 1. Using PBE, the Raman active T2g mode is 357 cm-1. While the calculated mode is 8.5% higher than the experimentally determined value, it still is within the typical accuracy of DFT calculated values.



The lower T1u IR-active mode (92 cm-1 in PBE) sits lower in frequency than can often be detected with standard room temperature IR spectroscopic techniques. The high-frequency T1u IR-active mode (386 cm-1 in PBE) does have a frequency that should be detectable for standard IR spectroscopic techniques. However, its value lies within the fingerprint region implying that in solvent-based nanoparticle synthesis experiments, such as the present case, rather than bulk or thin film solid-state methods, the isolation of such a mode within the spectra is impractical. Inclusion of the long-range part of the dynamical (i.e. non-analytical correction; see SI) implies that the LO/TO splitting for IR-active modes is negligible (i.e. < 1 cm-1) due to the highly covalent nature of Au2S. CONCLUSION

In summary, metastable Au2S nanoparticles without metallic Au impurity can be obtained via cation exchange from Cu2-xS. The transformation requires a significant rearrangement of the S sublattice, going from hcp in Cu2-xS to bcc in Au2S. This rearrangement entails a shift in every other plane and expansion of


Page 28 of 48

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the lattice. The exchange is highly directional proceeding through the pyramidal facets

and

not

the

basal

or

prismatic

facets.

Despite

the

required

rearrangement of the anion sublattice, the reaction can be carried out room temperature. This absence of heating, along with calculations of the reaction’s G

and

analysis

of

the

corresponding

BDE,

indicate

the

reaction

is

thermodynamically favorable. The ligand environment also played a key role as the exchange occurred in OLAM yet was hindered in the presence of TOP. HSAB theory was invoked to explain this observation given that TOP (softer base) would bind to Au+ (softer acid) rather than drive the extraction of Cu+. Optical characterization of Au2S was performed without the convoluted effects of metallic Au impurities encountered during direct synthesis methods that often cause discrepancies in the reported direct band gap values. We obtain a value of ~2.6 eV from the Tauc method in the present case; while G0W0+BSE calculations indicate a fundamental gap of 2.48 eV and an optical gap of 2.32 eV. The fundamental vs optical gap values differ due to the formation of excitons

with

a

Bohr

radius

98%) and gold(III) chloride hydrate (HAuCl4 · nH2O, 99%), %) were obtained from Strem Chemicals. Ethanol, methanol, and toluene were obtained from Fisher. All


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materials were used as received without additional purification. Air-free Schlenk line (nitrogen) techniques were used throughout the experimental procedure. Synthesis of Cu2-xS Nanocrystals (NCs). Cu2-xS NCs were prepared following the synthesis described by Kuzuya et al.42 with minor modifications. For 10-nm NPs, Cu(acac)2 (1 mmol), DDT (3 mL), and DOE (2 mL) were combined in a 25 mL three-neck flask and degassed under vacuum at 80 ˚C for 30 min. The flask was placed under N2 and the temperature was increased to 215 ˚C. After 1 h at 215 ˚C, the heating mantle was removed to cool down the flask until reaching room temperature. The particles were purified by three cycles of precipitation with ethanol, centrifugation at 8700 rpm for 10 min, followed by resuspension in toluene. The particles were stored in chloroform. The same procedure was followed for 14 nm Cu2-xS, except it was carried out in neat DDT (5 mL). Determination of Cu+ concentration. To determine the concentration of Cu+ from the copper sulfide nanoparticles, a known volume of the stock solution



was dissolved with the copper-complexing agent neocuproine in chloroform, and the UV-Vis absorbance was compared with a calibration curve. Cation-Exchange Reactions. For the cation-exchange reactions, HAuCl4·nH2O (0.025 mmol) was dissolved in chloroform with OLAM (1 mL) in a 25 mL threeneck flask under N2 at room temperature. A given volume of Cu2-xS NPs in chloroform equivalent to 0.025 mmol Cu+ was then added. The volume of chloroform used to dissolve the HAuCl4 · nH2O was varied such that the total reaction volume (chloroform + NCs + 1 mL OLAM) was 5 mL in all reactions. The cation exchange reactions were allowed to proceed under vigorous stirring for 20 min and 40 min, for the 10 nm and 14 nm Cu2-xS NCs, respectively. Afterwards, the exchanged NPs were purified by three cycles of precipitation with ethanol/methanol (1:1 v/v), centrifugation at 8700 rpm for 10 min, followed by re-suspension in toluene/OLAM (1000:1 v/v). The NPs were stored in chloroform. Transmission Electron Microscopy (TEM). Prior to imaging, samples loaded on to carbon coated nickel TEM grids and were pumped under high vacuum


Page 32 of 48

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conditions for 16 h at room temperature. HRTEM and HAADF-HRSTEM images were obtained on a Tecnai Osiris operating at 200 kV. To minimize particle damage, low beam currents were obtained by utilizing a spot size of 11 and, in some cases, a lower extraction voltage. STEM-EDS maps were obtained using a spot size of 6 corresponding to a probe current ~ 0.5 nA. X-ray Diffraction (XRD) Measurements. XRD analysis was performed on a Rigaku SmartLab® X-ray diffractometer equipped with a CuK radiation source and D/teX Ultra 250 detector, operating at 40 kV and 44 mA. XRD samples were prepared by drop casting a concentrated solution of NPs onto a zerobackground quartz holder. Optical Absorption Spectroscopy. Optical absorption spectra were obtained on a Jasco V-670 UV-Vis-NIR spectrophotometer and 1 cm path length quartz cuvettes. Tetrachloroethylene was used as the solvent to avoid interference in the NIR. Raman Spectroscopy. Confocal Raman spectroscopy was performed on a Thermo DXR Raman microscope using 532 nm radiation at 3.0 mW power with



Page 34 of 48

a 100X objective, and a 50µm pinhole aperture for an estimated spot size of 0.6µm. Density Functional Theory Calculations. Density functional theory calculations were performed using the Vienna ab initio Simulation Package (VASP).43 Atomic species

were

treated

within

the

projector

augmented

wave

(PAW)

pseudopotential formalism44,45 with valence configurations of 6s1 5d10 for Au and 3s2 3p4 for S utilizing the Perdew-Zunger parametrization of the local density approximation (LDA).46 For phonon calculations, the Perdew-Burke-Ernzerhof variant of the generalized gradient approximation47 was used in addition to the LDA. In order to ensure convergence of the basis, a 550-eV plane wave cutoff was used. A 6 × 6 × 6 Γ-centered Monkhorst-Pack k-point grid48

was used for

calculations of the electronic structure, while a 10 × 10 × 10 grid was used for phonon calculations. Spin-orbit coupling is explicitly included in calculations for the electronic structure. In order to improve the band gap calculation, the G0W0 approximation49,50 was employed to obtain the quasi-particle band gap via many-body perturbation theory. For the G0W0 calculation, 2496 bands (56


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occupied and 2,440 virtual states) were used along with a 200 eV cutoff and 120

frequency

grid

points

for

the

response

functions,

which

keeps

the

uncertainty in the band gap

Transformation of the Anion Sublattice in the Cation-Exchange

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