Abstract

The modification of chemical composition to improve desired material parameters is an effective method in materials science and engineering. In this work, Ca1-xSrxF2 solid solution is chosen as the subject. Nd3+ and Y3+ ions are used as dopants. We have found that spectral properties of Nd3+:Ca1-xSrxF2 and Nd3+,Y3+:Ca1-xSrxF2 crystals vary nonlinearly with the ‘x’. The X-ray diffraction (XRD) patterns and the density functional theory (DFT) calculations on Ca1-xSrxF2 solid solutions have ruled out the influence of matrix crystals on spectral properties. The rare-earth monomer centers of C4v or C3v symmetry, and the high order clusters are modeled. The calculated results show, that thermodynamic stabilities of the centers vary nonlinearly. Temperature-dependent dielectric losses and the results of projected density of states (pDOS) calculations also show nonlinear dependency. The nonlinearly evolved local structures from cubic to square antiprism sublattice cause the nonlinear variation of spectral properties. The methodology of rare-earth induced nonlinear structural evolutions is then proposed, which is useful for exploring new materials.

© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Tuning of composition or modification of atomic structure in order to obtain properties of interest is widely used in material science and engineering. For example, solid solutions with alloying elements have been used to improve mechanical properties in alloy fields [1,2]. Atomic sites or interstitials would be partially occupied with the second phase atoms and the inner strains are generated to prevent dislocation movement. Interestingly, many properties vary nonlinearly rather than linearly in the tuning range. Schoen and Mokkath et al. have reported that the magnetic damping and magnetic moments vary sharply in metallic alloys as a consequence of phase transition or magnetic phase transition [3,4]. Even with no phase transition, the electric resistivity varies nonlinearly in Si1-xGex miscible alloys [5]. Besides the alloys, the band structure of solid solutions BiOBr1-xIx and NaLa1-xBixS2 is also tuned nonlinearly. The band edges vary significantly at the point with 20% BiOI or NaBiS2 [6,7]. A “magic” composition in solid solution (ZnSnN2)1-x(ZnO)x is found and a short-range ordered system with line-compound like properties is discovered [8].

Calcium and strontium fluorides exhibit continuous solubility. The crystal structure does not change regardless of Ca:Sr ratios. The unit cell parameters of Ca1-xSrxF2 solution vary linearly with the ‘x’. Other physical parameters like lattice vibrations, thermal conductivity, dielectric constant and microhardness change gradually in the parabolic-like dependency [913]. In systems where both components share the same crystal structure (like CaF2-SrF2 solution) the atomic structures rarely vary nonlinearly. In order to induce nonlinear atomic structure change we include rare-earth ions into the CaF2-SrF2 solution. It is found that spectroscopic properties of Ca1-xSrxF2 solid solution change nonlinearly with the ‘x’. The first principles calculation and dielectric property measurements have revealed, that local structures of rare earth ions evolve nonlinearly. Nonlinear evolution in local structures of rare-earth ions contributes to the nonlinear variation of spectroscopic properties.

2. Experimental

Two series of crystals 0.5 at.% Nd3+:Ca1-xSrxF2 and 0.5 at.% Nd3+,5 at.% Y3+:Ca1-xSrxF2 (x = 0, 0.01, 0.05, 0.1, 0.3, 0.5 0.7, 1.0) were grown by the temperature gradient technique method [14]. High purity raw materials (> 99.995%) including NdF3, YF3, CaF2 and SrF2 were mixed stoichiometrically and 1 wt.% PbF2 was added as an oxygen scavenger. The mixtures were loaded to a multi-compartment graphite crucible and then was mounted in the furnace. The pressure in the furnace was kept to be 10−3 Pa. The temperature was increased to 1400 °C and was kept for 10 h in order to completely melt the loads. In growth process the temperature gradient was set to 1.5 °C/h.

The grown crystals were cut and polished for spectral measurements. To ensure uniformity of the results, samples were cut from the same parts of crystals. Room temperature absorption spectra were measured with a Jasco V-750 UV/VIS/NIR spectrometer. Photoluminescence properties were measured with a FLS980 time-resolved spectrofluorometer equipped with a 450 W xenon lamp and thermoelectrically cooled InGaAs detector. XRD patterns were collected using Rigaku Ultima-IV diffractometer (Japan) equipped with Cu x-ray lamp. The scans were performed in 20–70° (2θ) with 0.02° per step. For dielectric measurement samples were coated with silver electrodes, and temperature-dependent dielectric losses were measured by Novocontrol Broadband Dielectric Spectrometer (Germany) at frequency of 100 Hz at temperatures from 135 to 330 K.

Calculations were conducted by the plane-wave basis set method in the framework of DFT, as implemented in the VASP code [15,16]. The projector augmented-wave pseudopotential with exchange correlation function in the form of Perdew-Burke-Ernzerhof (PBE) was used to describe the mutual interactions [17,18]. The 3 × 3 × 3 or 2 × 2 × 2 supercells were selectively applied and a 1 × 1 × 1 Gamma k-grid was used to ensure that forces on individual atoms reached 0.01 eV·Å−1. The cut-off energy was set to 550 eV with electronic accuracy of 10−5 eV. The spin polarization was included in all calculations. The formation energy of a given compound was calculated by Eq. (1) [19]:

$$\Delta E = {E_{C{a_{1 - x}}S{r_x}{F_2}}} - (1 - x) \cdot {E_{C\textrm{a}{F_2}}} - x \cdot {E_{S\textrm{r}{F_2}}}$$
where ${E_{C{a_{1 - x}}S{r_x}{F_2}}}$, ${E_{Ca{F_2}}}$ and ${E_{Sr{F_2}}}$ denote the relaxation energy of Ca1-xSrxF2, CaF2 and SrF2, respectively. Formation energy of the clusters was given by Eq. (2):
$$\Delta E = ({E_{tot}} + {E_0}) - m \cdot {E_1} - n \cdot {E_2} - [m + n - {(m - n)^2}] \cdot {E_{corr}}$$
where Etot and E0 are the relaxed energy of Ca1-xSrxF2 with and without rare-earth ions, respectively; m and n denote the number of trivalent substitutional impurity atoms and interstitial fluorine ions within a cluster; E1 and E2 are the relaxed energy of Ca1-xSrxF2 containing [1RE3+−0Fi-] and [0RE3+−1Fi-] (RE = Nd, Y); Ecorr is the potential alignment and image charge corrections calculated by Eq. (3) [2022]:
$${E_{corr}} = (1 + g) \cdot \frac{{{q^2}\alpha }}{{2\varepsilon L}}$$
where g is scaling factor (for face-centered cubic structure the value of −0.34 was adopted [22]), q is the net charge, α the Madelung constant of 5.038 [23], ɛ and L are the static dielectric constant and supercell dimensions of Ca1-xSrxF2 crystal respectively. For pure CaF2 and SrF2, ɛ equals to 6.812 and 6.476 at 300 K [24], L equals to 10.9 Å and 11.6 Å respectively. Ecorr was approximately the same for both CaF2 and SrF2 (0.323 eV and 0.319 eV respectively). The calculation results show gradual change in the parameters with varied ratios of CaF2:SrF2. This agrees well with the experimental results [9,10]. The values of Ecorr of Ca1-xSrxF2 were calculated based on the strontium content x linearly. The projected density of states calculations were performed on basis of optimized structure with a 4 × 4 × 4 Gamma k-grid. The Coulomb potential with U = 6 and 1 for neodymium and yttrium, respectively, were considered in the Dudarev’s LSDA + U method [25].

3. Results and discussion

Figure 1(a-b) presents absorption spectra of 0.5% Nd3+:Ca1-xSrxF2 and 0.5% Nd3+,5% Y3+:Ca1-xSrxF2 crystals. Nd3+-doped alkaline earth fluorides have demonstrated excellent femtosecond laser performances, which is considered as a promising candidate for generation of high repetition rate ultrafast lasers [26,27]. There are two main absorption peaks corresponding to 4I9/24F5/2 + 2H9/2 transitions of Nd3+ ions. These two peaks at 791 and 797 nm have been proved belonging to cubic sublattice and square antiprism structure clusters, respectively, which are denoted as N1 and N2 in the work [28,29]. The absorption intensity of N1 decreases while that of N2 rises with increasing concentration of Sr2+. It is found that absorption intensity of N1 decreases sharply with addition of Sr2+ from 0 to 30 at.%, at the same time absorption intensity of N2 increases greatly. When the concentration of Sr2+ is higher than 30 at.%, the N1:N2 absorption intensity ratio varies insignificantly. As a comparison, absorption spectra of Nd3+,Y3+:Ca1-xSrxF2 samples are shown in Fig. 1(b-c). With addition of Sr2+, absorption of N1 decreases and that of N2 rises. It is similar with that of Nd3+:Ca1-xSrxF2 but varied in a slightly sharper style. The photoluminescence of Nd3+,Y3+:Ca1-xSrxF2 under different excitation wavelengths also vary nonlinearly. Figure 1(d) shows emission spectra of samples recorded under 791 or 797 nm excitation. The spectral bandwidth of emission band decreases when Sr2+ content increases. Significant change in spectral bandwidth is observed with Sr2+ concentration 0–30 at.%, while for 30–100 at.%, the change is small.

 figure: Fig. 1.

Fig. 1. Area normalized absorption spectra of (a) Nd3+:Ca1-xSrxF2 and (b) Nd3+,Y3+:Ca1-xSrxF2 solid solution crystals. (c) Sr2+ concentrations dependent normalized absorption intensity at 791 and 797 nm. (d) Photoluminescence spectra of Nd3+,Y3+:Ca1-xSrxF2 excited at 791 and 797 nm.

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XRD patterns of investigated samples are shown in Fig. 2. All diffraction peaks for Nd3+:Ca1-xSrxF2 and Nd3+,Y3+:Ca1-xSrxF2 crystals agree well with that of pure CaF2 or SrF2. It can be seen that the diffraction positions for mixed crystals gradually shift from CaF2 to SrF2. As shown in Fig. 2(c), the lattice parameters shift linearly with increasing concentration of Sr2+. It is quite understandable, since the two crystals share the same crystal structure but with different lattice parameters (CaF2: 5.46295 Å, SrF2: 5.86400 Å). The linear lattice parameter is consistent with Vegard’s relationship, suggesting that complete solid solution is formed. In order to verify the point and then to rule out influence of matrix crystals on nonlinear spectral properties, simulations on Ca1-xSrxF2 are performed. As shown in Fig. 3, total relaxed energy differences of the supercells are less than 0.01 eV with the varied bond distances and angles among strontium ions. Besides, formation energies of Ca1-xSrxF2 vary in a parabolic like behavior when the ‘x’ changes from 0 to 1. When ‘x’ equals to 0.5, the highest value is obtained in the parabola. The symmetric parabolic character of formation energy with the highest point at x = 0.5 means that CaF2 and SrF2 are miscible in any ratio without phase separation and structure variation. It implies that Ca1-xSrxF2 crystals are complete solid solutions, which is consistent with the XRD patterns and reported results [9].

 figure: Fig. 2.

Fig. 2. Powder XRD patterns of (a) Nd3+:Ca1-xSrxF2 and (b) Nd3+,Y3+:Ca1-xSrxF2 crystals. (c) Strontium concentrations dependent lattice parameter of Nd3+:Ca1-xSrxF2 crystals.

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 figure: Fig. 3.

Fig. 3. (a) Bond distances and (b) angles dependent relaxed total energy of Ca1-xSrxF2. (c) The nominal strontium concentrations dependent formation energy of Ca1-xSrxF2 crystal.

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The linear unit cell expansion cannot explain the nonlinear variation of spectral properties however. In fact, attention needs to be focused on trivalent lanthanides clusters formed in the fluorite crystals due to charge compensation effects [3034].

In this section, the rare-earth clusters containing Nd3+ or Y3+ are modeled and relaxed. Since Ca1-xSrxF2 crystals form complete solid solutions and the first coordination sphere of anions and cations influence the local structures of rare-earth ions greatly [35], concentrations of Sr2+ in the first cationic coordination shell of rare-earth are therefore considered rather than that of ‘x’ in Ca1-xSrxF2 solid solutions. Besides, the Ca0.5Sr0.5F2 supercells with fixed strontium concentrations are chosen to study influence of the first cationic coordination sphere on the evolution of rare-earth ions structures. We firstly calculate the monomers of C4v and C3v with interstitials Fi- at the nearest and next nearest site, respectively, because the relative stabilities of C4v and C3v determine the rare-earth clustering characteristics [35]. Lattice mismatch occurs in the plane connected two cubes, as shown in Fig. 4(d). Lattice mismatch will compete with the electrostatic interactions of RE3+ and Fi-. If the electrostatic interactions are stronger, interstitial Fi- will locate at the nearest site of the rare-earth creating C4v center. Otherwise, in order to reduce the lattice mismatch, it will locate at the next nearest site creating C3v. As shown in Fig. 4(a-b), the slight variation of formation energies of C3v centers in Nd3+ and Y3+ suggests that the lattice mismatch in C3v centers is almost independent on Sr2+ concentrations. However, for the C4v, lattice mismatch varies significantly with Sr2+ concentrations. The bond length of anions surrounding interstitial Fi- and RE3+ in C4v center is denoted as R(F1-F1) and R(F2-F2) in Fig. 4(d). As presented in Fig. 4(c), R(F1-F1) has a sharp increase when Sr2+ content change from 0.333 to 0.667, while R(F2-F2) changes smoothly. The lattice mismatch changes non-linearly instead of linearly, which contributes to the nonlinearly varied stabilities of C4v centers.

 figure: Fig. 4.

Fig. 4. Formation energy of C4v and C3v center in the (a) Nd3+ and (b) Y3+. (c) Concentrations dependent bond lengths in C4v center of the Nd3+ or Y3+ doped Ca1-xSrxF2. (d) Structure of C3v center with interstitial Fi- at the next nearest site and C4v center with interstitial Fi- at the nearest site. F1- and F2- are the normal fluorine and Fi- the interstitial fluorine. The R(F1-F1) and R(F2-F2) represent the corresponding bond length. Grey balls are F- anions and orange balls the RE3+ ions.

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The RE3+-Fi- pairs could be treated as an electric dipoles in C4v center. Dielectric spectra were measured to study the relationship between dipole’s resonant signals and contents of Sr2+. 0.5% Nd3+:Ca1-xSrxF2 samples were chosen and the temperature-dependent dielectric losses were measured. As presented in Fig. 5, there exists one resonant signal and it is ascribed to C4v center [36]. It is noted that other signals are also observed, but difficult to be distinguished. Stability of C4v centers is very important, so only C4v centers are discussed here. It can be seen that the peak position is at about 210 K when the ‘x’ equals to 0 and 0.1. Then, the position jumps to be at about 240 K when the ‘x’ equals to 0.3. The sharp increase from 0.1 to 0.3 indicates that activation energy of C4v vary dramatically with increasing concentration of Sr2+. Based on the Arrhenius equation, it is clear that the higher temperature, the larger activation energy. The trend of resonant signals is nearly the same with that of absorption and emission spectra. It is also very close to the varied formation energies of Nd3+ C4v centers, except the turning points. The turning points of dielectric and absorption spectra are at about x = 0.3. It is a little bit different with the calculated results that the points locate in the area of 0.3 ∼ 0.6. It is because the Sr2+ content used in calculations are different with the experimental ones. In order to reduce simulation costs on Ca1-xSrxF2 solid solutions, concentration of Sr2+ in the first cationic shell of rare-earth ions rather than the ‘x’ in Ca1-xSrxF2 is adopted in calculations. It should be noted here that bandwidths of the resonant signals are much broader in solid solution crystals. The mixing of Ca2+ and Sr2+ probably contributes to the broad signals. However, contributions from the new emerged centers could not be absolutely ruled out. The varied intensities of signals are the clues that support such statements. The number of C4v centers correlating with resonant intensities are different in the crystals. For solid solutions the resonant intensities are relatively low which suggests that quantities of C4v centers are small. The reduced portion of C4v centers could be transformed into other kinds of clusters. The position of resonant signals of dimer centers is reported to be at shoulders of C4v signals [36], which may contribute to the broad band.

 figure: Fig. 5.

Fig. 5. Temperature dependent dielectric losses of Nd3+:Ca1-xSrxF2 crystals at the frequency of 100 Hz.

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The pDOS of C4v center in Nd3+ is also investigated. Two crystals with Sr2+ concentrations in the first cationic shells of 0.333 and 0.667 are selected and calculated in Fig. 6. These two concentrations are representative. We also calculated the pDOS of samples with Sr2+ concentration of x = 0 and 1. The results are very close to that of x = 0.333 and 0.667 respectively. For the samples with Sr2+ concentration of 0.333, 2p states of Fi- energy levels are at −0.287 eV, −0.151 eV and −0.0156 eV, while for the 0.667, they shift to be at −0.231 eV, −0.0858 eV and −0.0130 eV, respectively. Besides, the intensity of lower energy levels at −0.287 eV and −0.151 eV decreases and that of the highest level at −0.0156 eV increases as the concentrations vary from 0.333 to 0.667. The result of Y3+ center in Fig. 7 is similar to that of Nd3+. The 2p states of Fi- energy levels are at −0.312 eV, −0.146 eV and −0.0138 eV, and they shift to be at −0.215 eV, −0.0495 eV and −0.0165 eV, respectively. The bonding characters indicate that stability of C4v centers is obviously weakened with rising concentration of Sr2+.

 figure: Fig. 6.

Fig. 6. pDOS of Nd3+ and interstitial Fi- in C4v center. Concentrations of Sr2+ in the first cationic coordination shell of Nd3+ are 0.333 and 0.667 in (a) and (b), respectively. (c) and (d) are the corresponding enlarged images.

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 figure: Fig. 7.

Fig. 7. pDOS of Y3+ and interstitial Fi- in C4v center. Concentrations of Sr2+ in the first cationic coordination shell of Y3+ are 0.333 and 0.667 in (a) and (b), respectively. (c) and (d) are the corresponding enlarged images.

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Based on the aforementioned discussions, it is known that relative stabilities of C4v and C3v are influenced by the Sr2+ content, as well as that of high order clusters. The more stable C4v center, the more stable cubic sublattice clusters; the more stable C3v center, the more stable square antiprism structure clusters [28]. With this in mind, high order clusters of Nd3+ and Y3+ are modelled and simulated. Formation energy of cubic sublattice and square antiprism structure clusters are presented in Fig. 8(a-b), respectively. As can be seen, when Sr2+ content in the first cationic coordination shell of rare-earth increases from 0 to 0.4, formation energy varies slightly, and follows a sharp increase in going from 0.4 to 0.6. Then it gradually approaches to that in pure SrF2. Compared with cubic sublattice clusters, formation energy of square antiprism structure centers firstly decreases and then increases, which means that the rising rate in the range from 0.4 to 0.6 is larger in square antiprism clusters. The square antiprism sublattice clusters are influenced more seriously than the cubic sublattice centers by Sr2+ content. Besides, as shown in Fig. 8(a-b), the cubic sublattice centers of Nd3+ have lower energy and are more stable than the corresponding Y3+, while the square antiprism sublattice clusters of Y3+ have lower energy and are more stable than that of Nd3+, which agrees well with the clustering characters of Nd3+ and Y3+ doped CaF2 and SrF2 crystals [28,35]. From Ref. [28], the strong repulsion of Fi--Flattice- around Y3+ transforms the cubic sublattice to square antiprism clusters easily. While for Nd3+, the repulsion of Fi--Flattice- is weaker, it is benefit for the stability of cubic sublattice centers. The research indicates that in CaF2, Nd3+ ions tend to form cubic lattice centers and the Y3+ ions tend to form square antiprism sublattice centers in SrF2. From Nd3+ to Y3+ and with the matrix from CaF2 to SrF2, stability of cubic sublattice clusters is reduced and that of square antiprism clusters enhanced. It is consistent with the results that absorption of N2 is more favored in Nd3+,Y3+:Ca1-xSrxF2 than that in Nd3+:Ca1-xSrxF2. The nonlinearly evolved local structures of rare-earth ions agrees well with the spectral properties.

 figure: Fig. 8.

Fig. 8. Formation energy of Nd3+ or Y3+ clusters versus concentration of Sr2+ in the first cationic shell of RE3+ ions. (a) and (b) represent the cubic sublattice and square antiprism structure clusters, respectively.

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4. Conclusion

In summary, spectral properties of Nd3+:Ca1-xSrxF2 and Nd3+,Y3+:Ca1-xSrxF2 crystals are observed to be varied nonlinearly. XRD patterns and the first principles calculations on Ca1-xSrxF2 have confirmed that the crystals are complete solid solutions. Influence of matrix crystals on the spectral properties is then ruled out. Calculations on monomer centers of C4v and C3v, as well as high order clusters are performed and the results show that thermodynamic stabilities of the centers vary nonlinearly with Sr2+ concentrations. Temperature-dependent dielectric losses and the projected density of state calculations confirm that local structures of Nd3+ evolve nonlinearly. The nonlinear spectral properties are therefore obtained.

Funding

National Natural Science Foundation of China (61905289, 61925508); Science and Technology Commission of Shanghai Municipality (20511107400, 20520750200); CAS Interdisciplinary Innovation Team (JCTD-2019-12); Instrument Developing Project of CAS (ZDKYYQ20210002).

Disclosures

The authors declare no conflicts of interests.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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30. J. Corish, C. R. A. Catlow, P. W. M. Jacobs, and S. H. Ong, “Defect aggregation in anion-excess fluorites. Dopant monomers and dimers,” Phys. Rev. B 25(10), 6425–6438 (1982). [CrossRef]  

31. P. J. Bendall, C. R. A. Catlow, J. Corish, and P. W. M. Jacobs, “Defect aggregation in anion-excess fluorites II. Clusters containing more than two impurity atoms,” J. Solid State Chem. 51(2), 159–169 (1984). [CrossRef]  

32. Y. K. Voronko, A. A. Kaminskii, and V. V. Osiko, “Analysis of the optical spectra of CaF2:Nd3+ (type 1) crystals,” Sov. Phys. JETP 22(2), 295–300 (1966).

33. Y. K. Voronko, V. V. Osiko, and I. A. Shcherbakov, “Investigation of the interaction of Nd3+ ions in CaF2, SrF2 and BaF2 crystals (type 1),” Sov. Phys. JETP 28(5), 838–844 (1969).

34. D. R. Tallant and J. C. Wright, “Selective laser excitation of charge compensated sites in CaF2:Er3+,” J. Chem. Phys. 63(5), 2074–2085 (1975).

35. F. K. Ma, F. Su, R. F. Zhou, Y. Y. Ou, L. J. Xie, C. M. Liu, D. P. Jiang, Z. Zhang, Q. H. Wu, L. B. Su, and H. B. Liang, “The defect aggregation of RE3+ (RE = Y, La∼Lu) in MF2 (M = Ca, Sr, Ba) fluorites,” Mater. Res. Bull. 125, 110788 (2020). [CrossRef]  

36. C. G. Andeen, J. J. Fontanella, M. C. Wintersgill, P. J. Welcher, R. J. Kimble, and G. E. Matthews, “Clustering in rare-earth-doped alkaline-earth fluorides,” J. Phys. C: Solid State Phys. 14(24), 3557–3574 (1981). [CrossRef]  

References

  • View by:

  1. M. Suzuki, T. Kimura, J. Koike, and K. Maruyama, “Strengthening effect of Zn in heat resistant Mg-Y-Zn solid solution alloys,” Scr. Mater. 48(8), 997–1002 (2003).
    [Crossref]
  2. M. P. Agustianingrum, S. Yoshida, N. Tsuji, and N. Park, “Effect of aluminum addition on solid solution strengthening in CoCrNi medium-entropy alloy,” J. Alloys Compd. 781, 866–872 (2019).
    [Crossref]
  3. M. A. W. Schoen, D. Thonig, M. L. Schneider, T. J. Silva, H. T. Nembach, O. Eriksson, O. Karis, and J. M. Shaw, “Ultra-low magnetic damping of a metallic ferromagnet,” Nat. Phys. 12(9), 839–842 (2016).
    [Crossref]
  4. J. H. Mokkath and U. Schwingenschlögl, “Magnetic phase transition in 2 nm NixCu1−x (0 ≤ x ≤ 1) clusters,” J. Phys. Chem. C 118(15), 8169–8173 (2014).
    [Crossref]
  5. P. R. Abel, A. M. Chockla, Y. M. Lin, V. C. Holmberg, J. T. Harris, B. A. Korgel, A. Heller, and C. B. Mullins, “Nanostructured Si1-xGex for tunable thin film lithium-ion battery anodes,” ACS Nano 7(3), 2249–2257 (2013).
    [Crossref]
  6. L. Kong, J. Q. Guo, J. W. Makepeace, T. C. Xiao, H. F. Greer, W. Z. Zhou, Z. Jiang, and P. P. Edwards, “Rapid synthesis of BiOBrxI1-x photocatalysts: Insights to the visible-light photocatalytic activity and strong deviation from Vegard’s law,” Catal. Today 335(SI), 477–484 (2019).
    [Crossref]
  7. A. BaQais, N. Tymińska, T. Le Bahers, and K. Takanabe, “Optoelectronic structure and photocatalytic applications of Na(Bi,La)S2 solid solutions with tunable band gaps,” Chem. Mater. 31(9), 3211–3220 (2019).
    [Crossref]
  8. J. Pan, J. J. Cordell, G. J. Tucker, A. Zakutayev, A. C. Tamboli, and S. Lany, “Perfect short-range ordered alloy with line-compound-like properties in the ZnSnN2:ZnO system,” npj Comput. Mater. 6(1), 63 (2020).
    [Crossref]
  9. R. E. Youngman and C. M. Smith, “Multinuclear NMR studies of mixed Ca1−xSrxF2 crystals,” Phys. Rev. B 78(1), 014112 (2008).
    [Crossref]
  10. R. K. Chang, B. Lacina, and P. S. Pershan, “Raman scattering from mixed crystals (CaxSr1−x)F2 and (SrxBa1-x)F2,” Phys. Rev. Lett. 17(14), 755–758 (1966).
    [Crossref]
  11. P. A. Popov, N. V. Moiseev, D. N. Karimov, N. I. Sorokin, E. A. Sulyanova, B. P. Sobolev, V. A. Konyushkin, and P. P. Fedorov, “Thermophysical characteristics of Ca1−xSrxF2 solid-solution crystals (0 ≤ x ≤ 1),” Crystallogr. Rep. 60(1), 116–122 (2015).
    [Crossref]
  12. M. V. Subrahmanya Sarma and S. V. Suryanarayana, “Dielectric studies of CaxSr1−xF2 mixed crystals,” J. Mater. Sci.: Mater. Electron. 1(4), 182–184 (1990).
    [Crossref]
  13. M. V. Subrahmanya Sarma and S. V. Suryanarayana, “Study of microhardness on CaxSr1-xF2 mixed crystals,” J. Mater. Sci. Lett. 5(12), 1277–1278 (1986).
    [Crossref]
  14. Y. Z. Zhou, “Growth of high quality large Nd:YAG crystals by temperature gradient technique (TGT),” J. Cryst. Growth 78(1), 31–35 (1986).
    [Crossref]
  15. G. Kresse and J. Hafner, “Ab initio molecular-dynamics for liquid-metals,” Phys. Rev. B 47(1), 558–561 (1993).
    [Crossref]
  16. G. Kresse and J. Furthmuller, “Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set,” Comput. Mater. Sci. 6(1), 15–50 (1996).
    [Crossref]
  17. P. E. Blöchl, “Projector augmented-wave method,” Phys. Rev. B 50(24), 17953–17979 (1994).
    [Crossref]
  18. J. P. Perdew, K. Burke, and M. Ernzerhof, “Generalized gradient approximation made simple,” Phys. Rev. Lett. 77(18), 3865–3868 (1996).
    [Crossref]
  19. S. Benny, R. Grau-Crespo, and N. H. de Leeuw, “A theoretical investigation of α-Fe2O3-Cr2O3 solid solutions,” Phys. Chem. Chem. Phys. 11(5), 808–815 (2009).
    [Crossref]
  20. C. Persson, Y. J. Zhao, S. Lany, and A. Zunger, “N-type doping of CuInSe2 and CuGaSe2,” Phys. Rev. B 72(3), 035211 (2005).
    [Crossref]
  21. G. Makov and M. C. Payne, “Periodic boundary-conditions in ab-initio calculations,” Phys. Rev. B 51(7), 4014–4022 (1995).
    [Crossref]
  22. S. Lany and A. Zunger, “Assessment of correction methods for the band-gap problem and for finite-size effects in supercell defect calculations: Case studies for ZnO and GaAs,” Phys. Rev. B 78(23), 235104 (2008).
    [Crossref]
  23. A. Jockisch, U. Schröder, F. W. de Wette, and W. Kress, “Relaxation and dynamics of the (111) surfaces of the fluorides CaF2 and SrF2,” J. Phys.: Condens. Matter 5(31), 5401–5410 (1993).
    [Crossref]
  24. C. Andeen, J. Fontanella, and D. Schuele, “Pressure and temperature derivatives of the low-frequency dielectric constants of the alkaline-earth fluorides,” Phys. Rev. B 6(2), 591–595 (1972).
    [Crossref]
  25. S. L. Dudarev, G. A. Botton, S. Y. Savrasov, C. J. Humphreys, and A. P. Sutton, “Electron-energy-loss spectra and the structural stability of nickel oxide: An LSDA + U study,” Phys. Rev. B 57(3), 1505–1509 (1998).
    [Crossref]
  26. Z. P. Qin, G. Q. Xie, J. Ma, W. Y. Ge, P. Yuan, L. J. Qian, L. B. Su, D. P. Jiang, F. K. Ma, Q. Zhang, Y. X. Cao, and J. Xu, “Generation of 103 fs mode-locked pulses by a gain linewidth-variable Nd,Y:CaF2 disordered crystal,” Opt. Lett. 39(7), 1737–1739 (2014).
    [Crossref]
  27. J. F. Zhu, L. Wei, W. L. Tian, J. X. Liu, Z. H. Wang, L. B. Su, J. Xu, and Z. Y. Wei, “Generation of sub-100 fs pulses from mode-locked Nd,Y:SrF2 laser with enhancing SPM,” Laser Phys. Lett. 13(5), 055804 (2016).
    [Crossref]
  28. F. K. Ma, D. P. Jiang, Z. Zheng, X. Q. Tian, Q. H. Wu, J. Y. Wang, X. B. Qian, Y. Liu, and L. B. Su, “Tailoring the local lattice distortion of Nd3+ by codoping of Y3+ through first principles calculation for tuning the spectroscopic properties,” Opt. Mater. Express 9(11), 4256–4272 (2019).
    [Crossref]
  29. F. K. Ma, P. X. Zhang, L. B. Su, H. Yin, Z. Li, Q. T. Lv, and Z. Q. Chen, “The host driven local structures modulation towards broadband photoluminescence in neodymium-doped fluorite crystal,” Opt. Mater. 119, 111322 (2021).
    [Crossref]
  30. J. Corish, C. R. A. Catlow, P. W. M. Jacobs, and S. H. Ong, “Defect aggregation in anion-excess fluorites. Dopant monomers and dimers,” Phys. Rev. B 25(10), 6425–6438 (1982).
    [Crossref]
  31. P. J. Bendall, C. R. A. Catlow, J. Corish, and P. W. M. Jacobs, “Defect aggregation in anion-excess fluorites II. Clusters containing more than two impurity atoms,” J. Solid State Chem. 51(2), 159–169 (1984).
    [Crossref]
  32. Y. K. Voronko, A. A. Kaminskii, and V. V. Osiko, “Analysis of the optical spectra of CaF2:Nd3+ (type 1) crystals,” Sov. Phys. JETP 22(2), 295–300 (1966).
  33. Y. K. Voronko, V. V. Osiko, and I. A. Shcherbakov, “Investigation of the interaction of Nd3+ ions in CaF2, SrF2 and BaF2 crystals (type 1),” Sov. Phys. JETP 28(5), 838–844 (1969).
  34. D. R. Tallant and J. C. Wright, “Selective laser excitation of charge compensated sites in CaF2:Er3+,” J. Chem. Phys. 63(5), 2074–2085 (1975).
  35. F. K. Ma, F. Su, R. F. Zhou, Y. Y. Ou, L. J. Xie, C. M. Liu, D. P. Jiang, Z. Zhang, Q. H. Wu, L. B. Su, and H. B. Liang, “The defect aggregation of RE3+ (RE = Y, La∼Lu) in MF2 (M = Ca, Sr, Ba) fluorites,” Mater. Res. Bull. 125, 110788 (2020).
    [Crossref]
  36. C. G. Andeen, J. J. Fontanella, M. C. Wintersgill, P. J. Welcher, R. J. Kimble, and G. E. Matthews, “Clustering in rare-earth-doped alkaline-earth fluorides,” J. Phys. C: Solid State Phys. 14(24), 3557–3574 (1981).
    [Crossref]

2021 (1)

F. K. Ma, P. X. Zhang, L. B. Su, H. Yin, Z. Li, Q. T. Lv, and Z. Q. Chen, “The host driven local structures modulation towards broadband photoluminescence in neodymium-doped fluorite crystal,” Opt. Mater. 119, 111322 (2021).
[Crossref]

2020 (2)

F. K. Ma, F. Su, R. F. Zhou, Y. Y. Ou, L. J. Xie, C. M. Liu, D. P. Jiang, Z. Zhang, Q. H. Wu, L. B. Su, and H. B. Liang, “The defect aggregation of RE3+ (RE = Y, La∼Lu) in MF2 (M = Ca, Sr, Ba) fluorites,” Mater. Res. Bull. 125, 110788 (2020).
[Crossref]

J. Pan, J. J. Cordell, G. J. Tucker, A. Zakutayev, A. C. Tamboli, and S. Lany, “Perfect short-range ordered alloy with line-compound-like properties in the ZnSnN2:ZnO system,” npj Comput. Mater. 6(1), 63 (2020).
[Crossref]

2019 (4)

L. Kong, J. Q. Guo, J. W. Makepeace, T. C. Xiao, H. F. Greer, W. Z. Zhou, Z. Jiang, and P. P. Edwards, “Rapid synthesis of BiOBrxI1-x photocatalysts: Insights to the visible-light photocatalytic activity and strong deviation from Vegard’s law,” Catal. Today 335(SI), 477–484 (2019).
[Crossref]

A. BaQais, N. Tymińska, T. Le Bahers, and K. Takanabe, “Optoelectronic structure and photocatalytic applications of Na(Bi,La)S2 solid solutions with tunable band gaps,” Chem. Mater. 31(9), 3211–3220 (2019).
[Crossref]

M. P. Agustianingrum, S. Yoshida, N. Tsuji, and N. Park, “Effect of aluminum addition on solid solution strengthening in CoCrNi medium-entropy alloy,” J. Alloys Compd. 781, 866–872 (2019).
[Crossref]

F. K. Ma, D. P. Jiang, Z. Zheng, X. Q. Tian, Q. H. Wu, J. Y. Wang, X. B. Qian, Y. Liu, and L. B. Su, “Tailoring the local lattice distortion of Nd3+ by codoping of Y3+ through first principles calculation for tuning the spectroscopic properties,” Opt. Mater. Express 9(11), 4256–4272 (2019).
[Crossref]

2016 (2)

J. F. Zhu, L. Wei, W. L. Tian, J. X. Liu, Z. H. Wang, L. B. Su, J. Xu, and Z. Y. Wei, “Generation of sub-100 fs pulses from mode-locked Nd,Y:SrF2 laser with enhancing SPM,” Laser Phys. Lett. 13(5), 055804 (2016).
[Crossref]

M. A. W. Schoen, D. Thonig, M. L. Schneider, T. J. Silva, H. T. Nembach, O. Eriksson, O. Karis, and J. M. Shaw, “Ultra-low magnetic damping of a metallic ferromagnet,” Nat. Phys. 12(9), 839–842 (2016).
[Crossref]

2015 (1)

P. A. Popov, N. V. Moiseev, D. N. Karimov, N. I. Sorokin, E. A. Sulyanova, B. P. Sobolev, V. A. Konyushkin, and P. P. Fedorov, “Thermophysical characteristics of Ca1−xSrxF2 solid-solution crystals (0 ≤ x ≤ 1),” Crystallogr. Rep. 60(1), 116–122 (2015).
[Crossref]

2014 (2)

2013 (1)

P. R. Abel, A. M. Chockla, Y. M. Lin, V. C. Holmberg, J. T. Harris, B. A. Korgel, A. Heller, and C. B. Mullins, “Nanostructured Si1-xGex for tunable thin film lithium-ion battery anodes,” ACS Nano 7(3), 2249–2257 (2013).
[Crossref]

2009 (1)

S. Benny, R. Grau-Crespo, and N. H. de Leeuw, “A theoretical investigation of α-Fe2O3-Cr2O3 solid solutions,” Phys. Chem. Chem. Phys. 11(5), 808–815 (2009).
[Crossref]

2008 (2)

S. Lany and A. Zunger, “Assessment of correction methods for the band-gap problem and for finite-size effects in supercell defect calculations: Case studies for ZnO and GaAs,” Phys. Rev. B 78(23), 235104 (2008).
[Crossref]

R. E. Youngman and C. M. Smith, “Multinuclear NMR studies of mixed Ca1−xSrxF2 crystals,” Phys. Rev. B 78(1), 014112 (2008).
[Crossref]

2005 (1)

C. Persson, Y. J. Zhao, S. Lany, and A. Zunger, “N-type doping of CuInSe2 and CuGaSe2,” Phys. Rev. B 72(3), 035211 (2005).
[Crossref]

2003 (1)

M. Suzuki, T. Kimura, J. Koike, and K. Maruyama, “Strengthening effect of Zn in heat resistant Mg-Y-Zn solid solution alloys,” Scr. Mater. 48(8), 997–1002 (2003).
[Crossref]

1998 (1)

S. L. Dudarev, G. A. Botton, S. Y. Savrasov, C. J. Humphreys, and A. P. Sutton, “Electron-energy-loss spectra and the structural stability of nickel oxide: An LSDA + U study,” Phys. Rev. B 57(3), 1505–1509 (1998).
[Crossref]

1996 (2)

J. P. Perdew, K. Burke, and M. Ernzerhof, “Generalized gradient approximation made simple,” Phys. Rev. Lett. 77(18), 3865–3868 (1996).
[Crossref]

G. Kresse and J. Furthmuller, “Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set,” Comput. Mater. Sci. 6(1), 15–50 (1996).
[Crossref]

1995 (1)

G. Makov and M. C. Payne, “Periodic boundary-conditions in ab-initio calculations,” Phys. Rev. B 51(7), 4014–4022 (1995).
[Crossref]

1994 (1)

P. E. Blöchl, “Projector augmented-wave method,” Phys. Rev. B 50(24), 17953–17979 (1994).
[Crossref]

1993 (2)

G. Kresse and J. Hafner, “Ab initio molecular-dynamics for liquid-metals,” Phys. Rev. B 47(1), 558–561 (1993).
[Crossref]

A. Jockisch, U. Schröder, F. W. de Wette, and W. Kress, “Relaxation and dynamics of the (111) surfaces of the fluorides CaF2 and SrF2,” J. Phys.: Condens. Matter 5(31), 5401–5410 (1993).
[Crossref]

1990 (1)

M. V. Subrahmanya Sarma and S. V. Suryanarayana, “Dielectric studies of CaxSr1−xF2 mixed crystals,” J. Mater. Sci.: Mater. Electron. 1(4), 182–184 (1990).
[Crossref]

1986 (2)

M. V. Subrahmanya Sarma and S. V. Suryanarayana, “Study of microhardness on CaxSr1-xF2 mixed crystals,” J. Mater. Sci. Lett. 5(12), 1277–1278 (1986).
[Crossref]

Y. Z. Zhou, “Growth of high quality large Nd:YAG crystals by temperature gradient technique (TGT),” J. Cryst. Growth 78(1), 31–35 (1986).
[Crossref]

1984 (1)

P. J. Bendall, C. R. A. Catlow, J. Corish, and P. W. M. Jacobs, “Defect aggregation in anion-excess fluorites II. Clusters containing more than two impurity atoms,” J. Solid State Chem. 51(2), 159–169 (1984).
[Crossref]

1982 (1)

J. Corish, C. R. A. Catlow, P. W. M. Jacobs, and S. H. Ong, “Defect aggregation in anion-excess fluorites. Dopant monomers and dimers,” Phys. Rev. B 25(10), 6425–6438 (1982).
[Crossref]

1981 (1)

C. G. Andeen, J. J. Fontanella, M. C. Wintersgill, P. J. Welcher, R. J. Kimble, and G. E. Matthews, “Clustering in rare-earth-doped alkaline-earth fluorides,” J. Phys. C: Solid State Phys. 14(24), 3557–3574 (1981).
[Crossref]

1975 (1)

D. R. Tallant and J. C. Wright, “Selective laser excitation of charge compensated sites in CaF2:Er3+,” J. Chem. Phys. 63(5), 2074–2085 (1975).

1972 (1)

C. Andeen, J. Fontanella, and D. Schuele, “Pressure and temperature derivatives of the low-frequency dielectric constants of the alkaline-earth fluorides,” Phys. Rev. B 6(2), 591–595 (1972).
[Crossref]

1969 (1)

Y. K. Voronko, V. V. Osiko, and I. A. Shcherbakov, “Investigation of the interaction of Nd3+ ions in CaF2, SrF2 and BaF2 crystals (type 1),” Sov. Phys. JETP 28(5), 838–844 (1969).

1966 (2)

Y. K. Voronko, A. A. Kaminskii, and V. V. Osiko, “Analysis of the optical spectra of CaF2:Nd3+ (type 1) crystals,” Sov. Phys. JETP 22(2), 295–300 (1966).

R. K. Chang, B. Lacina, and P. S. Pershan, “Raman scattering from mixed crystals (CaxSr1−x)F2 and (SrxBa1-x)F2,” Phys. Rev. Lett. 17(14), 755–758 (1966).
[Crossref]

Abel, P. R.

P. R. Abel, A. M. Chockla, Y. M. Lin, V. C. Holmberg, J. T. Harris, B. A. Korgel, A. Heller, and C. B. Mullins, “Nanostructured Si1-xGex for tunable thin film lithium-ion battery anodes,” ACS Nano 7(3), 2249–2257 (2013).
[Crossref]

Agustianingrum, M. P.

M. P. Agustianingrum, S. Yoshida, N. Tsuji, and N. Park, “Effect of aluminum addition on solid solution strengthening in CoCrNi medium-entropy alloy,” J. Alloys Compd. 781, 866–872 (2019).
[Crossref]

Andeen, C.

C. Andeen, J. Fontanella, and D. Schuele, “Pressure and temperature derivatives of the low-frequency dielectric constants of the alkaline-earth fluorides,” Phys. Rev. B 6(2), 591–595 (1972).
[Crossref]

Andeen, C. G.

C. G. Andeen, J. J. Fontanella, M. C. Wintersgill, P. J. Welcher, R. J. Kimble, and G. E. Matthews, “Clustering in rare-earth-doped alkaline-earth fluorides,” J. Phys. C: Solid State Phys. 14(24), 3557–3574 (1981).
[Crossref]

BaQais, A.

A. BaQais, N. Tymińska, T. Le Bahers, and K. Takanabe, “Optoelectronic structure and photocatalytic applications of Na(Bi,La)S2 solid solutions with tunable band gaps,” Chem. Mater. 31(9), 3211–3220 (2019).
[Crossref]

Bendall, P. J.

P. J. Bendall, C. R. A. Catlow, J. Corish, and P. W. M. Jacobs, “Defect aggregation in anion-excess fluorites II. Clusters containing more than two impurity atoms,” J. Solid State Chem. 51(2), 159–169 (1984).
[Crossref]

Benny, S.

S. Benny, R. Grau-Crespo, and N. H. de Leeuw, “A theoretical investigation of α-Fe2O3-Cr2O3 solid solutions,” Phys. Chem. Chem. Phys. 11(5), 808–815 (2009).
[Crossref]

Blöchl, P. E.

P. E. Blöchl, “Projector augmented-wave method,” Phys. Rev. B 50(24), 17953–17979 (1994).
[Crossref]

Botton, G. A.

S. L. Dudarev, G. A. Botton, S. Y. Savrasov, C. J. Humphreys, and A. P. Sutton, “Electron-energy-loss spectra and the structural stability of nickel oxide: An LSDA + U study,” Phys. Rev. B 57(3), 1505–1509 (1998).
[Crossref]

Burke, K.

J. P. Perdew, K. Burke, and M. Ernzerhof, “Generalized gradient approximation made simple,” Phys. Rev. Lett. 77(18), 3865–3868 (1996).
[Crossref]

Cao, Y. X.

Catlow, C. R. A.

P. J. Bendall, C. R. A. Catlow, J. Corish, and P. W. M. Jacobs, “Defect aggregation in anion-excess fluorites II. Clusters containing more than two impurity atoms,” J. Solid State Chem. 51(2), 159–169 (1984).
[Crossref]

J. Corish, C. R. A. Catlow, P. W. M. Jacobs, and S. H. Ong, “Defect aggregation in anion-excess fluorites. Dopant monomers and dimers,” Phys. Rev. B 25(10), 6425–6438 (1982).
[Crossref]

Chang, R. K.

R. K. Chang, B. Lacina, and P. S. Pershan, “Raman scattering from mixed crystals (CaxSr1−x)F2 and (SrxBa1-x)F2,” Phys. Rev. Lett. 17(14), 755–758 (1966).
[Crossref]

Chen, Z. Q.

F. K. Ma, P. X. Zhang, L. B. Su, H. Yin, Z. Li, Q. T. Lv, and Z. Q. Chen, “The host driven local structures modulation towards broadband photoluminescence in neodymium-doped fluorite crystal,” Opt. Mater. 119, 111322 (2021).
[Crossref]

Chockla, A. M.

P. R. Abel, A. M. Chockla, Y. M. Lin, V. C. Holmberg, J. T. Harris, B. A. Korgel, A. Heller, and C. B. Mullins, “Nanostructured Si1-xGex for tunable thin film lithium-ion battery anodes,” ACS Nano 7(3), 2249–2257 (2013).
[Crossref]

Cordell, J. J.

J. Pan, J. J. Cordell, G. J. Tucker, A. Zakutayev, A. C. Tamboli, and S. Lany, “Perfect short-range ordered alloy with line-compound-like properties in the ZnSnN2:ZnO system,” npj Comput. Mater. 6(1), 63 (2020).
[Crossref]

Corish, J.

P. J. Bendall, C. R. A. Catlow, J. Corish, and P. W. M. Jacobs, “Defect aggregation in anion-excess fluorites II. Clusters containing more than two impurity atoms,” J. Solid State Chem. 51(2), 159–169 (1984).
[Crossref]

J. Corish, C. R. A. Catlow, P. W. M. Jacobs, and S. H. Ong, “Defect aggregation in anion-excess fluorites. Dopant monomers and dimers,” Phys. Rev. B 25(10), 6425–6438 (1982).
[Crossref]

de Leeuw, N. H.

S. Benny, R. Grau-Crespo, and N. H. de Leeuw, “A theoretical investigation of α-Fe2O3-Cr2O3 solid solutions,” Phys. Chem. Chem. Phys. 11(5), 808–815 (2009).
[Crossref]

de Wette, F. W.

A. Jockisch, U. Schröder, F. W. de Wette, and W. Kress, “Relaxation and dynamics of the (111) surfaces of the fluorides CaF2 and SrF2,” J. Phys.: Condens. Matter 5(31), 5401–5410 (1993).
[Crossref]

Dudarev, S. L.

S. L. Dudarev, G. A. Botton, S. Y. Savrasov, C. J. Humphreys, and A. P. Sutton, “Electron-energy-loss spectra and the structural stability of nickel oxide: An LSDA + U study,” Phys. Rev. B 57(3), 1505–1509 (1998).
[Crossref]

Edwards, P. P.

L. Kong, J. Q. Guo, J. W. Makepeace, T. C. Xiao, H. F. Greer, W. Z. Zhou, Z. Jiang, and P. P. Edwards, “Rapid synthesis of BiOBrxI1-x photocatalysts: Insights to the visible-light photocatalytic activity and strong deviation from Vegard’s law,” Catal. Today 335(SI), 477–484 (2019).
[Crossref]

Eriksson, O.

M. A. W. Schoen, D. Thonig, M. L. Schneider, T. J. Silva, H. T. Nembach, O. Eriksson, O. Karis, and J. M. Shaw, “Ultra-low magnetic damping of a metallic ferromagnet,” Nat. Phys. 12(9), 839–842 (2016).
[Crossref]

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P. A. Popov, N. V. Moiseev, D. N. Karimov, N. I. Sorokin, E. A. Sulyanova, B. P. Sobolev, V. A. Konyushkin, and P. P. Fedorov, “Thermophysical characteristics of Ca1−xSrxF2 solid-solution crystals (0 ≤ x ≤ 1),” Crystallogr. Rep. 60(1), 116–122 (2015).
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C. Andeen, J. Fontanella, and D. Schuele, “Pressure and temperature derivatives of the low-frequency dielectric constants of the alkaline-earth fluorides,” Phys. Rev. B 6(2), 591–595 (1972).
[Crossref]

Fontanella, J. J.

C. G. Andeen, J. J. Fontanella, M. C. Wintersgill, P. J. Welcher, R. J. Kimble, and G. E. Matthews, “Clustering in rare-earth-doped alkaline-earth fluorides,” J. Phys. C: Solid State Phys. 14(24), 3557–3574 (1981).
[Crossref]

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G. Kresse and J. Furthmuller, “Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set,” Comput. Mater. Sci. 6(1), 15–50 (1996).
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Ge, W. Y.

Grau-Crespo, R.

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L. Kong, J. Q. Guo, J. W. Makepeace, T. C. Xiao, H. F. Greer, W. Z. Zhou, Z. Jiang, and P. P. Edwards, “Rapid synthesis of BiOBrxI1-x photocatalysts: Insights to the visible-light photocatalytic activity and strong deviation from Vegard’s law,” Catal. Today 335(SI), 477–484 (2019).
[Crossref]

Guo, J. Q.

L. Kong, J. Q. Guo, J. W. Makepeace, T. C. Xiao, H. F. Greer, W. Z. Zhou, Z. Jiang, and P. P. Edwards, “Rapid synthesis of BiOBrxI1-x photocatalysts: Insights to the visible-light photocatalytic activity and strong deviation from Vegard’s law,” Catal. Today 335(SI), 477–484 (2019).
[Crossref]

Hafner, J.

G. Kresse and J. Hafner, “Ab initio molecular-dynamics for liquid-metals,” Phys. Rev. B 47(1), 558–561 (1993).
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P. R. Abel, A. M. Chockla, Y. M. Lin, V. C. Holmberg, J. T. Harris, B. A. Korgel, A. Heller, and C. B. Mullins, “Nanostructured Si1-xGex for tunable thin film lithium-ion battery anodes,” ACS Nano 7(3), 2249–2257 (2013).
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Heller, A.

P. R. Abel, A. M. Chockla, Y. M. Lin, V. C. Holmberg, J. T. Harris, B. A. Korgel, A. Heller, and C. B. Mullins, “Nanostructured Si1-xGex for tunable thin film lithium-ion battery anodes,” ACS Nano 7(3), 2249–2257 (2013).
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P. R. Abel, A. M. Chockla, Y. M. Lin, V. C. Holmberg, J. T. Harris, B. A. Korgel, A. Heller, and C. B. Mullins, “Nanostructured Si1-xGex for tunable thin film lithium-ion battery anodes,” ACS Nano 7(3), 2249–2257 (2013).
[Crossref]

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S. L. Dudarev, G. A. Botton, S. Y. Savrasov, C. J. Humphreys, and A. P. Sutton, “Electron-energy-loss spectra and the structural stability of nickel oxide: An LSDA + U study,” Phys. Rev. B 57(3), 1505–1509 (1998).
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P. J. Bendall, C. R. A. Catlow, J. Corish, and P. W. M. Jacobs, “Defect aggregation in anion-excess fluorites II. Clusters containing more than two impurity atoms,” J. Solid State Chem. 51(2), 159–169 (1984).
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J. Corish, C. R. A. Catlow, P. W. M. Jacobs, and S. H. Ong, “Defect aggregation in anion-excess fluorites. Dopant monomers and dimers,” Phys. Rev. B 25(10), 6425–6438 (1982).
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Jiang, Z.

L. Kong, J. Q. Guo, J. W. Makepeace, T. C. Xiao, H. F. Greer, W. Z. Zhou, Z. Jiang, and P. P. Edwards, “Rapid synthesis of BiOBrxI1-x photocatalysts: Insights to the visible-light photocatalytic activity and strong deviation from Vegard’s law,” Catal. Today 335(SI), 477–484 (2019).
[Crossref]

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A. Jockisch, U. Schröder, F. W. de Wette, and W. Kress, “Relaxation and dynamics of the (111) surfaces of the fluorides CaF2 and SrF2,” J. Phys.: Condens. Matter 5(31), 5401–5410 (1993).
[Crossref]

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Y. K. Voronko, A. A. Kaminskii, and V. V. Osiko, “Analysis of the optical spectra of CaF2:Nd3+ (type 1) crystals,” Sov. Phys. JETP 22(2), 295–300 (1966).

Karimov, D. N.

P. A. Popov, N. V. Moiseev, D. N. Karimov, N. I. Sorokin, E. A. Sulyanova, B. P. Sobolev, V. A. Konyushkin, and P. P. Fedorov, “Thermophysical characteristics of Ca1−xSrxF2 solid-solution crystals (0 ≤ x ≤ 1),” Crystallogr. Rep. 60(1), 116–122 (2015).
[Crossref]

Karis, O.

M. A. W. Schoen, D. Thonig, M. L. Schneider, T. J. Silva, H. T. Nembach, O. Eriksson, O. Karis, and J. M. Shaw, “Ultra-low magnetic damping of a metallic ferromagnet,” Nat. Phys. 12(9), 839–842 (2016).
[Crossref]

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C. G. Andeen, J. J. Fontanella, M. C. Wintersgill, P. J. Welcher, R. J. Kimble, and G. E. Matthews, “Clustering in rare-earth-doped alkaline-earth fluorides,” J. Phys. C: Solid State Phys. 14(24), 3557–3574 (1981).
[Crossref]

Kimura, T.

M. Suzuki, T. Kimura, J. Koike, and K. Maruyama, “Strengthening effect of Zn in heat resistant Mg-Y-Zn solid solution alloys,” Scr. Mater. 48(8), 997–1002 (2003).
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Koike, J.

M. Suzuki, T. Kimura, J. Koike, and K. Maruyama, “Strengthening effect of Zn in heat resistant Mg-Y-Zn solid solution alloys,” Scr. Mater. 48(8), 997–1002 (2003).
[Crossref]

Kong, L.

L. Kong, J. Q. Guo, J. W. Makepeace, T. C. Xiao, H. F. Greer, W. Z. Zhou, Z. Jiang, and P. P. Edwards, “Rapid synthesis of BiOBrxI1-x photocatalysts: Insights to the visible-light photocatalytic activity and strong deviation from Vegard’s law,” Catal. Today 335(SI), 477–484 (2019).
[Crossref]

Konyushkin, V. A.

P. A. Popov, N. V. Moiseev, D. N. Karimov, N. I. Sorokin, E. A. Sulyanova, B. P. Sobolev, V. A. Konyushkin, and P. P. Fedorov, “Thermophysical characteristics of Ca1−xSrxF2 solid-solution crystals (0 ≤ x ≤ 1),” Crystallogr. Rep. 60(1), 116–122 (2015).
[Crossref]

Korgel, B. A.

P. R. Abel, A. M. Chockla, Y. M. Lin, V. C. Holmberg, J. T. Harris, B. A. Korgel, A. Heller, and C. B. Mullins, “Nanostructured Si1-xGex for tunable thin film lithium-ion battery anodes,” ACS Nano 7(3), 2249–2257 (2013).
[Crossref]

Kress, W.

A. Jockisch, U. Schröder, F. W. de Wette, and W. Kress, “Relaxation and dynamics of the (111) surfaces of the fluorides CaF2 and SrF2,” J. Phys.: Condens. Matter 5(31), 5401–5410 (1993).
[Crossref]

Kresse, G.

G. Kresse and J. Furthmuller, “Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set,” Comput. Mater. Sci. 6(1), 15–50 (1996).
[Crossref]

G. Kresse and J. Hafner, “Ab initio molecular-dynamics for liquid-metals,” Phys. Rev. B 47(1), 558–561 (1993).
[Crossref]

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R. K. Chang, B. Lacina, and P. S. Pershan, “Raman scattering from mixed crystals (CaxSr1−x)F2 and (SrxBa1-x)F2,” Phys. Rev. Lett. 17(14), 755–758 (1966).
[Crossref]

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J. Pan, J. J. Cordell, G. J. Tucker, A. Zakutayev, A. C. Tamboli, and S. Lany, “Perfect short-range ordered alloy with line-compound-like properties in the ZnSnN2:ZnO system,” npj Comput. Mater. 6(1), 63 (2020).
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S. Lany and A. Zunger, “Assessment of correction methods for the band-gap problem and for finite-size effects in supercell defect calculations: Case studies for ZnO and GaAs,” Phys. Rev. B 78(23), 235104 (2008).
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C. Persson, Y. J. Zhao, S. Lany, and A. Zunger, “N-type doping of CuInSe2 and CuGaSe2,” Phys. Rev. B 72(3), 035211 (2005).
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A. BaQais, N. Tymińska, T. Le Bahers, and K. Takanabe, “Optoelectronic structure and photocatalytic applications of Na(Bi,La)S2 solid solutions with tunable band gaps,” Chem. Mater. 31(9), 3211–3220 (2019).
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F. K. Ma, P. X. Zhang, L. B. Su, H. Yin, Z. Li, Q. T. Lv, and Z. Q. Chen, “The host driven local structures modulation towards broadband photoluminescence in neodymium-doped fluorite crystal,” Opt. Mater. 119, 111322 (2021).
[Crossref]

Liang, H. B.

F. K. Ma, F. Su, R. F. Zhou, Y. Y. Ou, L. J. Xie, C. M. Liu, D. P. Jiang, Z. Zhang, Q. H. Wu, L. B. Su, and H. B. Liang, “The defect aggregation of RE3+ (RE = Y, La∼Lu) in MF2 (M = Ca, Sr, Ba) fluorites,” Mater. Res. Bull. 125, 110788 (2020).
[Crossref]

Lin, Y. M.

P. R. Abel, A. M. Chockla, Y. M. Lin, V. C. Holmberg, J. T. Harris, B. A. Korgel, A. Heller, and C. B. Mullins, “Nanostructured Si1-xGex for tunable thin film lithium-ion battery anodes,” ACS Nano 7(3), 2249–2257 (2013).
[Crossref]

Liu, C. M.

F. K. Ma, F. Su, R. F. Zhou, Y. Y. Ou, L. J. Xie, C. M. Liu, D. P. Jiang, Z. Zhang, Q. H. Wu, L. B. Su, and H. B. Liang, “The defect aggregation of RE3+ (RE = Y, La∼Lu) in MF2 (M = Ca, Sr, Ba) fluorites,” Mater. Res. Bull. 125, 110788 (2020).
[Crossref]

Liu, J. X.

J. F. Zhu, L. Wei, W. L. Tian, J. X. Liu, Z. H. Wang, L. B. Su, J. Xu, and Z. Y. Wei, “Generation of sub-100 fs pulses from mode-locked Nd,Y:SrF2 laser with enhancing SPM,” Laser Phys. Lett. 13(5), 055804 (2016).
[Crossref]

Liu, Y.

Lv, Q. T.

F. K. Ma, P. X. Zhang, L. B. Su, H. Yin, Z. Li, Q. T. Lv, and Z. Q. Chen, “The host driven local structures modulation towards broadband photoluminescence in neodymium-doped fluorite crystal,” Opt. Mater. 119, 111322 (2021).
[Crossref]

Ma, F. K.

F. K. Ma, P. X. Zhang, L. B. Su, H. Yin, Z. Li, Q. T. Lv, and Z. Q. Chen, “The host driven local structures modulation towards broadband photoluminescence in neodymium-doped fluorite crystal,” Opt. Mater. 119, 111322 (2021).
[Crossref]

F. K. Ma, F. Su, R. F. Zhou, Y. Y. Ou, L. J. Xie, C. M. Liu, D. P. Jiang, Z. Zhang, Q. H. Wu, L. B. Su, and H. B. Liang, “The defect aggregation of RE3+ (RE = Y, La∼Lu) in MF2 (M = Ca, Sr, Ba) fluorites,” Mater. Res. Bull. 125, 110788 (2020).
[Crossref]

F. K. Ma, D. P. Jiang, Z. Zheng, X. Q. Tian, Q. H. Wu, J. Y. Wang, X. B. Qian, Y. Liu, and L. B. Su, “Tailoring the local lattice distortion of Nd3+ by codoping of Y3+ through first principles calculation for tuning the spectroscopic properties,” Opt. Mater. Express 9(11), 4256–4272 (2019).
[Crossref]

Z. P. Qin, G. Q. Xie, J. Ma, W. Y. Ge, P. Yuan, L. J. Qian, L. B. Su, D. P. Jiang, F. K. Ma, Q. Zhang, Y. X. Cao, and J. Xu, “Generation of 103 fs mode-locked pulses by a gain linewidth-variable Nd,Y:CaF2 disordered crystal,” Opt. Lett. 39(7), 1737–1739 (2014).
[Crossref]

Ma, J.

Makepeace, J. W.

L. Kong, J. Q. Guo, J. W. Makepeace, T. C. Xiao, H. F. Greer, W. Z. Zhou, Z. Jiang, and P. P. Edwards, “Rapid synthesis of BiOBrxI1-x photocatalysts: Insights to the visible-light photocatalytic activity and strong deviation from Vegard’s law,” Catal. Today 335(SI), 477–484 (2019).
[Crossref]

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G. Makov and M. C. Payne, “Periodic boundary-conditions in ab-initio calculations,” Phys. Rev. B 51(7), 4014–4022 (1995).
[Crossref]

Maruyama, K.

M. Suzuki, T. Kimura, J. Koike, and K. Maruyama, “Strengthening effect of Zn in heat resistant Mg-Y-Zn solid solution alloys,” Scr. Mater. 48(8), 997–1002 (2003).
[Crossref]

Matthews, G. E.

C. G. Andeen, J. J. Fontanella, M. C. Wintersgill, P. J. Welcher, R. J. Kimble, and G. E. Matthews, “Clustering in rare-earth-doped alkaline-earth fluorides,” J. Phys. C: Solid State Phys. 14(24), 3557–3574 (1981).
[Crossref]

Moiseev, N. V.

P. A. Popov, N. V. Moiseev, D. N. Karimov, N. I. Sorokin, E. A. Sulyanova, B. P. Sobolev, V. A. Konyushkin, and P. P. Fedorov, “Thermophysical characteristics of Ca1−xSrxF2 solid-solution crystals (0 ≤ x ≤ 1),” Crystallogr. Rep. 60(1), 116–122 (2015).
[Crossref]

Mokkath, J. H.

J. H. Mokkath and U. Schwingenschlögl, “Magnetic phase transition in 2 nm NixCu1−x (0 ≤ x ≤ 1) clusters,” J. Phys. Chem. C 118(15), 8169–8173 (2014).
[Crossref]

Mullins, C. B.

P. R. Abel, A. M. Chockla, Y. M. Lin, V. C. Holmberg, J. T. Harris, B. A. Korgel, A. Heller, and C. B. Mullins, “Nanostructured Si1-xGex for tunable thin film lithium-ion battery anodes,” ACS Nano 7(3), 2249–2257 (2013).
[Crossref]

Nembach, H. T.

M. A. W. Schoen, D. Thonig, M. L. Schneider, T. J. Silva, H. T. Nembach, O. Eriksson, O. Karis, and J. M. Shaw, “Ultra-low magnetic damping of a metallic ferromagnet,” Nat. Phys. 12(9), 839–842 (2016).
[Crossref]

Ong, S. H.

J. Corish, C. R. A. Catlow, P. W. M. Jacobs, and S. H. Ong, “Defect aggregation in anion-excess fluorites. Dopant monomers and dimers,” Phys. Rev. B 25(10), 6425–6438 (1982).
[Crossref]

Osiko, V. V.

Y. K. Voronko, V. V. Osiko, and I. A. Shcherbakov, “Investigation of the interaction of Nd3+ ions in CaF2, SrF2 and BaF2 crystals (type 1),” Sov. Phys. JETP 28(5), 838–844 (1969).

Y. K. Voronko, A. A. Kaminskii, and V. V. Osiko, “Analysis of the optical spectra of CaF2:Nd3+ (type 1) crystals,” Sov. Phys. JETP 22(2), 295–300 (1966).

Ou, Y. Y.

F. K. Ma, F. Su, R. F. Zhou, Y. Y. Ou, L. J. Xie, C. M. Liu, D. P. Jiang, Z. Zhang, Q. H. Wu, L. B. Su, and H. B. Liang, “The defect aggregation of RE3+ (RE = Y, La∼Lu) in MF2 (M = Ca, Sr, Ba) fluorites,” Mater. Res. Bull. 125, 110788 (2020).
[Crossref]

Pan, J.

J. Pan, J. J. Cordell, G. J. Tucker, A. Zakutayev, A. C. Tamboli, and S. Lany, “Perfect short-range ordered alloy with line-compound-like properties in the ZnSnN2:ZnO system,” npj Comput. Mater. 6(1), 63 (2020).
[Crossref]

Park, N.

M. P. Agustianingrum, S. Yoshida, N. Tsuji, and N. Park, “Effect of aluminum addition on solid solution strengthening in CoCrNi medium-entropy alloy,” J. Alloys Compd. 781, 866–872 (2019).
[Crossref]

Payne, M. C.

G. Makov and M. C. Payne, “Periodic boundary-conditions in ab-initio calculations,” Phys. Rev. B 51(7), 4014–4022 (1995).
[Crossref]

Perdew, J. P.

J. P. Perdew, K. Burke, and M. Ernzerhof, “Generalized gradient approximation made simple,” Phys. Rev. Lett. 77(18), 3865–3868 (1996).
[Crossref]

Pershan, P. S.

R. K. Chang, B. Lacina, and P. S. Pershan, “Raman scattering from mixed crystals (CaxSr1−x)F2 and (SrxBa1-x)F2,” Phys. Rev. Lett. 17(14), 755–758 (1966).
[Crossref]

Persson, C.

C. Persson, Y. J. Zhao, S. Lany, and A. Zunger, “N-type doping of CuInSe2 and CuGaSe2,” Phys. Rev. B 72(3), 035211 (2005).
[Crossref]

Popov, P. A.

P. A. Popov, N. V. Moiseev, D. N. Karimov, N. I. Sorokin, E. A. Sulyanova, B. P. Sobolev, V. A. Konyushkin, and P. P. Fedorov, “Thermophysical characteristics of Ca1−xSrxF2 solid-solution crystals (0 ≤ x ≤ 1),” Crystallogr. Rep. 60(1), 116–122 (2015).
[Crossref]

Qian, L. J.

Qian, X. B.

Qin, Z. P.

Savrasov, S. Y.

S. L. Dudarev, G. A. Botton, S. Y. Savrasov, C. J. Humphreys, and A. P. Sutton, “Electron-energy-loss spectra and the structural stability of nickel oxide: An LSDA + U study,” Phys. Rev. B 57(3), 1505–1509 (1998).
[Crossref]

Schneider, M. L.

M. A. W. Schoen, D. Thonig, M. L. Schneider, T. J. Silva, H. T. Nembach, O. Eriksson, O. Karis, and J. M. Shaw, “Ultra-low magnetic damping of a metallic ferromagnet,” Nat. Phys. 12(9), 839–842 (2016).
[Crossref]

Schoen, M. A. W.

M. A. W. Schoen, D. Thonig, M. L. Schneider, T. J. Silva, H. T. Nembach, O. Eriksson, O. Karis, and J. M. Shaw, “Ultra-low magnetic damping of a metallic ferromagnet,” Nat. Phys. 12(9), 839–842 (2016).
[Crossref]

Schröder, U.

A. Jockisch, U. Schröder, F. W. de Wette, and W. Kress, “Relaxation and dynamics of the (111) surfaces of the fluorides CaF2 and SrF2,” J. Phys.: Condens. Matter 5(31), 5401–5410 (1993).
[Crossref]

Schuele, D.

C. Andeen, J. Fontanella, and D. Schuele, “Pressure and temperature derivatives of the low-frequency dielectric constants of the alkaline-earth fluorides,” Phys. Rev. B 6(2), 591–595 (1972).
[Crossref]

Schwingenschlögl, U.

J. H. Mokkath and U. Schwingenschlögl, “Magnetic phase transition in 2 nm NixCu1−x (0 ≤ x ≤ 1) clusters,” J. Phys. Chem. C 118(15), 8169–8173 (2014).
[Crossref]

Shaw, J. M.

M. A. W. Schoen, D. Thonig, M. L. Schneider, T. J. Silva, H. T. Nembach, O. Eriksson, O. Karis, and J. M. Shaw, “Ultra-low magnetic damping of a metallic ferromagnet,” Nat. Phys. 12(9), 839–842 (2016).
[Crossref]

Shcherbakov, I. A.

Y. K. Voronko, V. V. Osiko, and I. A. Shcherbakov, “Investigation of the interaction of Nd3+ ions in CaF2, SrF2 and BaF2 crystals (type 1),” Sov. Phys. JETP 28(5), 838–844 (1969).

Silva, T. J.

M. A. W. Schoen, D. Thonig, M. L. Schneider, T. J. Silva, H. T. Nembach, O. Eriksson, O. Karis, and J. M. Shaw, “Ultra-low magnetic damping of a metallic ferromagnet,” Nat. Phys. 12(9), 839–842 (2016).
[Crossref]

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R. E. Youngman and C. M. Smith, “Multinuclear NMR studies of mixed Ca1−xSrxF2 crystals,” Phys. Rev. B 78(1), 014112 (2008).
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P. A. Popov, N. V. Moiseev, D. N. Karimov, N. I. Sorokin, E. A. Sulyanova, B. P. Sobolev, V. A. Konyushkin, and P. P. Fedorov, “Thermophysical characteristics of Ca1−xSrxF2 solid-solution crystals (0 ≤ x ≤ 1),” Crystallogr. Rep. 60(1), 116–122 (2015).
[Crossref]

Sorokin, N. I.

P. A. Popov, N. V. Moiseev, D. N. Karimov, N. I. Sorokin, E. A. Sulyanova, B. P. Sobolev, V. A. Konyushkin, and P. P. Fedorov, “Thermophysical characteristics of Ca1−xSrxF2 solid-solution crystals (0 ≤ x ≤ 1),” Crystallogr. Rep. 60(1), 116–122 (2015).
[Crossref]

Su, F.

F. K. Ma, F. Su, R. F. Zhou, Y. Y. Ou, L. J. Xie, C. M. Liu, D. P. Jiang, Z. Zhang, Q. H. Wu, L. B. Su, and H. B. Liang, “The defect aggregation of RE3+ (RE = Y, La∼Lu) in MF2 (M = Ca, Sr, Ba) fluorites,” Mater. Res. Bull. 125, 110788 (2020).
[Crossref]

Su, L. B.

F. K. Ma, P. X. Zhang, L. B. Su, H. Yin, Z. Li, Q. T. Lv, and Z. Q. Chen, “The host driven local structures modulation towards broadband photoluminescence in neodymium-doped fluorite crystal,” Opt. Mater. 119, 111322 (2021).
[Crossref]

F. K. Ma, F. Su, R. F. Zhou, Y. Y. Ou, L. J. Xie, C. M. Liu, D. P. Jiang, Z. Zhang, Q. H. Wu, L. B. Su, and H. B. Liang, “The defect aggregation of RE3+ (RE = Y, La∼Lu) in MF2 (M = Ca, Sr, Ba) fluorites,” Mater. Res. Bull. 125, 110788 (2020).
[Crossref]

F. K. Ma, D. P. Jiang, Z. Zheng, X. Q. Tian, Q. H. Wu, J. Y. Wang, X. B. Qian, Y. Liu, and L. B. Su, “Tailoring the local lattice distortion of Nd3+ by codoping of Y3+ through first principles calculation for tuning the spectroscopic properties,” Opt. Mater. Express 9(11), 4256–4272 (2019).
[Crossref]

J. F. Zhu, L. Wei, W. L. Tian, J. X. Liu, Z. H. Wang, L. B. Su, J. Xu, and Z. Y. Wei, “Generation of sub-100 fs pulses from mode-locked Nd,Y:SrF2 laser with enhancing SPM,” Laser Phys. Lett. 13(5), 055804 (2016).
[Crossref]

Z. P. Qin, G. Q. Xie, J. Ma, W. Y. Ge, P. Yuan, L. J. Qian, L. B. Su, D. P. Jiang, F. K. Ma, Q. Zhang, Y. X. Cao, and J. Xu, “Generation of 103 fs mode-locked pulses by a gain linewidth-variable Nd,Y:CaF2 disordered crystal,” Opt. Lett. 39(7), 1737–1739 (2014).
[Crossref]

Subrahmanya Sarma, M. V.

M. V. Subrahmanya Sarma and S. V. Suryanarayana, “Dielectric studies of CaxSr1−xF2 mixed crystals,” J. Mater. Sci.: Mater. Electron. 1(4), 182–184 (1990).
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M. V. Subrahmanya Sarma and S. V. Suryanarayana, “Study of microhardness on CaxSr1-xF2 mixed crystals,” J. Mater. Sci. Lett. 5(12), 1277–1278 (1986).
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Sulyanova, E. A.

P. A. Popov, N. V. Moiseev, D. N. Karimov, N. I. Sorokin, E. A. Sulyanova, B. P. Sobolev, V. A. Konyushkin, and P. P. Fedorov, “Thermophysical characteristics of Ca1−xSrxF2 solid-solution crystals (0 ≤ x ≤ 1),” Crystallogr. Rep. 60(1), 116–122 (2015).
[Crossref]

Suryanarayana, S. V.

M. V. Subrahmanya Sarma and S. V. Suryanarayana, “Dielectric studies of CaxSr1−xF2 mixed crystals,” J. Mater. Sci.: Mater. Electron. 1(4), 182–184 (1990).
[Crossref]

M. V. Subrahmanya Sarma and S. V. Suryanarayana, “Study of microhardness on CaxSr1-xF2 mixed crystals,” J. Mater. Sci. Lett. 5(12), 1277–1278 (1986).
[Crossref]

Sutton, A. P.

S. L. Dudarev, G. A. Botton, S. Y. Savrasov, C. J. Humphreys, and A. P. Sutton, “Electron-energy-loss spectra and the structural stability of nickel oxide: An LSDA + U study,” Phys. Rev. B 57(3), 1505–1509 (1998).
[Crossref]

Suzuki, M.

M. Suzuki, T. Kimura, J. Koike, and K. Maruyama, “Strengthening effect of Zn in heat resistant Mg-Y-Zn solid solution alloys,” Scr. Mater. 48(8), 997–1002 (2003).
[Crossref]

Takanabe, K.

A. BaQais, N. Tymińska, T. Le Bahers, and K. Takanabe, “Optoelectronic structure and photocatalytic applications of Na(Bi,La)S2 solid solutions with tunable band gaps,” Chem. Mater. 31(9), 3211–3220 (2019).
[Crossref]

Tallant, D. R.

D. R. Tallant and J. C. Wright, “Selective laser excitation of charge compensated sites in CaF2:Er3+,” J. Chem. Phys. 63(5), 2074–2085 (1975).

Tamboli, A. C.

J. Pan, J. J. Cordell, G. J. Tucker, A. Zakutayev, A. C. Tamboli, and S. Lany, “Perfect short-range ordered alloy with line-compound-like properties in the ZnSnN2:ZnO system,” npj Comput. Mater. 6(1), 63 (2020).
[Crossref]

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M. A. W. Schoen, D. Thonig, M. L. Schneider, T. J. Silva, H. T. Nembach, O. Eriksson, O. Karis, and J. M. Shaw, “Ultra-low magnetic damping of a metallic ferromagnet,” Nat. Phys. 12(9), 839–842 (2016).
[Crossref]

Tian, W. L.

J. F. Zhu, L. Wei, W. L. Tian, J. X. Liu, Z. H. Wang, L. B. Su, J. Xu, and Z. Y. Wei, “Generation of sub-100 fs pulses from mode-locked Nd,Y:SrF2 laser with enhancing SPM,” Laser Phys. Lett. 13(5), 055804 (2016).
[Crossref]

Tian, X. Q.

Tsuji, N.

M. P. Agustianingrum, S. Yoshida, N. Tsuji, and N. Park, “Effect of aluminum addition on solid solution strengthening in CoCrNi medium-entropy alloy,” J. Alloys Compd. 781, 866–872 (2019).
[Crossref]

Tucker, G. J.

J. Pan, J. J. Cordell, G. J. Tucker, A. Zakutayev, A. C. Tamboli, and S. Lany, “Perfect short-range ordered alloy with line-compound-like properties in the ZnSnN2:ZnO system,” npj Comput. Mater. 6(1), 63 (2020).
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A. BaQais, N. Tymińska, T. Le Bahers, and K. Takanabe, “Optoelectronic structure and photocatalytic applications of Na(Bi,La)S2 solid solutions with tunable band gaps,” Chem. Mater. 31(9), 3211–3220 (2019).
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Wang, J. Y.

Wang, Z. H.

J. F. Zhu, L. Wei, W. L. Tian, J. X. Liu, Z. H. Wang, L. B. Su, J. Xu, and Z. Y. Wei, “Generation of sub-100 fs pulses from mode-locked Nd,Y:SrF2 laser with enhancing SPM,” Laser Phys. Lett. 13(5), 055804 (2016).
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J. F. Zhu, L. Wei, W. L. Tian, J. X. Liu, Z. H. Wang, L. B. Su, J. Xu, and Z. Y. Wei, “Generation of sub-100 fs pulses from mode-locked Nd,Y:SrF2 laser with enhancing SPM,” Laser Phys. Lett. 13(5), 055804 (2016).
[Crossref]

Wei, Z. Y.

J. F. Zhu, L. Wei, W. L. Tian, J. X. Liu, Z. H. Wang, L. B. Su, J. Xu, and Z. Y. Wei, “Generation of sub-100 fs pulses from mode-locked Nd,Y:SrF2 laser with enhancing SPM,” Laser Phys. Lett. 13(5), 055804 (2016).
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M. P. Agustianingrum, S. Yoshida, N. Tsuji, and N. Park, “Effect of aluminum addition on solid solution strengthening in CoCrNi medium-entropy alloy,” J. Alloys Compd. 781, 866–872 (2019).
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J. Pan, J. J. Cordell, G. J. Tucker, A. Zakutayev, A. C. Tamboli, and S. Lany, “Perfect short-range ordered alloy with line-compound-like properties in the ZnSnN2:ZnO system,” npj Comput. Mater. 6(1), 63 (2020).
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F. K. Ma, P. X. Zhang, L. B. Su, H. Yin, Z. Li, Q. T. Lv, and Z. Q. Chen, “The host driven local structures modulation towards broadband photoluminescence in neodymium-doped fluorite crystal,” Opt. Mater. 119, 111322 (2021).
[Crossref]

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Zhang, Z.

F. K. Ma, F. Su, R. F. Zhou, Y. Y. Ou, L. J. Xie, C. M. Liu, D. P. Jiang, Z. Zhang, Q. H. Wu, L. B. Su, and H. B. Liang, “The defect aggregation of RE3+ (RE = Y, La∼Lu) in MF2 (M = Ca, Sr, Ba) fluorites,” Mater. Res. Bull. 125, 110788 (2020).
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F. K. Ma, F. Su, R. F. Zhou, Y. Y. Ou, L. J. Xie, C. M. Liu, D. P. Jiang, Z. Zhang, Q. H. Wu, L. B. Su, and H. B. Liang, “The defect aggregation of RE3+ (RE = Y, La∼Lu) in MF2 (M = Ca, Sr, Ba) fluorites,” Mater. Res. Bull. 125, 110788 (2020).
[Crossref]

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L. Kong, J. Q. Guo, J. W. Makepeace, T. C. Xiao, H. F. Greer, W. Z. Zhou, Z. Jiang, and P. P. Edwards, “Rapid synthesis of BiOBrxI1-x photocatalysts: Insights to the visible-light photocatalytic activity and strong deviation from Vegard’s law,” Catal. Today 335(SI), 477–484 (2019).
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J. F. Zhu, L. Wei, W. L. Tian, J. X. Liu, Z. H. Wang, L. B. Su, J. Xu, and Z. Y. Wei, “Generation of sub-100 fs pulses from mode-locked Nd,Y:SrF2 laser with enhancing SPM,” Laser Phys. Lett. 13(5), 055804 (2016).
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L. Kong, J. Q. Guo, J. W. Makepeace, T. C. Xiao, H. F. Greer, W. Z. Zhou, Z. Jiang, and P. P. Edwards, “Rapid synthesis of BiOBrxI1-x photocatalysts: Insights to the visible-light photocatalytic activity and strong deviation from Vegard’s law,” Catal. Today 335(SI), 477–484 (2019).
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Chem. Mater. (1)

A. BaQais, N. Tymińska, T. Le Bahers, and K. Takanabe, “Optoelectronic structure and photocatalytic applications of Na(Bi,La)S2 solid solutions with tunable band gaps,” Chem. Mater. 31(9), 3211–3220 (2019).
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M. A. W. Schoen, D. Thonig, M. L. Schneider, T. J. Silva, H. T. Nembach, O. Eriksson, O. Karis, and J. M. Shaw, “Ultra-low magnetic damping of a metallic ferromagnet,” Nat. Phys. 12(9), 839–842 (2016).
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J. Pan, J. J. Cordell, G. J. Tucker, A. Zakutayev, A. C. Tamboli, and S. Lany, “Perfect short-range ordered alloy with line-compound-like properties in the ZnSnN2:ZnO system,” npj Comput. Mater. 6(1), 63 (2020).
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Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Figures (8)

Fig. 1.
Fig. 1. Area normalized absorption spectra of (a) Nd3+:Ca1-xSrxF2 and (b) Nd3+,Y3+:Ca1-xSrxF2 solid solution crystals. (c) Sr2+ concentrations dependent normalized absorption intensity at 791 and 797 nm. (d) Photoluminescence spectra of Nd3+,Y3+:Ca1-xSrxF2 excited at 791 and 797 nm.
Fig. 2.
Fig. 2. Powder XRD patterns of (a) Nd3+:Ca1-xSrxF2 and (b) Nd3+,Y3+:Ca1-xSrxF2 crystals. (c) Strontium concentrations dependent lattice parameter of Nd3+:Ca1-xSrxF2 crystals.
Fig. 3.
Fig. 3. (a) Bond distances and (b) angles dependent relaxed total energy of Ca1-xSrxF2. (c) The nominal strontium concentrations dependent formation energy of Ca1-xSrxF2 crystal.
Fig. 4.
Fig. 4. Formation energy of C4v and C3v center in the (a) Nd3+ and (b) Y3+. (c) Concentrations dependent bond lengths in C4v center of the Nd3+ or Y3+ doped Ca1-xSrxF2. (d) Structure of C3v center with interstitial Fi- at the next nearest site and C4v center with interstitial Fi- at the nearest site. F1- and F2- are the normal fluorine and Fi- the interstitial fluorine. The R(F1-F1) and R(F2-F2) represent the corresponding bond length. Grey balls are F- anions and orange balls the RE3+ ions.
Fig. 5.
Fig. 5. Temperature dependent dielectric losses of Nd3+:Ca1-xSrxF2 crystals at the frequency of 100 Hz.
Fig. 6.
Fig. 6. pDOS of Nd3+ and interstitial Fi- in C4v center. Concentrations of Sr2+ in the first cationic coordination shell of Nd3+ are 0.333 and 0.667 in (a) and (b), respectively. (c) and (d) are the corresponding enlarged images.
Fig. 7.
Fig. 7. pDOS of Y3+ and interstitial Fi- in C4v center. Concentrations of Sr2+ in the first cationic coordination shell of Y3+ are 0.333 and 0.667 in (a) and (b), respectively. (c) and (d) are the corresponding enlarged images.
Fig. 8.
Fig. 8. Formation energy of Nd3+ or Y3+ clusters versus concentration of Sr2+ in the first cationic shell of RE3+ ions. (a) and (b) represent the cubic sublattice and square antiprism structure clusters, respectively.

Equations (3)

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Δ E = E C a 1 x S r x F 2 ( 1 x ) E C a F 2 x E S r F 2
Δ E = ( E t o t + E 0 ) m E 1 n E 2 [ m + n ( m n ) 2 ] E c o r r
E c o r r = ( 1 + g ) q 2 α 2 ε L

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