Judd-Ofelt Analysis Research Articles

Studies of luminescence traits and Judd-Ofelt analysis of Sm3+ activated oxyfluoride glasses

Novel Sm3+ activated oxyfluoride glass was synthesized via the melt-quenching approach with subsequent heat treatment. The X-ray diffraction measurement discloses the amorphous nature of prepared glasses. And, FTIR illustrates the molar surplus of Bi2O3 raises the network connectivity by creating bridging oxygen sites in the structure. The Judd-Ofelt (J-O) intensity parameters exhibit Ω4>Ω2>Ω6 trend, witnessing the rigidity of the glass structure and ionic bonding between Sm3+ ions and surrounding ligands. The 4G5/2 → 6H7/2 transition of Sm3+ is the most applicable for reddish-orange lasers due to their higher values of radiative transition probability, branching ratio, and stimulated emission cross-section. The optimum emission intensity is obtained with 30 mol% Bi2O3 and the corresponding decay time is 1.40 ms. Additionally, the F30 glass sample was lit in a reddish-orange region having a CCT value of 1689 K. The thermal luminescence quenching of the prepared glass was studied and the thermal stability parameters activation energy was estimated. Further, the contactless optical thermometry capability of the glass sample was explored within the range of 303 K–603 K using the luminescence intensity ratio (LIR) technique. Thus, the above studies on the glass sample suggest that it can be used as an active medium in lasers, contactless optical temperature sensing, and high-energy scintillator applications.

Host-sensitized colour-tunable emission and Judd-ofelt analysis for Dy3+-doped ZnGa2O4 phosphor through exciton-mediated energy transfer

Single-phase Dy3+-doped zinc gallate (ZnGa2O4) phosphors were synthesized using a conventional solid-state fabrication technique. The structural properties of the host phosphor were determined through X-ray powder diffraction (XRPD) and Rietveld refinement, revealing a cubic spinal structure with a space group of Fd3m. The reflectance properties of the host and doped samples were measured using UV–Vis spectroscopy. The obtained data were used to estimate the bandgap of all the synthesized samples, ranging from 4.18 to 3.69 eV, confirming the formation of a wide bandgap semiconductor. Morphological, compositional, and surface mapping analyses were conducted using a field emission scanning electron microscope, energy dispersive electron spectroscopy, and time-of-flight secondary ion mass spectroscopy. X-ray photoelectron spectroscopy was employed to confirm the oxidation state of the constituent elements and for an in-depth study of the crystal structure. Photoluminescence excitation and emission spectra were recorded to analyze the luminescent properties of the synthesized phosphors. It was confirmed that when using an excitation wavelength of 247 nm, all samples exhibited broad host emission with decreasing intensity. In contrast, Dy3+ emission displayed an increasing trend, confirming host sensitization in this phosphor. To analyze the radiative properties of the activator ion, theoretical analysis using the Judd-Ofelt theory was carried out. The results revealed an overlapping of orbitals between the O2− ion and Dy3+, indicating its higher-order covalent nature and the increased symmetric nature of the activator ion in the present host. This characteristic allowed for the generation of near-white light emissions. A concentration of 7 mol% of Dy3+ was observed to match well with achromatic white (0.32, 0.33) on the color chromaticity diagram. The luminous properties of this material suggest that it is a desirable candidate for use in LEDs and AC electroluminescent systems.

Development of Eu3+-Doped Oxyfluoride Glass for Active Laser Medium

In this work, Eu3+-doped barium sodium borate oxide and oxyfluoride glasses were fabricated by melt-quenching technique for investigated their physical, optical, photoluminescence and radiative properties. The emission spectra, observed under the 394 nm, show the emission band corresponding to the transitions of 5D0→7F1 (590 nm), 7F2 (613 nm), 7F3 (652 nm) and 7F4 (701 nm). The most intense emission band is the 5D0→7F2 transition at 613 nm. The emission light is shown the reddish-orange color according to the framework of CIE 1931 color space. The Judd-Ofelt analysis confirmed the potential for using the glass samples in this work for use as photonic applications. The results from the emission spectra and radiative properties show that the oxyfluoride glass sample has more lasing potential than the oxide glass sample.

White Light Emission and Judd-Ofelt Analysis of Dy3+ Doped Mixed Alkali Borate Glass for W-LEDs Material

The Dy3+ doped lithium sodium potassium borate glasses with white light-emitting were prepared by the melt quenching technique. In this work, optical, photoluminescence properties and Judd-Ofelt analysis of borate glasses have been investigated. For optical properties, Dy3+ doped glasses showed the absorption in visible and near-infrared region, which originate from 6H15/2 ground state to higher state. While the luminescence properties of Dy3+ doped glasses, the emission spectra were presented more intense at 484 nm (blue light) and 574 nm (yellow light) which are essential for white light emitting materials, whilst decay time decrease with an increase of Dy2O3 contents. The emission intensity of Dy3+ doped glasses were enhanced by adding Dy2O3 concentrations until 0.5 mol%, after that the emission intensities were decreased due to the concentration quenching effect. Judd-Ofelt is analyzed by using the absorption and photoluminescence results, The stimulated emission cross-section has been investigated in this work. The CIE 1931 chromaticity investigation shows that Dy3+ doped glass emitted light with white color. Hence, these glasses may be suitable candidates for use in W-LEDs material.

Judd–Ofelt Analysis and Spectroscopy Study of Tellurite Glasses Doped with Rare-Earth (Nd3+, Sm3+, Dy3+, and Er3+)

A series of glasses based on (80-y) TeO2-20 BiCl3-y RE2O3 (y = 0, 0.6 mol%; RE = Nd, Sm, Dy, and Er) were prepared. The thermal stability of the glass was determined by differential scanning calorimetry (DSC). The density and optical energy values of the prepared glass increased in the order of Sm2O3, Nd2O3, Dy2O3, and Er2O3. In addition, the glass doped with Er2O3 had the highest refractive index values compared to the other samples. Subsequently, Judd–Ofelt parameters (Ω2, Ω4, and Ω6) were obtained for the family of RE3+ trivalent rare-earth ions introduced as dopants in a tellurite glass. These parameters were calculated from the absorption spectra for each RE3+. The structures were studied by Raman spectroscopy deconvolution, which determined that TeO4, TeO3, TeO3+1, BiO6, and BiCl6 units had formed. In addition, the structural changes in the glass are related to the intensity ratio of TeO4/TeO3, depending on the type of rare-earth. For the optics and Judd–Ofelt parameters, the ray spectroscopy results of the prepared glass show that it is a good candidate for nonlinear optics fibers, a solid laser material.

Tuning phase and photoluminescent properties of ZrO2:Eu3+ coatings formed by plasma electrolytic oxidation and Judd-Ofelt analysis of composite materials

Eu3+ doped Zirconia coatings were synthesized by the electrochemical plasma electrolytic oxidation method in only 8 min from the pure zirconium substrate. The phase constitution from pure monoclinic to pure tetragonal and exactly in between was achieved by using different concentrations of Na3PO4 and NaAlO2 electrolytes. The complex emission spectra composed of Eu2+, Eu3+, and ZrO2 defect emission greatly depend on the excitation wavelength and phase constitution. Eu3+ photoluminescence properties depend on the phase, which is reflected by the different Stark splitting and different intensities of transitions. Thus, both phase and photoluminescent properties of ZrO2 coatings are fine-tuneable. Judd-Ofelt analysis was performed from the emission and excitation spectra, showing that all 3 intensity parameters depend linearly on the phase constitution, being largest in the pure monoclinic phase. The mixed phase has Judd-Ofelt parameters between those in pure phases. Eu3+ has 2.45 times more preference to get incorporated into the tetragonal than in the monoclinic phase in the mixed phase samples. The general equation for Judd-Ofelt parameters in a compound with mixed constituents and probability of incorporation is introduced, allowing also for a prediction of the spectrum shape based on the Judd-Ofelt parameters of pure-phase compounds. Python software code for estimating the percent of incorporation by multiple linear regression model is also provided.

Optical properties, Judd-Ofelt analysis and energy transfer processes of Eu3+ doped ZnS quantum dots

Quantum dots (QDs) of ZnS doped with different Eu3+ ion concentrations were synthesized using a chemical method. The X-ray diffraction (XRD) pattern showed that the prepared QDs were crystallized in the Zincblende phase and their size was estimated to be approximately 3 nm. The XRD pattern and XPS spectrum analysis showed that Eu3+ ions replaced Zn2+ ions in the crystal lattice. For the first time, the optical properties of Eu3+ doped ZnS QDs were studied using photoluminescence excitation (PLE), photoluminescence (PL) spectra, and Judd-Ofelt (J-O) theory. Ωλ (λ = 2, 4, 6) parameters were calculated from the PLE spectra of the samples. The luminescence quantum efficiency and properties of the ligand field of the material were calculated and compared with those of other lattice hosts. The energy transfer (ET) processes from the ZnS host to Eu3+ ion and between Eu3+ ions were also discussed in detail. The ET process from the ZnS host to the Eu3+ ion occurred through the exchange interaction. The dominant interaction between Eu3+ ions in the ET process is the dipole-dipole mechanism, which is determined by fitting the decay curve of the 5D0 level to the Inokuti-Hirayama model.

Synthesis, optical properties and Judd-Ofelt analysis of Eu3+ doped Ca2KMg2V3O12

The synthesis of undoped and the Eu3+ doped garnet-type vanadate Ca2KMg2V3O12 (CKMV) was achieved using a solid-state reaction method. The phase formation of the samples was confirmed through powder XRD analysis. The morphological properties of the material were examined using SEM, and elemental mapping through EDAX provided information about the elements present in the samples. The band gap energy of CKMV and CKMV:0.05Eu3+ was determined using DRS measurements. Photoluminescence properties of CKMV and CKMV: xEu3+ (x = 0.01–0.09) were investigated under excitation at 370 nm, with emission at 612 nm. Additionally, the dominant characteristic peak of Eu3+ was studied through photoluminescence emission under excitation at 472 nm. Lifetime decay analysis and CIE color coordinates were obtained. Judd-Ofelt intensity parameters were calculated based on the emission spectra, elucidating the radiative properties of CKMV:0.05Eu3+. Temperature-dependent photoluminescence demonstrated the good thermal stability of the optimized sample. From the temperature dependent life time analysis, the sensitivity of the material has been calculated. These findings suggest that this phosphor is well-suited for use in solid-state lighting applications.

An insight into Judd-Ofelt analysis and non-contact optical thermometry of LiCa2Mg2V3O12: Dy3+ phosphors for multifunctional applications

A series of Dy3+ doped LiCa2Mg2V3O12 phosphors have been synthesized by solid state method. The phase composition of the phosphor has been analyzed by X-ray powder diffraction and confirms a cubic phase with Ia-3d space group. The scanning electron microscope images of LiCa2Mg2V3O12:xDy3+ phosphor reveals the surface morphology and is further investigated by its energy dispersive X-ray spectrum. The elemental mapping analysis displays the uniform composition of the elements present in the phosphor. The band gap energy of the phosphors has been determined from the diffuse reflectance spectra. The Judd-Ofelt intensity parameters are determined from the absorption spectra and follows the trend Ω2 > Ω6 > Ω4. The photoluminescence spectra of phosphors excited at 338 nm have intense emission at 494 and 576 nm corresponding to 4F9/2→6H15/2 and 4F9/2→6H13/2 transition and is ascribed to the magnetic and electric dipole allowed transition respectively. The radiative parameters for the optimum dopant concentration x = 0.08 has been calculated. Temperature dependent PL spectra of phosphor displays the diverse thermal response of VO43− group and Dy3+ ion and this can be utilized for the development of thermosensor based on fluorescence intensity ratio (FIR). The phosphor have maximum absloute and relative sensitivity values of 0.0063 K−1 and 0.41% K−1 in the temperature range of 80–400 K. The optical properties of the phosphor suggest that it find applications in the fields of solid-state lighting, temperature sensing, optoelectronic devices and W-LEDs.

Effect of Eu2O3 Concentrations Doped Li-Na-K Borate Glasses on Luminescence Properties for Red Emission Material

This paper investigated the europium-doped lithium sodium potassium borate glasses (LNKBEu). Glass was made using a melt-quenching technique with a range of europium doping concentrations ranging from 0.0 to 5.0 mol%. The absorption spectra showed that photons in the visible light and near infrared ranges were absorbed by the LNKBEu glasses. Photon absorption at 394 nm can excite the mirror to emit a number of photons in the VIS region, such as 590, 613, 652, and 701 nm. The results showed that 3.0 mol% was the optimal concentration of LNKBEu glass. Therefore, 3.0LNKBEu glass was studied using Judd-Ofelt (JO) analysis, which revealed an interesting possibility of its use. This glass is a high power red laser device.

Optical characterization of Sm3+ doped phosphate glasses for potential orange laser applications

Undoped and Sm3+doped 45P2O5–45Na2O–2Al2O3–8BaO glasses were synthesized by the melt-quenching technique. The glass structure and luminescence properties were investigated by using Raman spectroscopy, scanning electron microscopy (SEM), spectroscopic ellipsometry, Judd-Ofelt theory and photoluminescence. Electron microscopy showed the homogeneity of samples. Raman spectroscopy revealed that the overall structure of the glass was unaffected by the doping of Sm3+ and ellipsometry was used to measure the optical constants. Judd-Ofelt (JO) analysis was performed on the absorption bands of Sm3+ (4f5) and the three phenomenological parameters (Ω2, Ω4, and Ω6) were computed and then used to determine radiative properties such as the radiative transition probability (Ar), the fluorescent branching ratio (βr), the stimulated emission cross-section (σe) and the radiative lifetime (τrad). Photoluminescence (PL) spectrum showed the typical four transitions of Sm3+ at wavelengths of 564, 600, 645 and 703 nm corresponding to 4G5/2 → 6H5/2, 6H7/2, 6H9/2 and 6H11/2, respectively. The spectroscopic quality factors Ω4/Ω6, the predicted lifetime (τrad) calculated using the JO method and the experimentally lifetime (τexp) for the 4G5/2 level were calculated and discussed. The glass color purity is as high as 98%, which makes it a potential candidate for laser emission.

Structure, photoluminescence, Judd-Ofelt analysis, and thermal stability studies of Eu3+-doped Ba2Tb8(SiO4)6O2 red phosphor with high color purity

In this study, a series of Eu3+-doped Ba2Tb8(SiO4)6O2 red-emitting phosphors were developed by using a conventional solid-state reaction technique. The crystalline structure, surface morphology, photoluminescence properties, energy transfer processes, and thermal behavior of the Eu3+-doped Ba2Tb8(SiO4)6O2 phosphors were studied. The X-ray diffraction patterns confirmed the formation of the phase, and the Rietveld refinement study revealed that the Eu3+-doped Ba2Tb8(SiO4)6O2 phosphors have a hexagonal crystal structure with the space group P63/m. Energy-dispersive X-ray analysis confirmed the homogenous distribution of Eu3+ ions over the Tb3+ sites. Photoluminescence (PL) spectroscopy was used to test the luminescent properties of the synthesized phosphors. The PL spectra showed that upon UV and blue light exposure, the Eu3+-doped Ba2Tb8(SiO4)6O2 phosphors exhibited red emission associated with the 5D0→7FJ transitions. The mechanisms of concentration quenching and energy transfer were analyzed using Blasse and Dexter's formula. Judd-Ofelt parameters (Ω2, Ω4) and other radiative parameters were analyzed using PL emission spectra to investigate the luminescence behavior of Eu3+-doped Ba2Tb8(SiO4)6O2 phosphors. The results of the thermal stability studies show that Eu3+-doped Ba2Tb8(SiO4)6O2 has good thermal properties with a high activation energy of approximately 0.23 eV. The calculated Commission International del'Eclairage coordinates (x = 0.62 and y = 0.36) of the prepared phosphors confirm that the emitted light is in the red portion with a high color purity of about 99.9%. These findings show that Eu3+-doped Ba2Tb8(SiO4)6O2 phosphors are a viable option for solid-state lighting technology.

Spectroscopic investigations and Judd-Ofelt analysis of Sm3+ doped Y2O3 transparent ceramics

Sm3+ doped yttria transparent ceramics (SmxY1-x)2O3 (x = 0.01, 0.015, 0.03) were fabricated by Spark Plasma Sintering method. Absorption spectra, as well as emission spectra and luminescence lifetime were carried out at room temperature. Judd-Ofelt (J-O) theory was used to calculate the Ωt (t = 2, 4, 6) intensity parameters. The spontaneous transition probabilities, radiative lifetime, branching ratio, and stimulated emission cross-sections have been calculated for 4G5/2 excited level. The emission cross section for the 4G5/2 → 6H7/2 transition at about 607 nm was calculated to be 6.73 × 10−22 cm2. The results indicate that Sm:Y2O3 ceramic may be a potential reddish orange-light laser material around 607 nm.

Organic mediated solvothermal synthesis, enhanced luminescence dynamics, photometric and Judd-Ofelt analyses of Zn2+ modified Gd2O3: Eu3+, Li+ nanophosphors for deep UV LEDs and security inks

Highly luminescent red emitting Zn2+ modified Gd2O3:Eu3+, Li + nanophosphors with superior colour purity were prepared by the organic mediated solvothermal combustion of metal-citrates in diethylene glycol. Structure, morphology, spectroscopic and luminescence dynamics of the nanophosphors were found to be sensitive to Zn2+ concentration. Simultaneous incorporation by Zn2+ and Li+ ions in Gd2O3:Eu3+ resulted in better emission features and improved photophysical radiative properties. Enhanced photoemission has resulted from the cooperative and combined roles caused by Li+ and Zn2+ ions, improvement of crystallinity, modifications of the crystal field and reduced symmetry around Eu3+ ions in Gd2O3. Photoemission intensity of the optimal zinc compensated phosphor with composition Gd1.71Eu0.1Li0.15Zn0.04O3 was found to be 1.82 times that of Gd1.75Eu0.1Li0.15O3 and it exhibited a lifetime of 1.467 ms with the highest colour purity of 97.06 %. Luminescence decay profiles of all the synthesized phosphors were found to follow single exponential behaviour. Judd-Ofelt analysis revealed that the emission intensity parameters were found to be optimum for Gd1.71Eu0.1Li0.15Zn0.04O3 phosphor, indicating the highest asymmetry of local environment around Eu3+ ions in this material. Better radiative and Judd-Ofelt intensity parameters obtained indicate that this highly luminescent red emitting phosphor can act as a promising material for high resolution phosphor coated displays, deep UV excited phosphor converted LEDs and for developing defence security inks.

Structural and optical properties of europium-doped sodium-lead-antimony glasses

Antimony-sodium-lead glasses doped with varying amounts of europium were synthesized using the melt quenching technique. To investigate the mutual effects between the dopant and the glass matrix, various methods and techniques were employed to analyze and characterize the glass samples. These methods included X-ray diffraction (XRD) for justifying the amorphous nature of the samples, differential scanning calorimetry (DSC) for analyzing thermal properties, Fourier transform infrared (FTIR) spectroscopy for studying functional groups in the 1400–400 cm-1 range, and peak deconvolution techniques used to analyze the defect impact in the 1100–800 cm-1 band region. UV–VIS spectroscopy was utilized for absorption analysis, optical band gap estimation, and Urbach energy calculation. Photoluminescence spectroscopy was employed in the UV–VIS-NIR range to investigate excitation, emission, lifetime decay, and local structure of Eu3+ ions within the disordered matrix, characterized by high polarizability content. Judd-Ofelt analysis and radiative parameters were obtained from emission spectra using a 464 nm excitation wavelength. The estimation of the optical band gap revealed broadening and shrinking with increasing Eu3+ ion concentration. The excitation spectra showcased the potential for emission under two distinct excitation mechanisms: single-photon excitation (1PE) and two-photon excitation (2PE). The quality of emitted light color was characterized using CIE chromaticity coordinates.

Structural, elastic and optical properties of rare earth ions (Nd3+, Dy3+, & Nd3+/Dy3+) incorporated B2O3+K2O+ZnO+ZnF2 glasses

Herein we report the effect of rare earth ion; REI (Nd3+, Dy3+, & Nd3+/Dy3+) on the structural, optical, luminescence and elastic characteristics of B2O3+K2O+ZnO+ZnF2 glasses produced via the melt-quenching process. The structural, optical, luminescence and elastic features of the produced glass samples were comprehensively characterised using XRD, FTIR, UV–Visible, Luminescence, and decay analysis methods. The XRD study shows that even after doping or co-doping with REIs, the glass samples exhibit amorphous characteristics. It was observed that physical parameter analysis revealed the occurrence of non-bridging oxygens, while FTIR analysis revealed the predominance of borate groups for all the prepared samples. Only transition peaks discovered in the BNd, BNdDy and BDy samples were affected, according to a UV–visible absorption spectra examination, while the rest were left unchanged. Ionic and covalency nature with the host were identified, respectively, followed by the Judd-Ofelt analysis for BNd and BDy glasses. Peak emission and lifetime data were analysed for samples of BNd, BDy, and BNdDy. The CIE diagram shows that the BDy emits warm white light with an efficiency of 81%. Using the Makishima - Mackenzie model, the structural compactness (elastic properties) of the manufactured sample was thoroughly addressed.

Influence of Ga Substitution on the Local Structure and Luminescent Properties of Eu-Doped CaYAlO4 Phosphors

Understanding the local environment of luminescent centers in phosphors serves as a blueprint for designing the luminescent properties of phosphors. Chemical substitution is a general strategy for engineering the local structure around luminescent center ions. In this study, we systematically investigate the luminescent properties of Ga-substituted Eu-doped CaYAlO4 (CYAGO:Eu) phosphors and the local structure of the Eu ions. The Ga substitution at the Al sites leads to a significant enhancement in the electric dipole transition of Eu3+ (5D0 → 7F2). The Judd–Ofelt analysis reveals that Eu3+ ions are substituted for Ca/Y, and the Ga substitution increases the asymmetricity of the local structure around the Eu ions because of the different ionic radii and electronegativities of Al and Ga. In addition, Eu2+ emission is missing regardless of the Ga substitution and post-hydrogen treatments. The present work provides deeper insight into the role of chemical substitution in oxide phosphors.

Judd-Ofelt analysis and Spectroscopic Investigation for doped Nd3+ lead phosphate Zinc glasses

Judd-Ofelt analysis and Spectroscopic Investigation for doped Nd3+ lead phosphate Zinc glasses

Influence of vanadium in sensitized luminescence mechanism and Judd-Ofelt analysis in Er3+/Ho3+ doped mixed ionic-electronic glass system

Er3+/Ho3+ Doped Al₂O₃-Na₂O–TeO2 mixed ionic-electronic glasses containing different concentrations of V₂O5 ranging from 0 to 2.0 mol% were prepared using melt-quenching method. The structural, optical and photoluminescence properties of the glass were studied using FTIR, UV–Vis, and photoluminescence spectroscopy measurements. XRD analysis confirms the amorphous nature of the glass system. The relative areas of TeO4 and TeO3 were measured to demonstrate the correlation of bridging/non-bridging oxygen that exist in the glass network. It was observed that the relatively high TeO3 indicates that the environment of the glass system is NBO-rich despite the increase in BO attributed to V2O5. Analysis on optical absorption edge by Tauc's plot revealed that EOpti decreases due to the prevalence of NBO in the glass system. The Judd-Ofelt oscillator strength, fexp increases accompanied with an anomalous drop at x = 1.0 mol% due to the competition between BO and NBO that has altered the covalency and asymmetry of the Er3+ with the local environment ligand. Meanwhile, the Judd-Ofelt parameter Ω2 decreases generally suggesting that the glass system has underwent some structural modification due to the increase in BO in the host matrix contributed by the VO5. Photoluminescence spectra revealed three dominant emissions in the green region (525 nm;2H11/2 ➝ 4I15/2, 532 nm; 5F4 + 5S2➝ 5I8, 547 nm;4S3/2 ➝ 4I15/2) and 2 emissions in the red region (659 nm; 5F5 ➝ 5I8, 662 nm; 4F9/2 ➝ 4I15/2). As vanadium increased, a decrease in photoluminescence intensity is observed as a result of concentration quenching between V4+ and Ho3+.

Effect of adding TiO2 as modifier on the optical thermometric ability of tellurium tungstate glass

This work investigates the effect of incorporating TiO2 on the optical properties of the Er3+/Yb3+ doped/codoped tungstate-based tellurite (TW) glasses. The optical bandgap and Urbach energy analysis indicates that the structure of the binary tungstate glass gets modified due to the incorporation of TiO2. The Judd-Ofelt analysis shows that the bonding between the activator and ligand oxygen ions is ionic in nature and the ionicity of the bond increases with the TiO2 content. The incorporation of TiO2 enhances the green and red UC emission intensity of the Er3+ doped TW (TW_0.6) glass by ∼ 39 and ∼ 140 times respectively. The relative sensitivity of the Er3+/Yb3+: TW glass having 10 mol% of TiO2 is found to be as high as ∼ 0.01236 K−1 at 300 K.