Structural, electronic and optical properties of chromium carbide (Cr 3 C) as potential counter electrode material: a first principle study

platinum

GJPAS/Volume 2/Issue 2/Jun -Dec/2023 cost, limited resources, and corrosion by iodine species in electrolyte solution seriously restricts the large-scale application of Pt-based CEs in DSSCs.Guo et al. (2015).Therefore, economic, stable, and effective non-Pt catalysts should be exploited to fabricate novel CEs.All transition metal (Ti, Zr, Hf, Ta, Nb, V, Cr, Mo, W, Fe, Co, Ni, etc.) compounds (TMCs), such as oxides, nitrides, carbides, sulphides, selenides, tellurides and phosphides, conducting polymers, carbon materials (mesoporous carbon, activated carbon, carbon black, conductive carbon, carbon dyes, carbon fibers, carbon nanotubes, fullerene and graphene), metals and alloys (Fe, Co, Ni, Pt, etc.), and their corresponding hybrids have been tested and developed as CE materials in DSSCs (Yun et al., 2014;Wu and Ma, 2014;Thomas et al., 2014).However, these CE materials face many challenges.Catalytic activity is an intrinsic characteristic of a catalyst, which is determined by the electronic structure of the catalyst.Thus, the catalytic mechanism of these materials (TMCs, conducting polymers and carbon materials) as CE catalysts in DSSCs is not clear even though they exhibit superior catalytic activity (Kim et al., 2018).In this case, predicting which CE materials will exhibit superior catalytic activity in DSSCs is exceedingly difficult (Wu et al., 2017).To overcome these challenges, the first-principle DFT calculations and the ab initio investigation, combined with advanced techniques, such as XRD, SEM, TEM, photovoltaic tests, and electrochemical tests, should be employed.Using these combinations would elucidate the relationship between the electronic structure and the catalytic activity of CE materials and reveal the transport properties of electrons and ions at the electrolyte/CE interface from the macro to atomic level, which is critical in establishing the catalytic mechanism of CE materials in DSSCs (Zhang et al., 2017).Finally, the structural design and functional modification of CE catalytic materials can be realized at atomic and molecular levels based on the relationship between the electronic structure and the catalytic activity, and between thechargetransportandtheinterfaceproperties.Elucidati ngthecatalyticmechanismwillprovidethe theoretical guidance andtechnicalsupporttocommercializeCEcatalyticmate rials,therebypromoting the rapid development of new solar cells (Yun et al., 2014;Wu and Ma, 2014;Thomas et al., 2014).
In this work, we study the structural, electronics and optical properties of Cr3C within the frame work of Density Functional Theory (DFT) and Density Functional Perturbation Theory as implemented in quantum espresso (GE).

Computational details
Geometric relaxation and electronic properties of Cr3C were performed by first principles approach based on plane-wave self-consistent field (PWSCF) program within the frame work of DFT as implemented in quantum-espresso simulation package.Giannozzi, et al. (2009).The simulation adopted the super cell in orthorhombic phase Cr3C with 16 ions, with 12 Chromium atoms and 4 Carbon atoms respectively.The core electrons were optimized by norm-conserving pseudo potentials of the standard solid-state pseudo potential library to model the interaction between valence electron and ionic core potential for Cr, and C. A generalized gradient approximation (GGA) functional of Perdew -Berke-Erzndof (PBE) as exchange correlation function is usedin order to treat electron-electron interaction.Pardew, Burke, Ernzerhof, (1996).The monkhorste-pack scheme k-points grid sampling was set as 6 × 10 × 6 for the irreducible Brillouin zone was used.400eV was chosen as kinetic energy cutoff.The initial structure obtained from materials project.Jain, et al. (2013).were geometrically relaxed for atomic coordinates and dimension of the cell using intrinsic Broyden-Fletcher -Goldfarb -Shanno (BFGS) algorithm.Onida, Reining, and Rubio, (2002).Until atomic maximum forces were less than 5 × 10 -5 eV and total energy during iterative process was changing by less than 0.0001Ry.The optical properties were calculated using real and imaginary parts of the dielectric tensor.It is well known that the main optical parameters of the crystal are related by their complex dielectric function; is the imaginary part of the dielectric function.The real and imaginary part of the dielectric function have been calculated using the linear response within the Density Functional Perturbation theory (DFPT) as implemented in Quantum ESPRESSO based on equation 2 and 3. Kootstra, De Boeij, and Snijders, (2000). (2) Where p is the momentum matrix element between states of n and !n the fermi distribution function is given by   n k f .While the crystal wave function is kn and corresponding n th eigen value is kn E .
The knowledge of electron loss function, real and imaginary parts of frequency dependent dielectric function expressions was used to compute other optical parameters namely; absorption index(), refractive index(), extinction index (), conductivity(), and reflectivity () as shown in the following equations (Abdullahi and Shaari, 2017).

Optical properties
Investigating the optical properties of materials plays a vital role in understanding their optoelectronic applications.We have calculated the optical properties of the material by evaluating the microscopic dielectric function via time dependent density functional theory (TDDFT).The first microscopic dielectric function describes the behavior of linear response of a material to the electromagnetic radiation field applied which displays the absorptive character of the material.Yabana et al. (2012).Real part of the dielectric describes how much material polarized as a result of induced electric dipole creation when electric field is applied; while imaginary part indicates how much material absorb photon energy.From equation 1, 2 and equation 3, it is clearly seen that Ꜫ 1 (ω) can be obtained using imaginary part, Ꜫ 2 (ω).The dielectric functions for the material consist of three components Ꜫ xx , Ꜫ yy , Ꜫ zz which are related to the polarizations along x, y, z directions.Figure 3(a), present the imaginary part of the dielectric function of Cr3C, we noticed the presence of prominent peaks at z-z direction.Interestingly, the compound can absorb photon energy up to 9.092eV as the imaginary line approaches zero.The relatively strong absorption in 0.304 -9.092eV energy range provides strong evidence that the compound has the potential to be used for detecting light within broadband range.The dielectric constant of the compound at high frequency along perpendicular Ꜫ (∞) direction was found to be 100.00.In both cases, these results indicate that the material could have a greater performance of the excellent efficiency in light harvesting for DSSC (Malik et al., 2020).Figure 3(b) presents the real part of the dielectric function of Cr3C, we noticed the presence of prominent peaks at z-z direction, and the prominent peak is at -150.00.The negative character of the real part indicates that the incident photons are totally reflecting in these regions for the material.These results are in agreement with some theoretical results of similar compound (Bagci et al., 2016).
Electron energy loss function is used in describing the loss in energy of a fast-moving electron traversing the material.Figure 3(c), present the electron energy loss function of Cr3C, the prominent peak was found to be 14.243eV.The sharp maxima peak of the energy loss function spectra indicates the existence of plasma resonance and this appear at a particular incident light frequency which correspond to the trailing edges in the reflection spectra sometimes called plasma frequency.
At this point of energy, the imaginary part of the dielectric function goes to zero indicating rapid reduction in reflectance.Figure 3(d), represent the absorption index of the title material, it is observed that the absorption spectrum begins from 0.607eV and rises sharply until attaining maximum peak at 9.73 x 10 -5 cm -1 which correspond to 0.910eV, and then decreases down to 14.85eV which reveal the broadband wavelengths absorption behavior of the compound.This compound shows good absorption coefficient in the region from 1.516eV to 11.819eV.A complex conductivity spectrum is a measure of photoconductivity that gives clear information on the electrical conductivity of a material.Figure 4 (c) shows the complex conductivity spectrum as a function of photon energy.It is shown that the maximum peak is located at 0.91eV corresponding to 55.651S -1 , indicating high conductance at low energy.Therefore, Cr3C is more conductive in the incident photon energy range from 0.910eV to 8.183eV.Reflectivity is the change in reflected photon energy from the surface to the photon energy incident on the surface.Figure 4 (d) present the changes in reflectivity spectrum with photon energy; the reflectivity spectrum starts to increase from about 15% until it reaches maximum level of 36.15% corresponding to photon energy value of 0.607eV and decreases drastically to a very low value.Indicating that the material is transmitting in visible wavelengths because of small reflectance within that energy range.

Conclusion
In summary, we have performed a comprehensive first principles study of the structural, electronics and optical properties of the transition metal carbides (Cr3C).Our calculated lattice parameters are found to be in excellent agreement with experiments and some GJPAS/Volume 2/Issue 2/Jun -Dec/2023 theoretical results.For the electronic structure calculations, our band structure results indicate the material is metallic in nature with possible high conductivity and the PDOS shows that the chemical bonding in Cr3C has a complex mixture of metallic, covalent, and ionic characters.While for the optical responses, we observed that the main peaks in the imaginary part of dielectric are due to electronic transitions from Cr-s, Cr-p, C-s, C-p.The variations inꜪ 2 (ω) along x, y, z varies with the possible nature of band structure of the material i.e., shows an opposite semiconducting nature.Our material reflects the possible strong optical absorption in both visible and ultra violet regions and is suitable for replacing Pt as Counter electrode in DSSC applications.The present study is believed to serve as a useful reference for the fabrication of this novel material for applications.
propertiesThe space group Pnma[62]  and point group mmm which is an orthorhombic crystal structure and the lattice constants are  = 4.525 Ǻ,  = 5.186 Ǻ,  = 6.659Ǻ and ∝ = β = γ = 90.00 .The calculation adopts a super cell orthorhombic phase Cr3C containing sixteen atoms; twelve chromium atom and four carbon atoms respectively.The normconserving pseudo potentials are chosen for the calculation; result is more consistent the experimental results than ultra-soft pseudo potentials.Venkatraman, and Neumann, (1990);Ganguly, Murthy, and Kannoorpatti, (2020).The relaxed unit cell of pure orthorhombic phase Cr3C is shown in Figure1.

Figure
Figure 2 (a) Calculated Band structure, (b) corresponding Density of state and (c) Partial Density of State of Cr3C within the DFT-GGA

Figure 3 :
Figure 3: (a) Imaginary part of the dielectric function of Cr3C, (b) Real part of the dielectric function of Cr3C, (c) Energy Loss function of Cr3C, (d) Absorption Index of Cr3C