Colloidal Synthesis and Photocatalytic Properties of Cu3NbS4 and Cu3NbSe4 Sulvanite Nanocrystals

Niobium sulvanites Cu3NbX4 (X = S, Se) have been theoretically predicted as promising candidates for solar photovoltaics and photocatalytic water splitting. This report outlines the first synthesis of Cu3NbS4 and Cu3NbSe4 in a nanocrystalline form. The crystal structures were investigated by X-ray diffraction, identity was confirmed by Raman spectroscopy, and the optoelectronic properties and morphology of Cu3NbS4 and Cu3NbSe4 nanocrystals were examined by UV–vis spectroscopy and transmission electron microscopy, respectively. To gain insight into the Cu3NbX4 formation, a mechanistic study was conducted for Cu3NbSe4 monitoring the nanoparticles’ formation as a function of reaction time. Methylene blue photodegradation tests were conducted to evaluate the photoactivity of Cu3NbS4 and Cu3NbSe4. The degradation rates, 2.81 × 10–2 min–1 and 1.22 × 10–2 min–1 proved the photocatalysts’ potential of nanoscale Cu3NbX4.


Dielectric Function and Absorption Spectra
To study the optical properties of a material from DFT, the complex dielectric function must first be determined. From the complex dielectric function, several optical properties may be derived. The complex dielectric function ( ) = ( ) + ( ) was calculated within the independent particle approximation (IPA) in which the imaginary part is determined by summing over the empty states, ε '( ()) (ω) = 4π ) ) Ω lim *→, 1 ) 3 2 -δ(ϵ .,-− ϵ 0,-− ω) .,0,-× ; .,-12 ! * = 0,->; 0,-= .,-12 ! * > (Eq. 1) where Ω is the volume of the primitive cell, q is the Bloch vector of the incident wave, wk are the k-point weights, u is the polarization of the incident wave, eα Cartesian unit vectors, and c and v denote the conduction and valence bands, respectively. The real part is determined by using the Kramers-Kronig transformation, Where P denotes the principle value. Further information on these equations can be found in the paper by M. Gajdoš et al 11 . The dielectric functions for each compound are shown in Figure S1. From the complex dielectric function, the absorption coefficient is determined from the following relation, where λ is the wavelength, and ε1, ε2 are the real and complex parts of the dielectric function, respectively. The calculated absorption coefficients are shown in Figure S2. The most notable feature of the absorption coefficients is the presence of two prominent peaks followed by a shoulder for both compounds, which can be ascribed to direct optical transitions between the valence band and the conduction band, namely between the Cu d-states and chalcogen pstates. These peaks can be seen as well from the imaginary part of the dielectric function between 3 and 6 eV. For Cu3NbS4, the peaks are located at 236 nm (5.2 eV), 289 nm (4.3 eV), and 345 nm (3.6 eV). For Cu3NbSe4, the peaks are located at 259 nm (4.8 eV), 301 nm (4.1 eV), and 388 nm (3.2 eV). The maximum value of the absorption is 8.7×10 5 and 8.9×10 5 cm -1 for Cu3NbS4 and Cu3NbSe4, respectively. The calculated absorption coefficient shown in Figure S2 can be relatively compared to the measured UV-vis absorbance spectra shown in Figure 1(e) as the absorbance A is directly proportional to the absorption coefficient, i.e., = × ln(10)/ , where d is the path length. The presence of the two peaks and shoulder in the absorption coefficient appears as two broad, flat peaks plus a shoulder in the UV-vis absorbance spectra, showing that the calculated and experimental spectra agree relatively well. Figure S1. Calculated real ε1 (a) and imaginary ε2 (b) dielectric functions within IPA for Cu3NbS4 (blue) and Cu3NbSe4 (red). Figure S2. Calculated absorption coefficient for Cu3NbS4 (blue) and Cu3NbSe4 (red).

Exciton Bohr Radius
At the nanoscale, the effects of quantum confinement can become prevalent for semiconducting materials that have very small particle sizes. Notable effects of quantum confinement include discretization of the energy levels and an increase in the size of the band gap. The characteristic size at which such effects may happen is the exciton Bohr radius. To understand whether quantum confinement effects are present for the sulvanite compounds, the exciton (electron-hole pair) Bohr radius was calculated. The exciton radius can be approximated using the following equation, where , is the hydrogen Bohr radius (0.053 nm), , is the electron mass, ε is the static dielectric constant, and µ is the reduced effective mass of the exciton. The reduced effective mass was calculated from the effective masses of the electron and hole, where the subscripts and ℎ denote the electron and hole, respectively. The static dielectric constant was determined within IPA from the complex dielectric function for ω=0. The resulting dielectric constants were found to be 7.49 and 8.66 for Cu3NbS4 and Cu3NbSe4, respectively. The relation between the electronic band structure and the effective masses is given by the following equation, where and run over the three Cartesian coordinates in reciprocal space, and : is the energy eigenvalue of the -th band. This expression is evaluated using a finite-difference stencil method along with high symmetry points on the band structure. 12 Table S1. Calculated values along R-X for the electron effective mass 2 * , hole effective mass 7 * , reduced effective mass , static dielectric constant , and exciton Bohr radius . The effective masses are in terms of the electron mass , . At the symmetry point R, there is a three-band degeneracy with corresponding hole effective masses; for the current calculation, the lowest hole effective mass was chosen. In terms of the electron mass , , the electron effective mass at X was found to be 1.313 , for Cu3NbS4 and 1.285 , for Cu3NbSe4. At R the hole effective mass was 0.531 , and 0.451 for Cu3NbS4 and Cu3NbSe4, respectively. From these results, the reduced effective mass of the systems is 0.378 , (S) and 0.334 , (Se) and produces an exciton Bohr radius of 1.050 nm (S) and 1.375 nm (Se). The above information is summarized in Table S1. Depending on the value of the exciton Bohr radius, the effects of quantum confinement can be categorized in two ways: strong confinement, in which the radius of the nanocrystal is smaller than effective masses, and weak confinement, in which the radius is larger than the effective masses. Given that the average measured particle sizes of 34 nm and 19 nm for Cu3NbS4 and Cu3NbSe4 ( Figure S3), respectively, are much larger than the calculated exciton Bohr radii, both types of nanocrystals exhibit weak quantum confinement. A similar calculation by Mantella et. al. 13 concluded that Cu3VS4 nanocrystals also are under weak quantum confinement, a result that can be expected due to the chemical and structural similarity between the sulvanite nanocrystals. Figure S3. Low-magnification TEM and particle size distribution of Cu3NbS4 and Cu3NbSe4. Intermediate compounds and control experiment for mechanism study Figure S4. HR-TEM of the time-dependent study product obtained at 5 and 30 minutes.

The Effect of Size and Strain on XRD diffraction pattern of Cu3NbSe4
The diffraction pattern obtained from standard powder X-ray diffraction is heavily dependent on the underlying structure of the material being analyzed. Oftentimes, peaks in the diffraction pattern are seen to undergo broadening and/or shift in position compared to an otherwise ideal sharp peak. Peak broadening and shifting can be ascribed to crystallite size and internal strain present in the sample, which are often seen in nanocrystals due to size confinement. To better understand the shift and broadening in the obtained XRD patterns, analysis of the peak profiles was done as follows.
The most popular method for analyzing the relationship between the crystallite size and peak broadening is through the Scherrer equation where D, K, λ, β, and θ are the average crystallize size, the Scherrer constant (usually taken as 0.9), the wavelength of the XRD used, the peak width, and the Bragg angle, respectively. Under this method, β is the corrected broadening of the measured pattern after subtracting instrumental broadening It is standard to take β as the full width at half-maximum (FWHM) of the peak profile, typically approximated as a Gaussian or Lorentzian function. From the Scherrer equation, 1/β versus cos(θ) is plotted and a linear fit applied. The slope of the linear fit corresponds to Kλ/D, which can readily be solved to obtain the average crystallite size.
Following Scherrer's equation, more sophisticated methods exist that account for other factors, most importantly internal strain. One such method is through the Williamson-Hall (WH) method, which assumes the broadening is composed of contributions from size and internal strain -./ = size + &,(%*+ (Eq. 10) The βsize is inferred from Scherrer's equation while βstrain can be determined in several ways, the simplest of which is the uniform deformation model (UDM) under which the strain ε is assumed uniform such that &,(%*+ = 4 tan (Eq. 11) Combining the two broadening terms, the following equation is obtained 012 cos = 4 sin + (Eq. 12) Plotting βcos(θ) versus 4sin(θ), a linear fit can be made, and the slope gives the strain ε and the y-intercept gives the average crystallite size. Figure S7 shows the Williamson-Hall plot using UDM for the diffraction pattern of Cu3NbSe4. The XRD peaks were fitted to a Gaussian function and their FWHM determined. The calculated average crystallite size and strain were determined to be 15.51 nm and 10.88×10 -4 , respectively. The average crystallite size is in good agreement with the results listed in Table S1. Notably, the dimension of the short side of the Cu3NbSe4 cuboids are a close match (15.33 nm vs 15.51 nm) while not being far off from the 22.25 nm of the long side of the cuboid. Furthermore, the calculated strain is consistent with the cuboid morphology of the obtained sulvanite-type nanocrystals in which the dimensions of the nanocrystals are constrained along one dimension compared to a perfect cube. Overall, the combination of size confinement and intrinsic strain within the sample will cause a shift and small broadening of the XRD peaks with respect to the bulk reference. Figure S6. Williamson-Hall plot of the diffraction pattern for Cu3NbSe4. Figure S7. (a) The particle with Nb concentration gradient shown in the red circle in figure  4b. (b) An isolated particle with Nb concentration gradient.