Defect clustering in an Eu-doped NaMgF3 compound and its influence on luminescent properties

We combined classical atomistic simulation and crystal field models to describe the origin of defects and their influence on luminescent properties of Eu-doped NaMgF3 in the orthorhombic phase.


Introduction
Perovskite compounds are a class of special materials that have attracted wide attention in recent years for interesting applications, such as magnetoelectrics, 1,2 photovoltaics devices, [3][4][5][6] light-emitting diodes, 7,8 lasers, 9,10 photocatalysis, 11 memristors, 12 and ionizing radiation detectors. [13][14][15] Fluoroperovskite materials, ABF 3 (where A and B stand for alkali and alkaline earth metals, respectively), are a sub-class of perovskite compounds. In particular, NaMgF 3 is a material inserted in this family, with interesting properties related to optics and ionizing radiation dosimetry. 16,17 Rare earth-doped NaMgF 3 compounds have been considered promising materials for personal dosimetry because of the effective atomic number, similar to human tissue, and high sensitivity at low dosages. 18,19 Unlike the other materials of this class, such as AMgF 3 (A= Rb, K, and Cs), NaMgF 3 presents an orthorhombic perovskite structure with space group Pbnm at room temperature and standard pressure. 20 Luminescent properties of NaMgF 3 nanoparticles doped with lanthanide ions and Mn, synthesized using a reverse micro-emulsion method, have been reported. 21,22 Furthermore, lanthanide ions doped into NaMgF 3 polycrystalline samples have also been prepared by the conventional solid-state reaction method. 23,24 In fact, lanthanide incorporation in compounds has been largely used to enhance luminescent properties.
In particular, Eu 3+ -doped materials are a well-known red emitting phosphors, widely used as spectroscopic probes because of their unique emission characteristics. [25][26][27] Valuable characterization information, such as local symmetry of the optically active ion, occupancy number, and Stark levels, can be obtained from emission characteristics of the Eu 3+ ion. However, in many cases, the Eu ion is incorporated in a host matrix and aliovalent substitution occurs. The difference between the ionic radii of both ions (doped and host) is an important factor in evaluating the influence of aliovalent substitution, giving rise to material defects. Identifying these defects is crucial to accurately describing the spectroscopic properties and understanding specific mechanisms relevant to their application in optics and ionizing radiation detectors. Mechanisms of charge compensation are not yet established for Eu 3+ -and Eu 2+ -doped NaMgF 3 . Some reports have suggested different types of charge compensation in materials of the same family (KMgF 3 28-30 and RbMgF 3 31 ) doped with different lanthanide ions. However, these discussions are based on ion sizes (doped and host), ignoring discussions about lattice solution energy. In addition, the symmetry site and coordination number of the optically active ion are not clear, as well as the substitution site in the host matrix. The optically stimulated luminescence (OSL) decay pattern and high sensibility of the NaMgF 3 :Eu 2+ compound for low dose levels are not fully established. Therefore, a systematic study is necessary to make predictions about the incorporation of defects in the NaMgF 3 structure.
Classical atomistic simulation is a reliable tool for modelling a range of ionic materials and to help understand theoretical and experimental results. In this methodology, interactions between atoms are determined by interatomic potentials that are essential to studying physical properties of the simulated systems. Several studies have been widely used to examine structural, mechanical, elastic, and dielectric properties in solid-state materials [32][33][34][35][36] . Furthermore, atomistic simulation is able to perform studies on defect properties with low computational cost, compared with other methodologies, and has been successfully employed to study defects. [37][38][39][40] In addition, atomistic simulation procedures, combined with crystal field theory, is an practical method for describing spectroscopic properties of lanthanide ion-doped compounds and their dopant-related effects. Recently, Otsuka et al. 41 performed a study from a spectroscopic point of view, combining atomistic simulation, the simple overlap model (SOM), 42 and the method of nearest neighbours 43 (theoretical models of crystal field). The combination of both methodologies successfully described local symmetry and coordination number of the optically active ion, crystal field parameters, crystal field strength, 7 F 1 stark sub-levels, and splitting.
Thus, in this work, we used a combination of classic atomistic simulation-based ionic models and crystal field models to study the orthorhombic phase of NaMgF 3 .
Firstly, atomistic simulation was used to describe structural properties and the defect formation process with the incorporation of Eu 3+ and Eu 2+ ions into NaMgF 3 . For this, we developed a new set of interatomic potentials to describe the interactions between ions for the compound in the orthorhombic phase and performed a study of the structural and elastic properties. We carried out a defect study to obtain the most favourable charge compensation mechanism. Secondly, crystal field models were used to study spectroscopic properties of Eu 2+ and Eu 3+ ion-doped NaMgF 3 . Detailed local geometry of the optically active ion in this host matrix was obtained. In addition, photoionization cross-section calculations, associated with the first-order kinetic model, gave us information about the OSL decay pattern and high sensibility of the Eu 2+ -doped NaMgF 3 compound.

Computational simulation
The atomistic simulation technique was used to study the perfect structure and defective lattice of orthorhombic NaMgF 3 , performed by GULP code. 44 Relaxation of the lattice parameters and atomic positions was completed to find the lowest energy.
A description of the structural properties of the system depends on a set of potential parameters, adopted for a reliable description of fundamental interactions between the ions. Long-range interactions were calculated by Coulomb potential and shortrange interactions by Buckingham potential. Eq. (1) shows the representation of repulsive (or Pauli repulsion) and attractive (or van der Waals interaction) terms of the Buckingham potential: where A, ρ, and C are parameters obtained by a fitting procedure, and r is interatomic distance between ions.
In addition, a model for efficient treatment of ionic polarization effects is necessary, and a simple model, known as the shell model, 45 was used. Ions in this model are represented by a core (massive, includes the nucleus plus core electrons) and shell (massless, includes valence electrons) connected by a harmonic constant.
The formal charge of the ion is obtained by the sum of the core and shell charges.
The defect calculation was performed using a two-region strategy. 46 This method is very useful for calculating defects in atomistic simulations and has been used successfully. [47][48][49][50][51] The crystal lattice is divided into two spherical regions (I and II), where the defect (or defect cluster) is placed in the centre of these regions. The inner region I is the portion of the crystal located around the defect, allowing explicit relaxation of all the ion positions under the action of a force field. Region II is more distant from the defect and can be treated using an approximate continuous method, since ions in this region exhibit an interatomic displacement smaller than the ions in region I. To obtain reliable results, a convergence test, with an appropriate radius for these regions, is necessary. In this work, we used 12 and 18 Å for regions I and II, respectively. This corresponds to approximately 1000 ions in the region I and 2400 ions in region II. The total energy ( ) can be calculated by the expression where is the energy of region I, is the energy of region 12 ( , ) + 2 ( ) 1 ( ) 2 ( ) II, and is the energy of the interaction region between them. 12 ( , )

Crystal field parameters and Stark levels of the 7 F 1 multiplet
Interaction between the lanthanide ion and its nearest neighbours (NNs) has been a discussion theme in research groups that work with lanthanide spectroscopy, for a long time. The point charge electrostatic model (PCEM) 52 was the first nonparametric model to discuss crystal field parameters from a theoretical point of view.
The PCEM considers that the bond between the lanthanide ion and its chemical surrounding is purely ionic, where the charge factor is equal to ligand valence and is located at the NN's position. Although some considerations of the PCEM have led to unsatisfactory results from a quantitative point of view, it has been the base model for the development of other theoretical models. The simple overlap model 42 used in our predictions is a theoretical model based on the PCEM, which has been largely used in lanthanide spectroscopy with satisfactory predictions. 53,54 The SOM introduces a small covalent character to describe Ln−NN chemical bonding. In this assumption, the effective interaction charge is defined as -ρ j g j e and is located around the Ln−NN middle distance (R j /2β). g j is the charge factor devoted to Ln−NN chemical bonding, R j is j-th NN distance from the Ln ion, e is the elementary charge, and β j = 1/(1±ρ j ) is a factor that determines the position of the effective charge in the middle distance. The minus sign is applied when the charge is closer to the Ln ion, and the plus sign is applied when the charge is closer to the ligand. ρ j = ρ 0 (R 0 /R j ) 3.5 describes the overlap of interacting wavefunctions, where R 0 is the smaller Ln−NN distance, and ρ 0 =0.05 is the maximum overlap between the 4f and 2s (or 2p) orbitals. 55 Through these considerations, the crystal field parameters ( ) of the SOM can be related to PCEM, as show Eq. 2: ( ) The 7 F 1 energy sublevels of Eu 3+ can be obtained through diagonalization of the crystal field matrix within the 7 F 1 manifold. 56 Thus,

Photoionization cross-section of trap levels
The photoionization cross-section (σ) is an essential quantity to understand the interaction processes of electromagnetic radiation with matter. Recently, Lima-Batista-Couto 57 proposed a model to obtain σ of localized traps in the band gap with activation energy E i with respect to the conduction band, based on time-dependent perturbation theory. The model describes the trap level by a three-dimensional isotropic harmonic oscillator wavefunction with angular frequency ω 0 , and the electron in the conduction band is described by the plane wavefunction. Following the same steps reported previously 57 and using the Fermi's golden rule, we obtain: where is an energy function, ω is the angular frequency of ( ) = 2 ℏ / * 0 incident electromagnetic radiation, m* is the electron effective mass, α is the fine structure constant, is Planck's reduced constant, c is the speed of light, and k is the ℏ wavevector of the electron. This expression is obtained considering all multipole terms in the Hamiltonian that couple the linear moment of the electron with the radiation electromagnetic field. This model was applied successfully to predict σ in promising materials for personal dosimetry and explain the mechanism of electron de-trapping with light stimulation. 57,58 3 Results and discussion

Interatomic potentials of NaMgF 3
To analyse the structural properties and influence of defect clustering on the luminescent properties of the compound, describing the interactions between ions of the materials through a reliable set of interatomic potentials is necessary. We developed a new set of interatomic potentials for the orthorhombic phase of NaMgF 3 from an empirical fitting procedure, carried out with GULP code. 44 The empirical fitting was used to obtain Buckingham potential parameters for the Na−F interaction. The potential parameters used for Mg−F and F−F interactions were taken from a previous study 33 and have already been tested and validated for compounds of the same family, AMgF 3 (A = K, Cs, and Rb). Table 1 shows the interatomic potentials and shell model parameters used in all calculations of this work. A short range potential cutoff of 12 Å was used.
This set of interatomic potentials was validated, and the calculated lattice parameters of the NaMgF 3 compound are in excellent agreement with X-ray diffraction values, as well as mechanical properties. Elastic and dielectric constants are close to experimental values (see next section). The fluoride precursors NaF and MgF 2 are commonly used to synthesize NaMgF 3 . In addition, the same set of potentials is also capable of modelling precursor fluorides (NaF and MgF 2 ). Even though the focus of this work was to analyse the orthorhombic NaMgF 3 phase, we were able to show that this set of interatomic potentials is transferable to the cubic phase of NaMgF 3 , as well.
Calculations of the various precursor fluoride properties and cubic NaMgF 3 are shown in the supporting information (see Tables S1-S7). These facts are important validation characteristics for successfully calculating defect properties. Table 1 Buckingham potential and shell parameters for NaMgF 3 .
Interaction  Table 2 presents a comparison between calculated and experimental data from lattice parameters and cell volumes for orthorhombic NaMgF 3 . A relative error of less than 0.82% was calculated for all lattice parameters and cell volumes with respect to X-ray diffraction data. 59 Table 3 shows the most relevant interatomic distances for orthorhombic NaMgF 3 calculated in this work compared to experimental data. 59 The distances presented a relative error below 3% in all cases. These results show that our atomistic simulation has good acceptance in the reproduction of NaMgF 3 structural

Structural properties of the orthorhombic NaMgF 3
properties. In addition, a similar relative error was observed for all properties studied for cubic NaMgF 3 using the same set of interatomic potentials, as shown in the supporting information.

Fig. 1
The crystalline structure of NaMgF 3 in an orthorhombic lattice with space group Pbnm. Na and Mg sites are shown in detail. The elastic constants (C 11 , C 22 , C 12 , C 13 , C 23 , C 33 , C 44 , C 55 , and C 66 ) of NaMgF 3 in the orthorhombic phase are shown in Table 4, and the values calculated in this work are compared with experimental data. 60 The elastic constants satisfy Born's criteria and prove its mechanical stability. The reproducibility of these properties validates the potentials and transferability, which is crucial for modelling physical properties under conditions different from the initial fitting procedure. The bulk modulus, shear modulus, static dielectric constant ( 0 ), and high-frequency dielectric constant (  ) for orthorhombic NaMgF 3 are also shown in Table 4. In addition, our results show excellent transferability of these potentials for cubic NaMgF 3 (see supporting information). Having successfully completed this first step, we next analysed defect properties and their influence on spectroscopic properties of NaMgF 3 .

Defect calculations
The process of incorporating Eu 3+ and Eu 2+ ions into the NaMgF 3 compound requires a charge compensation mechanism to stabilize the local structure and accommodate extra charge in the relaxed structure. Interatomic potential used to describe Eu−F interactions was taken from a previous study for modelling natural apatite crystals, 61 and have already been tested and validated for Rare-Earth Fluorides.
The incorporation of defects into the crystalline structure, obtained by our atomistic simulation, can estimate the preferred doping site and mechanism of charge compensation most favourably. Firstly, we consider the various possible schemes of charge compensation for the incorporation of Eu 3+ and Eu 2+ in the NaMgF 3 compound. Tables 5 and 6 show the proposed chemical reaction schemes, expressed in Kröger-Vink notation, 62 Table 5. For the other reactions, a similar procedure is employed.
where E def is the defect formation energy, and E latt is lattice energy. More details regarding the calculation of solution energies are found in Ref. 48.
Tables S8-S12 in the supporting information show defect and lattice energies required to perform the solution energy calculations.
Incorporating the Eu 3+ into Mg 2+ site Incorporating the Eu 3+ into Na + and Mg 2+ sites Table 6 Solid state reactions in the Kröger-Vink notation for Eu 2+ -doped NaMgF 3 .

Schemes
Incorporating the Eu 2+ into Na + site Incorporating the Eu 2+ into Mg +2+ site  In fact, the valence of ions is a determining factor for Eu 3+ entering into the Mg 2+ site instead of the Na + site. The ionic radius varies with coordination number,   Table 6) for incorporation of Eu 2+ into the Na site of NaMgF 3 . The most favourable mechanism of charge compensation is through the sodium vacancy (scheme XV) and anti-site (scheme XVIII), both with energy solutions of approximately 1.5 eV (see red arrow). Analyses of scheme XXI show (see Table 6, but not shown in Fig. 3 The most probable mechanism of Eu 3+ and Eu 2+ ion incorporation into NaMgF 3 , charge compensation is illustrated in Fig. 4. Analysing the proposed chemical reactions and calculation of solution energies, we see that when calculations are carried out considering defects and the respective mechanism of charge compensation, as a defect cluster, the solution energy is less than when calculated as isolated defects. The configuration of the local site is modified in terms of distances and distortions. Understanding these changes is of great importance for a better understanding of luminescent properties of optically active ions in the host matrix.  Table 7 shows the interatomic distances (d) from the atomistic simulation after doping Eu 3+ and Eu 2+ ions into NaMgF 3 for the most favourable schemes found in this work. The percentage difference between EuF and NaF (or MgF) interatomic distances is represented by Δ(%). The NaF and MgF distances are taken from the pure NaMgF 3 phase (see Table 3) for comparison. We note that some distances are reduced, while others are increased for both cases (schemes) involving Eu 2+ . For the cluster , the atoms drastically approach Eu 2+ with distances of less than 3 ( • + ′ ) Å. For Eu 3+ , in contrast with Eu 2+ , all distances increase after doping. In this case, Δ(%) is around 10% for all interactions.

Local Structure of the Eu 3+ ion
In order to analyse the local symmetry and charges transferred in Eu−F chemical bonding and to calculate the crystal field parameters and Stark levels from the 7 F 1 multiplet, relaxed positions of Eu 3+ and its NNs are necessary. These positions   69, for comparison. The radial coordinates are given in angstroms, and the angular coordinates are given in degrees. The centroid (F1, F2, F3) coming out of the x'-y' plane is taken as the z'-axis.
We chose the principal axis of symmetry (z'-axis) by diagonalizing the tensor of the quadrupolar field, which is experienced by the optically active ion. In this case, the eigenvector takes the highest eigenvalues. The centroid (coming out the x'-y' plane) between the F1, F2, and F3 atoms is taken as the z'-axis to measure the spherical coordinates. in crystal field calculations by employing the same charge factor to equivalent atoms.
Thus, we have used the charge factor g 1 to yellow atoms and g 2 to orange atoms.
Atomistic simulation was used to better understand the true nature of the defects in NaMgF 3 , giving us information about spatial coordinates of the Eu 3+ ion, which is not easily obtained by X-ray diffraction because of the low concentration of the Eu ion in the host matrix. Notably, a C 3 symmetry operation (Fig. 5) following a σ h operation (reflection plane that contains the x'-y' plane) takes the same structural pattern, approximately. The bond distances illustrated in Fig. 5 can be found in table 8.
A combination of C 3 and σ h operations is termed S 6 symmetry in group theory. 56 In this case, a distorted S 6 point symmetry occurs because all distances are slightly different, and the angles differ from that of ideal S 6 symmetry. Once in S 6 point symmetry, the electric dipole 4f-4f transitions are forbidden, and the distorted S 6 symmetry explains the weak electric dipole 4f-4f transitions of Eu 3+ observed in NaMgF 3 .

Fig. 5
Local symmetry of the optically active ion, and the axis adopted to obtain spherical coordinates. The centroid coming out the x'-y' plane is taken as the z'-axis.
Spectroscopic properties of Eu 3+ in the Na sites must be quite different from Eu 3+ substituting Mg 2+ , due to low symmetry of the Na site. In addition, our simulation shows that there is also distortion when Eu 2+ substitutes Na. This suggests that Eu 2+ must be in a site with very low symmetry, which induces a high intensity 4f-4f transition. In fact, 4f-4f emission from Eu 2+ in NaMgF 3 has intensity comparable with broad 4f 6 5d 1 -4f 7 emission, which is an allowed transition and occurs with a high transition probability. On the other hand, experimental results show that Eu 3+ in low symmetry sites are less unlikely, and this has also been predicted in our simulations, showing that Eu 3+ in a Na site is less probable. Table 9 shows charge factors and the set of crystal field parameters, , for the distorted S 6 site. The were calculated using spherical coordinates of Eu 3+ ion incorporation into the Mn site of NaMgF 3 (Table 8), a set of charge factors (g 1 and g 2 ) that describes the interaction Eu−F in this dielectric medium, and the maximum overlap, ρ 0 , between 4f wavefunctions with ligand orbitals. In this case, we used the value (ρ 0 = 0.05) obtained by Axe and Burns. 55 Notably, all are nonzero, as expected, because the local structure of the optically active ion is distorted. The also allow for identification of Eu 3+ ion symmetry, as well as predicting the 7 F 1 state energy sublevels.

Crystal Field Parameters
In ideal S 6 symmetry, 56  and . We observe that the contribution of values that represent S 6 symmetry are 6 6 much higher than the others. and have approximately a 10% contribution in  . Table 9 Crystal field parameters ( in cm -1 ) and charge factors † using β − and β + . 0.034 0.031 † β − and β + define the charge factor position around the middle distance of Eu−F. The minus signal means that g is closer to Eu 3+ , and the plus sign indicates that g is closer to the ligands. A rotation (30.5°) about the principal axis was carried out to eliminate the imaginary part of . 2 2 This leads us to conclude that Eu 3+ occupies is a distorted S 6 point symmetry.
Furthermore, we have calculated using β − and β + , which define the charge factor positions around the middle distance of EuF. 42 The minus signal means that g is closer to the Eu 3+ ion, and the plus signal means that g is closer to the ligands. This parameter is a way (according to the SOM) to include covalence effects on the chemical bond because the charge is localized in a middle distance (R/2β) instead of being located at the position of the ligand, as proposed by the PCEM. In this case, the use of β + leads to a lower contribution from that does not belong to ideal S 6 symmetry. In addition, the phenomenological charge factors, adjusted to reproduce the 7 F 1 state energy sublevels, are higher.
We also use the model proposed by Lima et al. 70 to calculate charge transferred to the Eu−F chemical bond. This model is valid for high symmetry systems, in which only one charge factor is needed to describe the system. With ideal S 6 point symmetry, the model would be well applied, but for the sake of comparison, we have calculated one of the charges through this model using the following expression: Thus, we obtain using . This value is closer to g 1 adjusted with = 0.594 ∆ ( ) = 2.8 β + (see Table 9).
The sign defines the position of the 7 F 1 state ground sublevel from the 2 0 barycentre. We see in Table 8 that it is correctly predicted using β − and β + because 2 0 is negative, and the 7 F 1 state ground sublevel is non-degenerate. We will discuss this point in more detail in the next section. level. We use a set of phenomenological charge factors in the calculations of to reproduce the energy sublevels and, consequently, the splitting. Our predictions were carried out using β − and β + for comparison. corresponding to the 5 D 0 -7 F 0 transition, two peaks from 5 D 0 -7 F 1 , two peaks from 5 D 0 -7 F 2 , and four peaks from 5 D 0 -7 F 4 . 5 D 0 -7 F 1 is a magnetic dipole transition, which is not influenced by the crystalline environment. The number of lines and intensities in relation to the 5 D 0 -7 F 2 transition indicates if the system is lower or higher in symmetry.

7 F 1 state energy sublevels of the Eu 3+ ion
The other transitions are electric dipole moment transitions which are strongly influenced by the crystalline environment.
The second peak of the 5 D 0 -7 F 1 transition is doubly degenerate, and the 7 F 1 splitting is less than 100 cm −1 . The emission spectrum reported by Gaedtke and William 22 shows that the 5 D 0 -7 F 1 transition is approximately 50% more intense than the 5 D 0 -7 F 2 transition. This suggests that the Eu 3+ ion occupies point symmetry with a distorted inversion centre, although the emission spectrum shows peaks corresponding to the 5 D 0 -7 F 0 and 5 D 0 -7 F 2 transitions.
Schuyt and William, 24 based on the Tanner diagram, 72 suggested that the Eu 3+ occupies sites with C s , C nv or C n symmetry because the 5 D 0 -7 F 0 transition is presented in the emission spectrum. C s is part of low symmetry groups, which is not the case here because the 7 F 1 splitting is less than 350 cm -1 (Ref. 73). Analysing the number of lines for each transition in the emission spectrum and comparing it with the Tanner diagram 72 indicates C 3v or C 4v symmetry. Previous work carried out with Eu 3+ -doped KMgF 3 suggested the same symmetry. [28][29][30] However, C 3v , C 4v , and C n are symmetry groups without inversion centres. The crystal field parameters related to the odd part of the crystal field potential is different from zero for this symmetry set (C 3v , C 4v , and C n ). In this case, the 5 D 0 -7 F 2 transition, allowed by electric dipole and strongly influenced by the environment, would be more intense than the transition 5 D 0 -7 F 1 . This is not observed in the NaMgF 3

Photoionization cross-section and OSL decay pattern of NaMgF 3 :Eu 2+
Polycrystalline NaMgF 3 :Eu 2+ has been shown to be a suitable material for application in personal dosimetry. The material has high sensitivity and is able to monitor small doses, having a linear dose-response behaviour between μGy dose levels up to approximately 100 Gy. 18 However, this behaviour and the mechanism of electron de-trapping are not completely explained in the literature.
In this section, we discuss this point based on the photoionization cross-section Using the value of calculated here, we estimate the OSL decay pattern of NaMgF 3 :Eu 3+ based on the first-order kinetic approximation (no re-trapping), which assumes the OSL signal decay with stimulation time is due to de-trapping of captured electrons and subsequent radiative recombination. Fig. 6 (inset) shows the experimental and theoretical OSL decay patterns. The experimental OSL decay curve was obtained after irradiation with an X-ray dose of 219 mGy. 77 The decay time is slower than that exhibited in the commercial material, Al 2 O 3 :C. 58 We note that the theoretical curve deviates slightly from the experimental curve because the model used here is the first-order kinetic model.
The rate at which electrons captured in the trap are optically excited to the conduction band is proportional to σ, and the OSL decay pattern is governed by σ. Our predictions show that σ of NaMgF 3 is on the same order of magnitude (10 −20 m 2 ) as the calculated value for Al 2 O 3 :C. 58 This explains the high sensibility when stimulated with blue light.

Conclusion
In summary, we combined classical atomistic simulation and crystal field models to describe the origin of defects and their influence on luminescent properties of Eu-doped NaMgF 3 in the orthorhombic phase. We proposed a new set of interatomic potentials that reproduce the main properties of the orthorhombic phase.
Defect calculations based on these interatomic potentials provide information regarding the energetic balance of dopant incorporation in this fluoroperovskite compound. In addition, using crystal field calculations, we explored, in detail, the type of defect and spectroscopic properties of the optically active ion. The main findings of this work are summarized below.
-The new set of interatomic potentials reproduced structural and elastic properties in the orthorhombic phase and precursor fluorides. In addition, the interatomic potential is transferable to the cubic phase, consistent with the literature.
-Defect calculations show that incorporation of Eu 3+ ions into the Mg site, compensated by the Na vacancy, is the most energetically favourable. Further, the Eu 2+ ion prefers to incorporate into the Na site, compensated by a Na vacancy or anti-site, in the host matrix. In addition, the solution energy with Eu 2+ is lower than with Eu 3+ .
-We predict the local symmetry and 7 F 1 energy sub-levels of the Eu 3+ ion by using the simple overlap model and the local geometry obtained in defect calculations.
-The weak intensity of the 5 D 0 -7 F 1 transition, as well as the small splitting of the second peak of the 5 D 0 -7 F 1 transition (observed in emission spectrum as doubly degenerate), occurs due to the distortion in S 6 local symmetry occupied by Eu 3+ ions.
-Our predictions of the photoionization cross-section and OSL decay pattern show that NaMgF 3 :Eu 2+ presents a high sensibility for stimulus over a large range of wavelengths.
The new insights presented in this work show the importance of defect calculations, combined with crystal field and photoionization cross-section models, to successfully describe the luminescent properties of lanthanide-doped compounds.

Conflicts of interest
There are no conflicts to declare.