Md. Bayjid Hossain Parosh,
Md Saiduzzaman*,
Jahirul Islam,
Nusrat Jahan Nisha* and
Istiak Ahmed Ovi
Department of Materials Science and Engineering, Khulna University of Engineering & Technology (KUET), Khulna-9203, Bangladesh. E-mail: msaiduzzaman@mse.kuet.ac.bd; nusrat.jahan.nisha.mse@gmail.com
First published on 2nd April 2025
Inorganic, non-toxic halide perovskites have emerged as photovoltaic field breakthroughs because of their outstanding physical properties, which make them viable for sustainable energy systems. The structural properties along with electronic, mechanical and thermal properties of Mg3PX3 (X = Cl, and Br) are evaluated by first-principles density functional theory (DFT) calculations executed via the CASTEP code employing GGA-PBE functional. The phonon dispersion results indicate that these compounds are dynamically stable because positive frequency readings show they would be suitable for experimental production. Structural and bandgap calculations required the dual use of hybrid HSE06 and GGA-PBE functionals to achieve better accuracy and resulted in 5.260 Å for Mg3PCl3 and 5.478 Å for Mg3PBr3. The calculated bandgap values are 2.297 eV for GGA-PBE and 3.093 eV for HSE06 with Mg3PCl3 and 1.506 eV for GGA-PBE and 2.187 eV for HSE06 with Mg3PBr3. The positive elastic constant C44 indicates structural stability in addition to unfavorable Cauchy pressure values that create brittle and rigid structural behaviors together with the Paugh's ratio and Poisson's ratio at low levels. The magnetic properties of Mg3PX3 (X = Cl and Br) compounds create opportunities in quantum research because these compounds exhibit diamagnetic behavior. High thermal efficiency calculated by thermal analysis enables the materials to expand their functional capabilities. Experimentation demonstrates that Mg3PX3 (X = Cl and Br) compounds show their exceptional optical characteristics and potential for superior photodetectors and UV protective materials. This research delivers essential knowledge about Mg3PX3 (X = Cl and Br), which prepares the way for the upcoming experimental development of sustainable materials for energy technologies.
Photovoltaic cells have become vital aspects of green energy technologies because they can effectively generate electrical energy from solar power.5 Over the past few years, various perovskite-based materials have attracted massive interest in solar energy systems because of their exceptional photovoltaic and energy conversion characteristics.6 First investigated nearly two decades ago as piezoelectric and ferroelectric compounds in metal oxides, perovskites have transformed into versatile material for thin films of absorber layer and other solar cell related.7 The exceptional flexibility and performance of certain materials have established them as essential components in LEDs and renewable energy technologies, driving global research and development to satisfy the rising demand for sustainable energy solutions.8 Many materials are inherently limited, yet practical application of many materials requires materials that combine physical stability and high quality, but often the materials required for high-performance devices do not give both qualities.9 So, they are actively working to develop cost-effective alternatives that can stand up to extreme conditions without degrading.10 The perovskite-based compounds stand out as particularly attractive in that they exhibit properties that make them attractive for use in sensors, photovoltaics, optoelectronics, high-temperature superconductors, and semiconductors.11 Specific to need advanced nanostructures, such as nanowires, nanocrystals, and nanoparticles can be created, with unique structural adaptability.12 The versatility of perovskite-based systems implies that they will provide a more economical and flexible route to advanced technologies than conventional silicon-based ones.13
A3MX3 compounds (A = Mg, Ca, Sr, Ba; M = N, P, As, Sb; X = F, Cl, Br, I) utilized in photovoltaic devices were the subject of recent research. Band-edge transitions, tunneling, thermal characterization, bandgap, and estimated efficacy are among the properties that these materials may exhibit.14 The analysis showed that these compounds possess properties similar to halide perovskites currently used in solar cell technology. Ghosh et al. (2024) investigated the physical characteristics of inorganic halide A3BX3 perovskites used as the absorber layer for solar cells with better effectiveness. The study also depicts that Sr3AsI3 solar cells retain more than 28% of power conversion efficiency (PCE) in terms of conversion of energy.15 Hossain et al., (2024) utilized first-principles DFT calculations to investigate the structural, electronic, mechanical, optical, thermodynamic, and thermoelectric properties of lead-free Sr3ZBr3 (Z = As, Sb) compounds with their direct band gap semiconducting nature, improved optical and mechanical properties under pressure, and high thermoelectric performance, and are tantamount for optoelectronic and thermoelectric applications.16 Based on the results of first principles DFT calculation, the pressure-induced reduction of the bandgap and enhanced optical and mechanical properties along with high thermoelectric performance, Abdulhussein H. A., et al., (2025) suggest that lead-free cubic Ca3SbX3 (X = Cl, Br) is a potential candidate for use as the solar absorber, surgical instrument, and thermoelectric devices.17 In the study, Chahar et al. (2024) used GGA and HSE06 functionals to compute the structural, electronic, and optical properties of the novel perovskite halide Mg3AsCl3 with an indirect bandgap, low reflectivity, and outstanding dielectric properties which make it a promising candidate for various electronic device applications.18 Apurba et al. [2024] investigated the Ca3PX3 (X = I, Br, Cl) system physical properties and calculated the tunability of their band gaps under tensile and compressive strain.19 This study utilizes DFT calculations to investigate the structural, mechanical, electronic, and optical properties of Mg3PF3 fluoro-perovskite, demonstrating its ductility, a direct bandgap of 3.88 eV, and significant potential for solar cell applications owing to its advantageous dielectric properties and ionic bonding characteristics.20 The ability of thermoelectric materials to transform thermal energy into electrical energy makes them essential for use in cooling systems, power generation, and sensor technologies, among other uses.
In this study, DFT calculations are performed employing first principles to study the properties of the new Mg3PX3 (X = Cl, Br) compounds in the vacuum case and the hydrostatic pressure case. Overall, one aims to understand the physical properties of these lead-free, non-toxic materials with the application of hydrostatic pressure and to investigate the structural and electronic transitions under such pressure. The band gap tunability under hydrostatic pressure is systematically considered using various exchange–correlation functionals such as GGA-WC, Hybrid-HSE06, GGA-PBESol, and GGA-PBE to verify their accuracy in predicting band gap values. To our knowledge, there have been no previous theoretical or experimental studies on these compounds. This research is intended to generate insights that may be of value in the development of optoelectronic as well as photovoltaic technologies.
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In eqn (2), Es denotes the enthalpy of the specific compound. Etot denotes the total computed energy for the whole compound. N is the total number of atoms present in the structure. The structural data are plotted in Table 1, such as the lattice parameter a (Å), cell volume V (Å3), and formation enthalpy ΔEf (eV per atom).
Compound | Lattice constant, a (Å) | Cell volume, V (Å3) | Enthalpy, ΔEf (eV per atom) | Tolerance factor, t | |||
---|---|---|---|---|---|---|---|
GGA-PBE | Previous work [GGA-PBE]29 | Hybrid HSE06 | GGA-PBE | Hybrid HSE06 | |||
Mg3PCl3 | 5.26 | 5.24 | 5.22 | 145.59 | 142.16 | −3.60 | 0.82 |
Mg3PBr3 | 5.48 | 5.46 | 5.43 | 164.40 | 159.83 | −3.32 | 0.81 |
The condition for being thermodynamically stable, the formation enthalpy, must remain negative of the compound.30 Table 1 shows the data of the optimized structure, and there is a negative value of formation enthalpy in each case, which validates that the studied photovoltaic compound is thermodynamically stable with a negative value. The bromine-based compound has higher negative formation energy magnitudes than Mg3PCl3. Apart from the thermodynamic stability, there is also cubic stability. A compound should be considered a cubically stable structure when the tolerance factor of a compound should remain 0.813 to 1.107.31 From Table 1, this studied geometrically optimized structure has a fine tolerance factor where the condition is fully carried out. Following the data plotted in Table 1 confirms the crystal stability of the compound. This optimized structure complies with all the conditions of stability. Table 1 also represents the basic structural data of the compound, such as cell volume and lattice parameters. The cell volume for Mg3PCl3 and Mg3PBr3 is 145.586 Å3 and 164.397 Å3, respectively. The lattice parameters are 5.260 Å and 5.478 Å, similar to the previous data presented in Table 1. This indicates the accuracy of this work. Where all the data is carried by substituting the halogen site of the compound with Cl and Br, a trend is primarily observed when a bigger halogen is substituted to the site of the compound by replacing both cell volume and lattice parameter of the compound is increasing. As the atomic radius of the halogen increases, the total cell volume and lattice parameter increase. It also can be said that in Mg3PCl3, the atoms of this compound are more closely packed as their atomic radius and cell volume are lower compared to Mg3PBr3.
Table 2 shows the bond length data of the studied material. Generally, the distance between two nuclei of a bond in an atom is termed this distance. Here, the bonding between Mg–Cl and Mg–P is the shortest, which denotes they have a strongly bonded structure than other bonding. When a heavier halogen is placed in the X position, the bond length increases in the structure. One thing to notice is that Mg is bonding similarly strongly with P and X atoms here. The shorter the bond length, the stronger the bond is. Among them, P–X shows the lowest bonding strength, which indicates that the nuclei of P and X are much closer than other bonded nuclei.
Compound | Bond | Length (Å) |
---|---|---|
Mg3PCl3 | P–Cl | 3.72 |
Mg–Cl | 2.63 | |
Mg–P | 2.63 | |
Mg3PBr3 | P–Br | 3.87 |
Mg–Br | 2.74 | |
Mg–P | 2.74 |
In Fig. 3, the band structure calculations for Mg3PCl3 and Mg3PBr3 used two exchange–correlation functionals, namely GGA-PBE and HSE06, to generate the graphs. The calculated band gap by GGA-PBE functional for Mg3PCl3 amounts to 2.297 eV, but when HSE06 functional is used, it predicts a higher band gap value of 3.093 eV. The band gap estimation for Mg3PBr3 using GGA-PBE leads to 1.506 eV, but when HSE06 is applied, it results in 2.187 eV. The band structures demonstrate direct band-gap characteristics at the Γ point because VBM and CBM energies occur at the identical high-symmetry point of the Brillouin zone. The larger band gaps predicted by the HSE06 functional relative to GGA-PBE are in line with the general tendency of HSE06 to yield more accurate values for band gaps, due to the inclusion of some fraction of exact Hartree–Fock exchange, which corrects the underestimation of band gaps by GGA-PBE.43,44 The perspective drawn from using both GGA-PBE and HSE06 functionals emphasizes the selection of an efficient exchange–correlation functional to ensure an accurate prediction of the band gap.44 The GGA-PBE Method incorporates a band structure model that ignores the effects of electronic exchange and correlation, and this tends to underestimate the band gap value deficits for both Mg3PCl3, which is 2.297 eV, and Mg3PBr3, which is 1.506 eV. The HSE06, which accurately predicts the band gap of both Mg3PCl3 and Mg3PBr3, gives more accurate band gaps of 3.093 eV and 2.187 eV, respectively. This tendency for other reports on the halide perovskites that have demonstrated previously a band gap lower than HSE06 has been achieved for these compounds.41
The Fig. 4 bar chart illustrates band gaps of Mg3PX3 (X = Cl and Br) compounds obtained from GGA-WC, GGA-PBEsol, GGA-PBE, and Hybrid-HSE06 exchange–correlation functionals. The band gaps are stated in eV units. The band gaps starting from value 0 up to four eV are presented visually. It is noticed that the Hybrid-HSE06 method provided the greatest gaps, as expected from more complicated systems that involve the use of exact exchange. Gaps from GGA-PBE are always lower than the other methods in this comparison, showing a great value of band gap underestimation. The GGA-WC and GGA-PBEsol provide values that are more favorable than these two but do not reach the same results as GGA-PBE.45 This comparison highlights the importance of functional choice in predicting electronic properties, with HSE06 being the most reliable for accurate band gap estimation in optoelectronic materials.
The band structure analysis of Mg3PCl3 and Mg3PBr3 reveals their semiconducting nature with direct band gaps, making them suitable for optoelectronic applications. The HSE06 functional provides more accurate band gap predictions compared to GGA-PBE, highlighting the importance of advanced exchange–correlation functionals in computational materials science. The larger band gap of Mg3PCl3 compared to Mg3PBr3 reflects the influence of halide electronegativity on electronic properties. These insights provide a foundation for further experimental and theoretical studies on these materials for advanced optoelectronic devices. Table 3 represents the band gap with other functional like GGA-WC and GGA-PBEsol with the comparison of previous data.
Fig. 5 reveals the Total density of states (TDOS), and Fig. 6 shows the Partial Density of States (PDOS) of Mg3PCl3 and Mg3PBr3, giving important information regarding the electronic structure and their physical properties. The DOS plots demonstrate the distribution of electronic states about energy (eV), with the x-axis representing energy levels and the y-axis indicating the number of states per unit of energy. As with both compounds, the importance of the valence band (VB) is dominant and shifted towards the lower energy range (negative values), while the conduction band (CB) occupies the highest degree of positive energy. The presence of a gap with zero or negligible states that falls between the VB and CB demonstrates the optoelectronic potential power of the system, which, as an important parameter, is defined as the band gap. Mg3PCl3 is known to have a wider band gap than Mg3PBr3. As a pattern in their band structures, the band gap decreases with the increasing atomic size of the halide from Cl to Br. This phenomenon is resulted due to the increased strength in electronegativity of chlorine which increases the ionic character of the bonds thus widening the band gap. Furthermore, the peaks of lesser sharpness in valence and conduction bands serve as evidence of attributed electronic states localized sharply signifying the potential effect on carrier mobility alongside the optical properties of the DOS plots.
The states located closer to the upper and lower limits of the band in Mg3PBr3 have better carrier connectivity when placed against Mg3PCl3. Due to this, Mg3PBr3 is better suited for high-performance applications like transistors and photodetectors. Therefore, the DOS analyses for the two compounds verify their distinguishing features as being semiconductor in nature as well as showcase the degree of impact the selection of halide has on the electrical properties of these compounds. These findings form the basis of how these materials should be processed as well as incorporated into various optoelectronic devices including solar cells, LEDs, and sensors where regulation and control of band gap as well as motion of charge carriers is highly important. Once again, the comparison of Mg3PCl3 and Mg3PBr3 sheds light on the interrelations of the properties of halides including the magnitude of their electronegativity and size and the ability for the materialization of new technological devices.
Fig. 7 shows the structural or electronic configuration of a specific component of a Mg3PX3 (X = Cl and Br) with the arrangement of the Mg and (P) atoms in proximity exhibiting a periodic lattice characteristic of a Perovskite-like structure. The numbers (6.798 × 10−1, 5.287 × 10−1) correlate with the electron density contours, bond length, or atomic distances that explain the stability and the electrical properties of the structure material. The pattern created by the Mg and P atom's crystal structure with the fluctuation in values indicates non-homogeneous electron density.
This elusive bond provides crucial features such as conductive capabilities, the band gap, and optical behaviors, making the material might be useful in various fields such as solar cells and LEDs. Thermodynamic stability and mechanical stamina may very well be enhanced by using P instead of those flowing, energetic perovskites. These higher regions of free electrons hint at stronger bonds or localized electron states, while weak interactions suggest enduring voids as opposed to weak lattices containing stronger bonds. To enable robust electronic components and high-efficiency photovoltaic devices with real-world practicality, these details are important for optimizing the material's performance. The image broadens the simple knowledge posited of material science in a more fundamental atomistic understanding as a base for further computational studies to develop next-generation optoelectronic materials. By studying the bond patterns and electron cloud distribution, scientists can optimize compounds to give the desired response when subjected to external pressure or heat, enabling them to make materials with more functionality and greater stability. This structural analysis not only highlights the potential of Mg3PX3 (X = Cl and Br) for advanced applications but also contributes to the broader field of perovskite research, offering insights into the role of different elements in shaping material properties.
The absorption spectra for both Mg3PX3 (X = Cl and Br) compounds show equivalent absorption characteristics that reach their highest point between 2.0 × 105 cm−1 to 3.0 × 105 cm−1. Peak positions along with absorption strength distinguish these two compounds from one another. The peak absorption coefficient of Mg3PCl3 exceeds that of Mg3PBr3 because it reaches approximately 2.8 × 105 cm−1 while Mg3PBr3 peaks at around 2.6 × 105 cm−1. Mg3PBr3 starts absorbing light at higher photon energy than Mg3PCl3 indicating that the absorption edge shows a redshift. The expansion of the ionic radius together with the reduced electronegativity forces of bromine lowers bandgap energy while promoting photon absorption at lower energies in the spectrum. The electronic band structures differentiate the way the two halides absorb light energy. The redshifted bandgap spectrum of Mg3PBr3 improves photon absorption throughout the visible wavelengths. The red edge effect in Mg3PBr3 enhances its suitability for optoelectronic applications requiring expanded energy reach because it is a candidate in solar cell and device development. Lower energy light interacts more effectively with Mg3PCl3 crystals because of its elevated absorption coefficient; thus, this material might be an appropriate alternative for high-efficiency photodetector and UV protective applications. Fig. 14, shows the wavelength vs. absorption spectra where the highest absorption is found between 100–300 nm range of wavelength and the absorption coefficient is around 2.8 × 105 cm−1 range which indicates the absorption in the UV region. In addition to the energy band gap, the absorption coefficient and its relation to wavelength play a crucial role in determining the suitability of materials for photodetector and UV protective applications. A strong absorption coefficient in the UV and visible range enhances a material's efficiency in such applications. Snaith et al.52 demonstrated this range of absorption can be appropriate for detectors. Rony et al.31 studied TlBX3 (B = Ge, Sn; X = Cl, Br, I) and found the highest absorption spectra in the UV range as compared to this study and predicted they can be used in photodetector as the major peaks are in the UV region. A high refractive index in the UV range enhances light–matter interaction, which is crucial for photodetector efficiency.53 The data calculated from the refractive index ensures this finding and enhances the probabilities of the prediction of the materials that can be used as photodetectors. The imaginary part of the dielectric function (ε2) also cross-checks these findings with a greater ε2 at the UV region which is discussed in the upcoming sections.
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The wide conductivity spectrum indicates that both compounds achieve maximum values between 5.0–5.5 S m−1 thereby demonstrating their suitability for electronic and optoelectronic applications. The conductivity measurements of Mg3PCl3 and Mg3PBr3 show both comparable trends and distinguishing characteristics regarding peak performance. Mg3PBr3 achieves the highest conductivity peak value of 5.4 S m−1 yet Mg3PCl3 reaches 5.1 S m−1 as its peak value. The charge transport mechanisms in Mg3PCl3 are extended longer than those of Mg3PBr3 while the range of operation is broader. Mg3PBr3 starts conducting at lower energies because its charge transportation activation energy remains lower than that of Mg3PCl3. Bromine provides increased delocalization to the electron cloud because its larger ionic radius and lower electronegativity properties lead to better charge mobility. Mg3PBr3 attains better peak conductivity levels than Mg3PCl3 but its conductivity values decrease faster with rising energy than the slower fading performance of Mg3PCl3 across the energy range. The comparatively stable charge transport capabilities of Mg3PCl3 position it as a suitable material for long-term field-effect transistors (FETs), sensors, and photodetectors applications. Mg3PBr3 shows advantageous peak conductivity values which enable its use in high-frequency electronic devices along with charge-storage applications because it ensures swift charge transfer processes. The optical conductivity characteristics of Mg3PBr3 improved further because it combined its redshifted absorption edge with a wider absorption range in the visible part of the spectrum. Mg3PBr3 shows promising performance characteristics for photovoltaics and photodetectors because its increased conductivity matches its redshifted absorption properties. Mg3PCl3's wider conductivity range, coupled with high absorption capability, makes it a suitable candidate for both long-lasting optoelectronic device applications and might be used in UV-detecting materials.
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The reflectivity spectra (ρ) measured against photon energy show different optical characteristics between the two compounds. The optical properties of Mg3PCl3 show greater reflectivity reaching 0.78 at 20.5 eV photon energy than the reflectivity of 0.58 at 18 eV for Mg3PBr3. The reflectance peak in Mg3PCl3 appears sharp causing stronger light reflectance in the ultraviolet (UV) spectrum which proves its capability to function as a UV reflection material. The broad and weak absorption peak of Mg3PBr3 matches its previously recorded absorption energy shift together with its reduced photon energy values. The visible spectrum (VR) shows moderate reflectivity effectiveness between the two compounds where Mg3PCl3 produces slightly higher reflectivity values than Mg3PBr3. Mg3PCl3 demonstrates better reflectivity due to its higher absorption coefficient as well as its sharp photon peak thus addressing opportunities in high-energy optical coatings, UV reflectors, and photonic devices.54 The wide spectral reflectivity area of Mg3PBr3 makes it suitable for applications where broad spectral response is needed including solar energy harvesting, optical sensors along anti-reflective coatings. The photodetectors and photovoltaic cells benefit from increased light–matter interaction because of the declining reflectivity pattern beyond peak regions in both materials. The substitution of halogens controls how optics behave in distinct ways since chlorine creates stronger UV protection along with improved reflectivity and bromine generates broader spectral wavelength capabilities with increased visible light absorption. Studies demonstrate how Mg3PX3 (X = Cl and Br) compounds allow reflectivity customization for unique applications thus establishing them as future optical coating and window and mirror technology candidates. The adjustment of optical properties by altering halide composition unlocks various potential uses for advancing optics together with producing unique solutions for different industrial applications.
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The collective electron oscillation peaks of Mg3PCl3 and Mg3PBr3 appear differently in terms of position and strength. The main photon peak of Mg3PCl3 occurs at 20.5 eV where it reaches a maximum value of 10 indicating intense collective electron motions which produce substantial energy loss at that frequency. The photon interaction strength in Mg3PBr3 is lower compared to other materials since its principal loss peak at 18 eV serves as a broad and less intense resonance. Mg3PBr3 displays numerous smaller absorption peaks below 15 eV thus indicating interband transitions which are more complex than in Mg3PCl3. The higher photon energy of Mg3PCl3 indicates it possesses both a larger bandgap structure and stronger electronic binding forces that resulted in previously observed enhancements of absorption coefficient and high conductivity range. Lower photon energy in Mg3PBr3 matches up with both its shifted absorption spectrum in the red direction and its improved charge mobility characteristics because of greater electron delocalization and reduced requests for excitation energy. Physical observations suggest that Mg3PCl3 shows promise as both a deep UV photon device and high-frequency optoelectronic element, and Mg3PBr3 demonstrates suitability for visible-light photon applications as well as sensing needs and energy collection applications. The dissimilar outcomes regarding energy loss between the two halide forms indicate that Mg3PX3 (X = Cl and Br) materials open a wider area of application and can be promising prospects for dielectric coatings as well as transparent conductive materials and advanced photon nanostructures.
ε(ω) = ε1(ω) + iε2(ω) | (6) |
Optoelectronic devices depend heavily on the dielectric function to determine their efficiency and performance levels.56 Fig. 10(a) displays the real part of the dielectric function ε(ω) for Mg3PX3 (X = Cl and Br) as it depicts how the materials respond to electromagnetic fields by storing electric energy. Mg3PBr3 attains its highest value of 8.5 F m−1 within its photon energy curve but Mg3PCl3 achieves just slightly lower at 7 F m−1. The dielectric strength of Mg3PBr3 reaches higher levels compared to other test materials which indicates superior static dielectric constant capability. The transition from dielectric to metallic response in both materials becomes noticeable as photon energy rises because they both show a strong reduction in ε(ω) until reaching zero and establishing photon behavior. The ε(ω) = 0 threshold occurs at lower frequencies in Mg3PBr3 while supporting its previously documented tendency of redshifted optical properties and lower photon energy. The behavior of both materials features minor variations before stabilizing at zero energy levels when energy reaches higher values. The ε(ω) response indicates Mg3PBr3 would excel at capacitive power storage and electronic devices and solar cell layers but Mg3PCl3 offers superior performance in optical and photon device applications.
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Fig. 10 Calculated (a) dielectric function (real), (b) dielectric function (imaginary), (c) refractive index (real), and (d) refractive index (imaginary) of Mg3PX3 (X = Cl and Br). |
The dielectric properties offer a fundamental understanding of optical wave–material interactions which prepares the basis for evaluating both energy dissipation and absorption behaviors using the imaginary part of the dielectric function. Mg3PCl3 shows a significant absorption peak near 8 eV, and Mg3PBr3 also shows a similar peak; however, it's at approximately 7 eV, and this lower energy peak is interesting which is shown in Fig. 10(b). This downward shift is because of Br's heavier mass compared to Cl's, resulting in weaker bonding, and subsequently, less energy is required for electron movement. Moreover, the peak sizes differ, and this suggests variations in electron movement. These findings demonstrate that we can easily adjust the optical properties of these materials by changing the halide, and this gives us options for making light devices that operate in different spectral regions.57 This ability is further aided by changing halides and altering optical properties, leading to easier production and implementation.58
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Fig. 10(c) reveals the optical dispersion characteristics of materials by showing Mg3PX3 (X = Cl and Br) refractive index against photon energy n(ω) behavior. The refractive index for Mg3PCl3 and Mg3PBr3 starts at a high initial value when the photon energy is low yet Mg3PBr3 reaches this peak value first before Mg3PCl3 which indicates more robust light interaction and slower phase velocity within that range. Photon energy rise leads to multiple oscillations in both materials which match interband transition patterns together with decreasing refractive index values. The observed intensity patterns in the refractive index fit with dielectric function measurements, which show that Mg3PBr3 provides stronger optical responses in lower-energy regions compared to Mg3PCl3 when demonstrating higher refractive index stability at elevated photon frequencies. Using higher photon energies, both materials display decreased optical refraction, which makes them valuable for high-energy optics, antireflective coatings, and tunable refractive index materials for photonic devices. The variations in the refractive index demonstrate that Mg3PBr3 fits visible and near-infrared operating spectra better than Mg3PCl3, which excels at UV and high-energy optical systems. The refractive index behavior demonstrates it can be suitable for energy applications together with optical sensor design because accurate refractive index control is essential. Further understanding of material optical behavior stems from analyzing n(ω)'s dispersion characteristics since ε2(ω) enables absorption loss and energy dissipation analysis.
A photon energy spectrum shows distinctive dispersion characteristics in the refractive index n(ω) measurements of Mg3PX3 (X = Cl and Br) materials according to Fig. 10(d). The high refractive index values observed in Mg3PCl3 and Mg3PBr3 operate at lower photon energy points while the peak value of Mg3PBr3 stands above Mg3PCl3 showing superior light confinement abilities and slower phase velocity response. The optical refraction decreases while photon energy rises, causing n(ω) to diminish.60 Two primary inter-band electronic transitions appear in both curves, but Mg3PCl3 demonstrates faster decreasing refractive response patterns after 10 eV compared to Mg3PBr3, displaying a broader refractive spectrum response. Both Mg3PBr3 perform better for visible and infrared optical needs, but Mg3PCl3 opens the door of very much suitable for UV-based applications and high-energy optical coating requirements. The observed refractive index patterns demonstrate suitable properties for building photon guides together with optoelectronic devices as well as photonic materials that need adjustable optical properties. The study of optical response and energy dissipation requires analysis of the imaginary part of the dielectric function ε2(ω) because this quantity represents both absorption characteristics and photon energy loss in materials.
Compound | C11 (GPa) | C12 (GPa) | C44 (GPa) | C12–C44 (GPa) |
---|---|---|---|---|
Mg3PCl3 | 86.90 | 20.02 | 34.41 | −14.39 |
Mg3PBr3 | 86.74 | 27.98 | 30.07 | −2.09 |
The physical phenomena whether a material is stiff or ductile can be calculated from this calculation. All the mechanical characteristics will be concluded from this calculation. Some parameters are included in this study such as shear modulus (B), bulk modulus (G), elastic modulus (E), Poisson's ratio (v), and Paugh's ratio, etc. Each parameter can be calculated from the formula as follows:64
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Shear modulus, G = ⅕(C11 + C12 − 3C44) | (9) |
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The spinodal requirement that is equivalent to bulk modulus (B) is another benchmark to be regarded as mechanically stable.65 From Table 5, the bulk modulus is positive which recommends this is mechanically stable. Bulk modulus has another significance, it is the property of a material that denotes the resistance to fracture.67 Mg3PBr3 has the largest bulk modulus of 47.57 GPa among them, so it shows more resistance than Mg3PCl3 which has 42.32 GPa, when fracture occurs. Low bulk modulus also represents softness.
C12–C44 represents the Cauchy pressure of a material. It is a crucial parameter for a compound to determine the ductile/brittle nature of a compound. If the Cauchy pressure is positive, it implies the compound is ductile and the negative value declares the brittleness.68 The outcome of this computation is shown in Table 4 and the Cauchy pressure is found consistently negative for both of them. It represents the stiff nature of the compound. Mg3PCl3 is more brittle than Mg3PBr3 with a more negative value of −14.39 GPa. Heavier halogen substitution lowers the brittleness of the compound in Cauchy pressure calculation. A recent study by Rahman et al.66 on Mg3PF3 shows a similar kind of negative Cauchy pressure which validates the findings of this study. From Table 5, when the halogen is replaced from Cl to Br, the bulk, shear, and elastic modulus decrease. It is evident from Table 5 that, the bulk, Young's, and shear modulus of chloride photovoltaic perovskite is superior to Mg3PBr3 in this computation. High bulk modulus makes this compound well-suitable in construction sectors, and pressure vessels in which high-strength materials are needed without deformation.69 The shear modulus G is a parameter that indicates the ability to resist deformation on loading. In this research, both materials exhibit higher shear with a value of 34.02 GPa for Mg3PCl3 and 29.80 GPa for Mg3PBr3 and that denotes higher plastic deformation ability of the compound. There are other parameters to confirm the ductile/brittle nature of a compound such as Poisson's ratio (ν), and Paugh's ratio (B/G). There is a threshold magnitude of each parameter which confirms the phenomenon of the compound. For Poisson's ratio, If the compound has a greater Poisson's ratio than 0.26 it will be considered a ductile material and if the value is lower than this it is brittle.70 Table 5 ensures that Mg3PCl3 and Mg3PBr3 both exhibit a brittle nature. Mg3PCl3 Is more brittle with a value of 0.183 and Mg3PBr3 is closer to the value of ductility with a magnitude of 0.240 visualized in Fig. 11. At the 1.75 value of Paugh's ratio, the conversion of brittle to ductile occurs. In this computation, the compound Mg3PX3, based on the information shown in Table 5, Mg3PCl3 has 1.24 and Mg3PBr3 has 1.60 which is less than the threshold and that is determining the brittle nature of the compound. These results cross-checked the findings of Cauchy pressure. This highly brittle nature makes this compound applicable in energy and shock absorber sectors.71 This is shown graphically in Fig. 12. “μm” is known as the machinability index of a material. A high index of machinability indicates the soft, malleable nature of the material. In this particular research, this index is much lower. Mg3PCl3 has 1.23 and 1.58 for Mg3PBr3, and this is a much lower value. Based on this index, this material can't be easily shaped with higher friction and lower lubricity. The heavier halogen replacement makes this material softer in the study. Hardness measures a material's ability to maintain its shape under stress. Higher hardness shows more resistance to stress, and in this study, Mg3PCl3 has a hardness value of 8.72, and Mg3PBr3 has 5.98, which is much higher in general. As the higher hardness exhibits a much lower machinability index, the compound can be used in engineering tools and wear-resistant surface coatings.72 Rahman et al.66 studied a similar kind of compound Mg3PF3 and found comparable data shown in Table 5.
Anisotropy can be termed as a phenomenon of a material showing different properties in different directions.73 The formulas to determine crystal anisotropy are mentioned below:
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For cubic symmetry,
![]() | (18) |
The Zener isotropic factor,
![]() | (19) |
To achieve isotropic behavior, the Zener factor is A1 = A2 = A3 = 1, but in this study, this value is larger than 1; for Mg3PCl3, it is 1.029, and 1.023 for Mg3PBr3, which confirms the anisotropic nature of the compound.74 Also, from the ELATE tool's 3D representation of Young, Poisson's, and shear moduli, the graphical output shows different types of structure in each spheroid case. The difference in the representation also confirms the anisotropic nature of the compound.75 The ELATE graphical representations are presented in Fig. 13. And the 2D plots generated from ELATE of these moduli are also shown in Fig. 15, and 16.
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Fig. 13 The 3D illustration of (a) Young modulus, (b) shear modulus, and (c) Poisson ratio of Mg3PX3 (X = Cl and Br). |
![]() | (20) |
![]() | (21) |
Vm = [⅓(2VT−3 + VL−3)]−⅓ | (22) |
![]() | (23) |
![]() | (24) |
![]() | (25) |
Tm = (554 + 5.911C11) ± 300 K | (26) |
Compound | Vt (m s−1) | Vl (m s−1) | Vm (m s−1) | Kmin (W m−1 K−1) | Kph (W m−1 K−1) | θD (K) | Tm (K) |
---|---|---|---|---|---|---|---|
Mg3PCl3 | 119![]() |
458![]() |
31![]() |
0.0459 | 50.98 | 304.44 | 1066.59 |
Mg3PBr3 | 92![]() |
550![]() |
24![]() |
0.0501 | 20.95 | 280.83 | 1065.67 |
Transverse sound velocity (Vt) is the speed with which the transverse (shear) waves move through a material. Longitudinal sound velocity (Vl) suggests the velocity of propagations of the compressional or longitudinal waves. Transverse velocity is the velocity at which a wave material can travel perpendicular to the fibers, while longitudinal velocity is the velocity at which a wave material can travel along the fibers.78 Therefore, Vm is the arithmetic average of the two velocities and gives an overall estimate of wave speed.79
For Mg3PCl3, the calculated value of Vt is 119106.9 m s−1, Vl is 458
543 m s−1 and Vm is 31
420.22 m s−1. For the compound Mg3PBr3, the values of Vt, Vl, and Vm are 92
654.17 m s−1, 550
426.2 m s−1, and 24
493.77 m s−1, respectively. The longitudinal sound velocities are much higher than the transverse velocities for both materials. The calculation shows that the Vt and Vm of Mg3PCl3 is higher than that of which means that the acoustic wave transmission in the material and thus it may be stiffer than that of Mg3PBr3. Also, Mg3PBr3 has a higher longitudinal velocity which implies that the material transmits longitudinal waves more effectively. Vm is essential to determine other thermal parameters for thermal conductivity. Mg3PCl3 demonstrates greater Vm with improved collective oscillations of lattice vibrations that relate well with enhanced mechanical strength and efficient heat conduction. All of these sound velocities are correlated with the material's elastic constants and its mechanical behavior. Higher velocities also mean a stiffer and more robust material and hence is capable of withstanding mechanical and thermal stresses. Thus, in terms of heat transfer or vibration damping requirements, Mg3PCl3 would be preferred because of its more or less balanced acoustic characteristics.
Lattice thermal conductivity (Kph) is a heat transport property that defines how well a material supports the passage of heat by lattice vibrations.80 Minimum thermal conductivity (Kmin) is thermal conductivity at the lowest, restricted by the atomic structure and density of the material.81 The compound Mg3PCl3 shows the Kph value of 50.9857 W m−1 K−1 and Kmin value is 0.0459 W m−1 K−1 while in the case of Mg3PBr3 the values of Kph at 20.95515 W m−1 K−1 and Kmin at 0.05015 W m−1 K−1. Both Kph for the compounds are significantly higher than Kmin and show contribution from phonon transport to thermal conductivity. In comparison with Mg3PBr3, the value of Kph is much higher, which points to a greater potential of Mg3PCl3 for heat transfer to the crystal lattice. This is consistent with its higher Vm suggesting better phonon transport behavior in the material. Notably, the values of the Kmin are closer for both compounds, indicating the possibility of an atomic-scale restriction for thermal transport in both materials. As a result, Mg3PCl3 is more suitable for utilization in applications where it would act as a superior heatsink, in the form of thermal paste or electronic parts for example. Mg3PBr3 with lower Kph values applicable for insulation. Also, low values of Kph indicate that each material has a fundamental limitation regarding its ability to transfer heat per unit area, the limitation being firmly anchored in the atomic structure of a given material.
Debye temperature characterizes the upper limit of vibrational densities in a material and depends on its stiffness and lattice bonding strength.82 Melting temperature (Tm) is the temperature at which the material changes from a solid to a liquid state and therefore its suitability for use under high temperatures.83,84 The θD of Mg3PCl3 is 304.44 K, and the melting Tm is 1066.59 K, while for Mg3PBr3, the value of θD is 280.83 K and Tm is 1065.67 K. Due to the higher θD value for Mg3PCl3, which has a more rigid atomic bonding structure and stiffer lattice than the Mg3PBr3. Both materials have low melting points, around 1065 K, indicated to have comparably high-temperature stability. The graphical representation of the Debye temperature is shown Fig. 14. The slightly higher θD of Mg3PCl3 suggests efficient high heat resistance. The Debye temperature is essential in determining the lower temperature heat capacity of a material and its expansion coefficient. The observed higher θD of Mg3PCl3 as compared to Mg3PBr3 indicates that it may have better thermal resistance and a lower coefficient of thermal expansion. This means that the two materials can be substituted for each other for use in high-temperature applications so long as other characteristics are desirable.
Mg3PCl3 shows superior results compared to Mg3PBr3 for sound velocity, lattice thermal conductivity, and Debye temperature properties and hence is considered to be more appropriate for high thermal conductivity and structural applications. The compound Mg3PBr3, although showing somewhat lower thermal stability, is also preferable in applications where the material with lower thermal conductivity is preferable. It was also noted that these two materials have similar melting features, which indicates that they have comparable properties under severe thermal conditions.
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