Calculating and analyzing the relationship between thermal conductivity and microstructure in rare-earth doped fluoride crystals

Calculating and analyzing the relationship between thermal conductivity and microstructure in rare-earth doped fluoride crystals | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Calculating and analyzing the relationship between thermal conductivity and microstructure in rare-earth doped fluoride crystals Kexin Liu, Dapeng Jiang, Gang Bian, Zhen Zhang, Zhonghan Zhang, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5272029/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Rare earth (RE) ion-doped fluoride crystals have shown great application potential in various fields, attracting the attention of many researchers. The abnormal thermal transformation behavior of RE ion-doped fluoride crystals leads to the singularity and weakness of their application fields. Here, the influence of different structural characteristics of RE ion-doped fluoride crystals on the variation of thermal conductivity is further analyzed using phonon scattering calculation. Firstly, based on the effect of the phonon scattering mechanism on the thermal conductivity of RE ion-doped fluoride, a comprehensive analysis examines the diverse factors that affect the abnormal thermal behavior of different doping types and fluoride crystals. The actual thermal conductivity characteristics are predicted to optimize the crystal performance in various application fields of RE ion-doped fluoride crystals. Next, the influence mechanism of mass and radius difference caused by RE ion doping structure on the thermal conductivity of RE ion-doped fluorides is deeply investigated. Ultimately, a theoretical foundation for behavior and influence of disorder crystals' thermal conductivity is established. Physical sciences/Engineering Physical sciences/Materials science RE ions fluoride crystal thermal conductivity phonon scattering mass and radius Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 Figure 13 Figure 14 1 Introduction RE ion-doped fluoride crystals have garnered significant interest owing to their remarkable capabilities in laser, TBCs, thermoelectric material, and other domains 1 – 3 . Among these, thermal behavior is a crucial performance that restricts the application of RE ion-doped fluoride crystals. Thermal conductivity equires additional optimization based on the application fields. The thermal conductivity of RE ion-doped fluoride shows abnormal behavior. When RE ions are inserted in fluoride crystals, the thermal conductivity exhibits significant abnormal characteristics. For instance, when Yb 3+ are doped at 0.1 at.%, the thermal conductivity drops by 50% compared to pure CaF 2 crystals 4 , 5 . Furthermore, the thermal conductivity of RE ion-doped fluoride single crystal transitions from a crystalline state to an amorphous state as the doping concentration rises. In previous work 6 , RE ions replace calcium ions in RE ion-doped fluoride crystal structures to form interstitial fluoride ions, which cause point defects. The number of RE ion clusters rises as the doping concentration increases because of the dipole action that aggregates the RE ions into clusters. The thermal conductivity eventually drops and the thermal conductivity behavior is similar to that of glass. Among them, the primary reason for the continuous change in thermal conductivity between crystalline and amorphous with concentration is that in RE ion-doped fluoride, disordered structures like point defects and clusters coexist with the original fluoride lattice order structure, which leads the competition between defect phonon scattering and phonon-phonon scattering with concentration 7 – 10 . Therefore, based on the point defects and cluster structure transformation, the effects of various cluster structures generated by RE ion-doped fluoride crystals at different doping concentrations on the thermal conductivity are explored by phonon scattering coefficient calculation. The influences of different doping ions and fluoride matrices in RE ion-doped fluoride crystals on the thermal conductivity are provided 11 , 12 . In different RE ion-doped fluoride systems, the calculated results of the phonon scattering coefficient have a favorable correlation with the variation of thermal conductivity of RE ion-doped fluoride crystals, providing a qualitative explanation for the abnormal thermal behavior of RE ion-doped fluoride crystals 13 . In addition, the differences between RE ions and lattice ions in RE ion-doped fluoride are analyzed by using the intrinsic characteristics of various cluster structures. The impact of variations in mass and radius on thermal conductivity is thoroughly discussed. The refinement and classification of mass field and strain field on the glass state transition of thermal conductivity are explored, and the factors influencing the transition from a crystalline to an amorphous state of RE ion-doped fluoride crystal are provided with a detailed explanation. 2 Microstructure influences the thermal conductivity of RE ion-doped fluoride crystals The insertion of RE ions into fluoride crystals significantly alters the system's microstructure, leading to the abnormal variation in thermal conductivity. According to the variation trend of thermal conductivity with doping concentration, it can be divided into two stages. With lower doping concentrations (< 1 at.%), the RE ion-doped fluoride systems mainly generate point defects and exhibit a transition in thermal conductivity between a crystalline state and a crystalline-like state. At high doping concentrations (> 1 at.%), the complex cluster structure predominantly influences the thermal conductivity of RE ion-doped fluorides, displaying thermal behavior comparable to that of glass. The influences of point defects and clusters on the thermal conductivity of RE ion-doped fluoride crystals are discussed. A parameter called phonon scattering coefficient is introduced to describe the thermal behavior of RE ion-doped fluorides 13 . The decisive factor of phonon scattering is the structure modification of RE ion-doped fluorides, that is, the variation trends of the mass and radius with doping. The phonon scattering coefficient is calculated by Eq. ( 1 ). The thermal conductivity of the fluoride crystals is related to the scattering of phonons, as shown in Eq. (2) 13 . Hence, the phonon scattering coefficient reveals the relationship between the microstructure and the thermal conductivity variation in RE ion-doped fluorides. $$\Gamma ={x_i}\left[ {{{\left( {\frac{{{M_i} - \overline {M} }}{{\overline {M} }}} \right)}^2}+\varepsilon {{\left( {\frac{{{\delta _i} - \overline {\delta } }}{{\overline {\delta } }}} \right)}^2}} \right]$$ 1 $$\:\kappa\:\propto\:{{\Gamma\:}}^{-0.5}$$ 2 Where i represents element species of RE ion-doped fluorides; x stands for the proportion of elements; M represents the atomic mass of RE ion-doped fluorides; δ stands for the ion radius of RE ion-doped fluorides. 2.1 Point defects influence RE ion-doped fluorides' thermal conductivity with low doping concentration When doping a modest amount of RE ions, the doped fluoride systems produce point defects, which cause progressive disorder, intense phonon scattering, and diminished thermal conductivity. The relationship between the point defect phonon scattering coefficients of doped with CaF 2 , SrF 2, and BaF 2 for different kinds of RE doped with concentration is calculated according to Eq. ( 1 ), as shown in Fig. 1 , to investigate the variation of the point defect phonon scattering coefficients in fluoride crystals with doping RE ions. Figure 1 a shows that the point defect phonon scattering coefficients change approximately as a linear function relation with the concentration when the doping concentration is less than 0.1 at.%. Next, the increasing trends of point defect phonon scattering coefficients steadily slow down as the doping concentration increases. When reaching a certain doping concentration, the point defect phonon scattering coefficients are close to a maximum value. In other words, the point defects significantly impact the RE:CaF 2 systems' thermal conductivity at this concentration. The point defects caused by the doping of RE ions start to transform into clusters under the influence of dipole interaction, and the factors of clusters on the thermal conductivity then start to dominate 8 . Furthermore, the point defect phonons scattering coefficients increase with the number of doped RE atoms rising, as indicated by the curve variation rule in Fig. 1 a. This phenomenon may be due to the gradual increase in the difference between the mass and radius of RE ions and the lattice calcium ions. As a result, the system's mass field and strain field fluctuations enhance, lattice distortion and disorder degree surrounding RE ions increase, and the phonon scattering becomes intense 14 – 16 . By comparing the point defect phonon scattering coefficients with the atomic number of different fluoride crystals doped with RE ions, similar conclusions can also be obtained in RE ion-doped SrF 2 crystal systems (Fig. 1 b). Whereas, the scattering coefficients of point defect phonons of RE ion-doped BaF 2 crystals are slightly opposite to that of CaF 2 and SrF 2 systems (Fig. 1 c). Among them, the point defect phonon scattering coefficient of the Y:BaF 2 system is significantly larger than that of the BaF 2 crystals doped with lanthanide RE ions 17 . The main reason is the mass and radius difference between Y 3+ and Ba 2+ is greater than that of the lanthanide RE ions and Ba 2+ , while the mass and radius difference between Y and Ca/Sr ions is smaller than that between lanthanide RE ions and Ca/Sr ions. The variation trends and maximum values of the point defect phonon scattering coefficient differ for various fluoride systems. According to Fig. 2 , the point defect phonon scattering coefficient in RE ion-doped CaF 2 crystals changes sharply with doping concentration. Compared with the SrF 2 and BaF 2 systems, the RE ion-doped CaF 2 systems have higher peak values of the point defect phonon scattering coefficients. Moreover, the doping concentration of CaF 2 crystal is the lowest when it reaches the peak of the point-defect phonon scattering coefficient (Fig. 1 ). In other terms, CaF 2 crystal embedded with RE ions is more likely to produce point defect to cluster transformation, resulting in more severe phonon scattering. The relationship between the point defect phonon scattering coefficient and thermal conductivity of RE ion-doped fluorides can be semi-quantitatively analyzed 18 by a functional relationship (Eq. ( 2 )) 19 . Figure 3 illustrates the variation rule of thermal conductivity that can be derived by the point defect phonon scattering coefficient of RE ion-doped Ca/Sr/BaF 2 (Fig. 1 ). At the doping concentration of ≤ 1 at.%, the thermal conductivity rapidly decreases, and then is stable with the doping concentration rising 15 , 20 . The increasing doping atomic number leads to an obvious changing trend of thermal conductivity and inferior thermal conductivity values. At low concentrations, the thermal conductivity of RE ion-doped fluorides varies dramatically due to the change in atomic types. However, as the doping concentration increases, the difference in fluoride systems’ thermal conductivity with different atomic types becomes less noticeable. For different fluoride systems, the changing trend of thermal conductivity of CaF 2 crystals is more significant and the thermal conductivity value reduces drastically. Additionally, the glass-like thermal conductivity transition of RE ion-doped fluorides is qualitatively explored by contrasting the calculated and measured thermal conductivity values. Firstly, by comparing the doping of different kinds of RE ions, the 0.5 at.%Yb:CaF 2 has been transformed into glass-like thermal conductivity, while the glass-like thermal conductivity of 1at.%Ce:CaF 2 is not distinct. Therefore, RE ion-doped fluoride systems with large atomic numbers are prone to glass-like thermal conductivity behavior. It is consistent with the previous conclusion that fluoride crystals with large atomic numbers have low thermal conductivity and considerable phonon scattering. The CaF 2 crystal system has strong point defect phonon scattering, the thermal conductivity value decreases rapidly, and the transition from crystalline to amorphous thermal conductivity is more likely to occur under the same doping concentrations and types of doping atoms when only evaluating the doping concentration without taking the influence of the fluoride matrix on thermal conductivity. The variation of thermal conductivity is shown in Fig. 4 (red dotted lines). The thermal conductivity data drop substantially with large point defect phonon scattering coefficient in the RE ion-doped CaF 2 systems, which also has a similar relationship with the above-mentioned 4 , 21 – 24 . 2.2 Clusters influence RE ion-doped fluorides' thermal conductivity with high doping concentration It is assumed that the configurations of clusters change to the highest order under extremely high doping concentrations. According to Eq. ( 1 ), the variation laws of cluster phonon scattering coefficient with concentration are calculated, as shown in Fig. 5 . The cluster phonon scattering coefficient in RE ion-doped fluoride crystals grows progressively and shows a great tendency as concentration increases. This phenomenon indicates that cluster phonon scattering has an additive effect as the number of clusters rises, which causes extreme changes in thermal conductivity and the transition from a crystalline to an amorphous state. In addition, the cluster scattering coefficient increases with the atomic number of doped RE ions, which exerts enormous influences on the thermal conductivity of crystals (according to Eq. ( 2 )) 25 , 26 . Depending on the difference in doping atomic types, the thermal conductivity is connected to the phonon scattering coefficients of highest-order cluster configurations. For the lanthanide RE elements with small atomic numbers, the highest-order clusters of the RE ion-doped fluoride systems have relatively small order and simple configurations. As shown in Fig. 5 a, the highest-order clusters are a tetramer, and the cluster phonon scattering coefficients are low when the doped RE ions are La, Ce, Pr, and other low atomic number elements, which has little influence on the change trend and value of thermal conductivity. However, the highest-order cluster is hexamer when the doped RE ions are Ho, Er, Yb, and Lu. The increase of cluster phonon scattering coefficients causes the thermal conductivity to transition into an amorphous state 13 , 26 . As illustrated in Fig. 6 , the influences of various cluster structure types on the cluster phonon scattering and thermal conductivity are examined. In La/Nd/Gd:Ca/SrF 2 crystal systems, the cluster phonon scattering coefficients of all kinds of cluster configurations are gradually enhanced with doping concentration, and the growth rate accelerates dramatically at high concentrations. It is demonstrated that the increase of doping concentration has a beneficial effect on the cluster phonon scattering coefficient, aggregation degree increases rapidly, thermal conductivity exhibits a significant amorphous change, and thermal conductivity values fall abruptly. Furthermore, under the same concentration of RE ions doping, the cluster configuration progressively becomes more complex, indicating that the cluster phonon scattering coefficient increases. The cluster configuration gradually transforms from a monomer to a higher-order configuration, such as a dimer, trimer, tetramer, or pentamer, and the cluster phonon scattering steadily enhances. In a word, the doping concentration of RE ions and intricate cluster configuration result in phonon scattering, which leads to the enhancement of thermal resistance and the decrease of thermal conductivity. To further study the influence mechanism of different kinds of fluoride matrices on thermal conductivity in RE ion-doped fluorides, Y:CaF 2 , Y: SrF 2, and Y:BaF 2 are taken as examples, as illustrated in Fig. 7 . It further proves the impact of doping concentrations and cluster types on thermal conductivity. The thermal conductivity declines abruptly in complex clusters and high doping concentrations. For various fluoride matrices, the cluster phonon scattering coefficient of the Y:CaF 2 system changes strongly with doping concentration and doping has an obvious negative effect on heat transfer behavior. The relationship between the scattering coefficient of cluster phonons and thermal conductivity will not be demonstrated again, since the relationship between phonon scattering and thermal conductivity is already provided in Eq. ( 2 ) and explained in 2.1 above. Next, the heat transfer of glass-like thermal conductivity in fluoride systems is analyzed by comparing the calculated thermal conductivity values with the measured thermal conductivity data 15 , 20 . Initially, the system's thermal conductivity transitions into a glass-like thermal behavior when the doping concentration is ≤ 1at.%. The 1 at.% Ce:BaF 2 and 1 at.% Yb:BaF 2 both show crystalline thermal conductivity behavior, however the thermal conductivity of 1 at.% Ce:CaF 2 and 1 at.% Yb:CaF 2 has started to change to a glass-like state. Among them, 1 at.% Yb:CaF 2 has a more apparent glass-like thermal conductivity than 1 at.% Ce:CaF 2 , as demonstrated in Fig. 8 a,b (purple dotted lines). The thermal conductivity behavior is negatively impacted by atomic number and it is relatively easy to obtain a thermal conductivity behavior similar to that of glass. It is deduced that the thermal conductivity of RE ion-doped fluoride systems can transition from a crystalline state to a non-crystalline state within a critical value, which is approximately 1at.%. It is also confirmed that the cluster phonon scattering coefficients of RE ion-doped CaF 2 systems are higher in each cluster configuration than those of the SrF 2 systems. RE ions doping on CaF 2 crystals are more likely to produce a transition from crystalline thermal conductivity to amorphous thermal conductivity. As illustrated in Fig. 8 a and b (yellow dotted lines), the thermal conductivity of Ce/Yb:CaF 2 in the high-temperature region is greater than that of Ce/Yb:BaF 2 , despite the system's thermal conductivity changing to a glass-like thermal conductivity with high doping concentration. The impact mechanism of the fluoride matrix on thermal conductivity is necessary and the effect of RE ions doping on thermal conductivity cannot be considered only. Pure crystals of BaF 2 have a lower thermal conductivity than CaF 2 , as Fig. 8 c illustrates. The direct effect of the fluoride matrix on the thermal conductivity trend cannot be entirely reversed by doping RE ions, even though the thermal conductivity declines through doping RE ions. As a result, the thermal conductivity of La/Yb:BaF 2 is lower 4 , 21 – 24 . 3 Influence of different concentration mass and radius phonon scattering on thermal conductivity of RE ion-doped fluoride crystals The phonon scattering coefficient primarily includes radius scattering and mass scattering in the system structure, as shown in Eq. ( 1 ), which states that the thermal conductivity values of RE ion-doped fluoride crystals are closely related to the difference of mass and radius in the microstructure, such as point defects and clusters. The mass/radius scattering of the point defect and cluster phonon scattering coefficient mechanism of RE ion-doped fluoride crystals are researched, and the relationship between the variation of thermal conductivity of RE ion-doped fluoride and the microstructure of mass and radius is described 27 – 32 . 3.1 Influence of low-concentration mass and radius phonon scattering on thermal conductivity The RE ions replacement and interstitial fluoride ions compensation appear in the doped calcium fluoride system at low doping concentrations, resulting in a high concentration of point defects. The formation of point defects causes the shortwave phonon scattering of RE ion-doped fluoride to rise, and the thermal conductivity values reduce. The impact of radius and mass scattering on the thermal conductivity of RE ion-doped fluoride is concretely studied based on the point defect phonon scattering in 2.1 above. As illustrated in Figs. 9 and 1 a, the mass scattering and total scattering of RE ion-doped CaF 2 exhibit comparable variation tendencies and approximately equal values. The mass scattering values of RE ion-doped CaF 2 are significantly greater than the radius scattering values. Therefore, the mass difference between RE ions and lattice Ca ions is dominant. The mass phonon scattering of RE ion-doped CaF 2 influences the heat conduction behavior, the system's thermal conductivity changes from a crystalline to a crystal-like state, and the thermal conductivity value reduces but the changing trend does not significantly alter. Furthermore, when the doping concentration of RE ions increases, the mass scattering of the doped CaF 2 growth trend gradually slows down, and the radius scattering growth trend steadily increases. The radius scattering of RE ion-doped CaF 2 could have a significant impact on the thermal conductivity from a crystal-like state to a glass-like state with high doping concentration 30 , 33 , 34 . For different RE ions doping, both mass and radius scattering increase with the increase of atomic number, which is consistent with the variation rule of the total phonon scattering coefficient. As demonstrated in the supplemental information, comparable results have also been reached for SrF 2 and BaF 2 systems doped with RE ions (Figs. S1 and S2). The mass and radius phonon scattering coefficients of low doping Y/La/Yb:Ca/Sr/BaF 2 systems are extracted, and the thermal conductivity of various fluoride matrices is proved, as shown in Fig. 10 . For the different fluoride matrices, the CaF 2 inset with RE ions has the highest mass phonon scattering coefficients (Fig. 10 a). However, the largest radius scattering coefficient is seen in the RE ion-doped BaF 2 , as shown in Fig. 10 b. The radius and mass scattering coefficients are opposite influences on the fluoride matrices with low doping concentrations. Compared to the radius scattering coefficient, the mass scattering coefficient is substantially greater. Hence, the mass scattering coefficient displays a profound impact on thermal conductivity. In the low doping concentration, the calcium fluoride systems’ thermal conductivity diminishes, resulting in heat transfer behavior that is similar to that of the crystal. The contribution of mass scattering and radius scattering of RE ion-doped fluoride to the thermal conductivity at low doping concentration is investigated, as shown in Fig. 11 , as the thermal conductivity can be calculated using Eq. (2) 19 . When the doping concentration is less than 1 at.%, the impact of mass and radius phonon scattering on thermal conductivity is noticeable. The variation trend of thermal conductivity is steadily stable with doping concentration when the doping concentration is more than 1at.%. Similar to the total defect phonon scattering, mass phonon scattering has a considerable influence on thermal conductivity, leading to the decline of thermal conductivity. The thermal conductivity is barely impacted by radius phonon scattering 35 , 36 . In addition, the thermal conductivity estimated by mass and radius scattering coefficients is low when various RE ion species have large RE atomic numbers. For RE ion-doped SrF 2 and BaF 2 systems, there is a comparable variation tendency (see supplementary information Figs. S3 and S4). 3.2 Influence of high-concentration mass and radius phonon scattering on thermal conductivity Under high-concentration doping, the point defects of RE ions gradually gather to form clusters, leading to the scattering of long-wavelength phonons, which reduce the thermal conductivity and further transform into an amorphous state. Based on the cluster phonon scattering coefficients in 2.2 above, the specific influence factors and value ranges of cluster mass scattering and radius scattering on the thermal conductivity of RE ion-doped fluoride are investigated, for example, the CaF 2 systems. Due to the high doping concentrations, the crystal systems form several different kinds of clusters. The mass and radius scattering coefficients are calculated by taking the highest-order cluster as an example. Figure 12 illustrates mass and radius phonon scattering steadily enhance as high doping concentration and atomic number, which exerts the opposite influence on the doped fluoride systems’ thermal conductivity. Moreover, the changing trend of both the mass and radius scattering coefficients with doping concentration are comparable to total defect phonon scattering (Fig. 5 a). The cluster radius phonon scattering coefficients are larger than the cluster mass phonon scattering coefficients. Then, the cluster radius phonon scattering coefficients vary considerably more than that of point defects. Consequently, the radius scattering is sensitive to cluster generation behavior. The impact of radius scattering on the trend change in the thermal conductivity of RE ion-doped fluoride (from crystalline to amorphous thermal conductivity) is necessary, and it plays a major role 37 – 39 . The mass and radius scattering of the highest-order clusters grows with the increasing atomic number for various RE ions doping. The system of SrF 2 doped with RE ions exhibits the same conclusions (supplemental information Fig.S5). Next, fluoride systems that generate various types of clusters are analyzed to further demonstrate the effects of mass phonon scattering and radius phonon scattering of clusters on the thermal conductivity of different crystal systems (Fig. 13 ). The mass and radius phonon scattering increase and the heat transfer reaction decreases as cluster complexity (from monomer to highest-order cluster) rise. Conversely, with SrF 2 and BaF 2 crystals, CaF 2 crystals possess larger cluster mass and radius scattering values. The RE ion-doped CaF 2 crystal is easier to alter to the glass-like state further demonstrating the critical role that cluster phonon scattering plays in reducing thermal conductivity and achieving glass-like thermal behavior. Using Eq. ( 1 ), the effect of cluster mass and radius differences on thermal conductivity is further evaluated. Figure 14 shows the trend of Y:Ca/Sr/BaF 2 thermal conductivity with doping concentration. The considerable changes in thermal conductivity induced by radius phonon scattering coefficient with doping concentration, and radius difference affects positively on the thermal conductivity of RE ion-doped fluoride at high doping concentrations. Among them, the radius scattering of various cluster types has a regular influence on the thermal conductivity of RE ion-doped fluoride. The highest-order cluster has a more substantial impact on thermal conductivity. The difference in radius scattering of various fluoride matrices on thermal conductivity is not easily observed. It is further demonstrated that radius phonon scattering makes the thermal conductivity transition to an amorphous state during the generation of clusters. Moreover, the mass and radius phonon scattering rise as the cluster combination degree increases. Under mass scattering and radius scattering, RE ion-doped fluoride's thermal conductivity exhibits abnormal thermal behavior. For different fluoride matrices, the thermal conductivity results due to mass and radius scattering of calcium fluoride are at the lowest value 35 , 38 – 43 . 4 Conclusion In conclusion, the investigation of RE ion-doped fluoride's abnormal thermal conductivity has been conducted, accompanying a thorough examination of the interaction between phonon scattering and thermal conductivity. Firstly, under different RE ions and fluoride matrices, the impact of diverse point defects and cluster structures at varying concentrations on thermal conductivity is explored. The relationship between the calculated thermal conductivity of phonon scattering and the actual measured thermal conductivity data has been analyzed. Furthermore, the influence of phonon scattering caused by the difference in mass and radius on the abnormal thermal properties of RE-doped fluoride has been systematically explored. The phonon scattering coefficient calculation has demonstrated that the thermal conductivity of fluoride crystals diminishes with increasing doping concentration and atomic number, which can rapidly transition into a glass-like state. The complexity and superposition of the clusters also lead to a decline in the thermal conductivity of RE ion-doped fluoride at high concentrations. Next, for various fluoride crystals, it has been discovered that CaF 2 crystals doped with RE ions are more susceptible to the formation concentration of clusters, leading to a transition of the glass-like thermal conductivity. Due to the large mass of Ba atoms in BaF 2 crystal, the thermal conductivity of RE ion-doped BaF 2 is not easy to transition to a glass-like state, but the thermal conductivity value is always at the lower value. Moreover, the calculated thermal conductivity of phonon scattering matches well with the actual measured thermal conductivity data. Additionally, it has been discovered that the thermal characteristics of RE ion-doped fluoride crystals are influenced by the mass and radius discrepancies between RE-doped ions and lattice ions in a variety of point defects and cluster structures. Among them, under the different concentrations, the variation in mass and radius causes the RE ion-doped fluoride's thermal conductivity to decrease. However, after the generation of clusters in high doping concentration, the radius scattering coefficient's variation degree is more than the mass scattering coefficient compared to the point defect with low concentration. It is mainly that radius disorder caused by the alteration in ionic radius, and this distortion of the lattice exhibits an association with the amorphous transformation of thermal conductivity. For various fluoride systems, the CaF 2 crystal has the highest mass scattering coefficient. Whereas CaF 2 has the biggest radius scattering coefficient at high concentrations, BaF 2 has the largest at low concentrations. These factors cause the system structure to become disorder, which finally causes the thermal conductivity of RE ion-doped fluorides to change to an amorphous state. Thus, the thermal behavior of RE ion-doped fluoride can be universality calculated and analyzed using the phonon scattering coefficient, which also offers theoretical support for other research fields on RE ion-doped fluoride systems. Consequently, further research on the heat conduction of RE ion-doped fluoride will better integrate theoretical simulations with experimental tests, creating the way for thorough thermal analyses of the RE ion-doped fluoride crystals and extending the range of applications. Nonetheless, additional investigation and validation are necessary due to the lack of intuitive structural characterization. Declarations Conflicts of interest There is no conflict of interest in this manuscript. Author Contribution Investigation, data curation, validation, formal analysis, and writing – original draft (Kexin Liu); resources, supervision, funding acquisition, project administration, and writing – review & editing (Dapeng Jiang, Gang Bian, Zhen Zhang, Zhonghan Zhang and Liangbi Su). All authors participated in discussing and editing the manuscripts. 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Song, Journal of the European Ceramic Society, 2023, 43, 6909–6915. G. Chen, C. Li, H. Jia, H. Li, S. Li, B. Gong, L. An and K. Chen, Journal of the European Ceramic Society, 2023, 43, 2586–2592. M. Tihtih, J. E. F. M. Ibrahim, M. A. Basyooni, E. Kurovics, W. Belaid, I. Hussainova and I. Kocserha, Ceramics International, 2023, 49, 1947–1959. A. J. Wright, Q. Wang, S.-T. Ko, K. M. Chung, R. Chen and J. Luo, Scripta Materialia, 2020, 181, 76–81. Y. Wang, Y.-J. Jin, T. Wei, Z.-G. Wang, G. Cao, Z.-Y. Ding, Z.-G. Liu, J.-H. Ouyang, Y.-J. Wang and Y.-M. Wang, Journal of Alloys and Compounds, 2022, 918. Additional Declarations No competing interests reported. Supplementary Files Supplementalmaterial.docx Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-5272029","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":366704301,"identity":"a1ea4f78-ad3b-4365-8598-c5d731207ab7","order_by":0,"name":"Kexin Liu","email":"","orcid":"","institution":"Chinese Academy of Sciences","correspondingAuthor":false,"prefix":"","firstName":"Kexin","middleName":"","lastName":"Liu","suffix":""},{"id":366704302,"identity":"2874b814-fc87-4d5b-940f-c91f199fe003","order_by":1,"name":"Dapeng Jiang","email":"","orcid":"","institution":"Chinese Academy of Sciences","correspondingAuthor":false,"prefix":"","firstName":"Dapeng","middleName":"","lastName":"Jiang","suffix":""},{"id":366704303,"identity":"185b6e43-ec2e-41a9-9e6d-a9d0ed829535","order_by":2,"name":"Gang Bian","email":"","orcid":"","institution":"Chinese Academy of Sciences","correspondingAuthor":false,"prefix":"","firstName":"Gang","middleName":"","lastName":"Bian","suffix":""},{"id":366704304,"identity":"c16d1b22-7645-46df-a8b8-4b6824bb7697","order_by":3,"name":"Zhen Zhang","email":"","orcid":"","institution":"Chinese Academy of Sciences","correspondingAuthor":false,"prefix":"","firstName":"Zhen","middleName":"","lastName":"Zhang","suffix":""},{"id":366704305,"identity":"abc09fd5-03ab-4ae4-b48d-cdd5f412f7da","order_by":4,"name":"Zhonghan Zhang","email":"","orcid":"","institution":"Chinese Academy of Sciences","correspondingAuthor":false,"prefix":"","firstName":"Zhonghan","middleName":"","lastName":"Zhang","suffix":""},{"id":366704306,"identity":"cf0e530d-d321-47ba-8dc5-ef1bd684126d","order_by":5,"name":"Liangbi Su","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABBUlEQVRIie2Rv2rDMBCHzxiUxc4sY4pfQWMLJX4VCc82BS8Z2qAu5yXd8xgBQ+ioIGiXZE+3di6FdHMphZ77Z1ScsVB9w50GfdzvOACP508SakNVspGmegHAhpXgR4moSXGk0lcJXFITR8TKFuravN1eVePkWe0fBeTjkQn2HUwqlyJ2Sq9vNvc1S8uWUzCFkQyTORS1U+FKmxjvFKblslck4wApgFHaHUyvP3ol2bYdKTkp4fshBSiYjfFSIY9X/ZQAObCDU8TmSdsTNDWLytWppJwYKTybi8IdrCns6wvOqqzZtg/d9DzPGmt33XTiDvaN/X3Q7l+XGj7QbPCHx+Px/GM+AQlqVqECGak7AAAAAElFTkSuQmCC","orcid":"","institution":"Chinese Academy of Sciences","correspondingAuthor":true,"prefix":"","firstName":"Liangbi","middleName":"","lastName":"Su","suffix":""}],"badges":[],"createdAt":"2024-10-16 02:38:13","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-5272029/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-5272029/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":66922519,"identity":"8debfc9f-25d9-473c-949f-02510ae0fbad","added_by":"auto","created_at":"2024-10-18 04:56:01","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":2579292,"visible":true,"origin":"","legend":"\u003cp\u003e(a)Point defect phonon scattering coefficients of RE:CaF\u003csub\u003e2\u003c/sub\u003e crystals with doping concentration; (b)Point defect phonon scattering coefficients of RE:SrF\u003csub\u003e2\u003c/sub\u003e crystals with doping concentration; (c)Point defect phonon scattering coefficients of RE:BaF\u003csub\u003e2\u003c/sub\u003e crystals with doping concentration.\u003c/p\u003e","description":"","filename":"Figure1.tif.png","url":"https://assets-eu.researchsquare.com/files/rs-5272029/v1/f2cf3480df51bd3844c0b77e.png"},{"id":66921208,"identity":"227675a7-cafb-4b56-bbb6-84f84460c4e8","added_by":"auto","created_at":"2024-10-18 04:32:01","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":2507845,"visible":true,"origin":"","legend":"\u003cp\u003e(a)Point defect phonon scattering coefficients of Y/La/Yb:Ca/Sr/BaF\u003csub\u003e2\u003c/sub\u003e crystals with doping concentration.\u003c/p\u003e","description":"","filename":"Figure2.tif.png","url":"https://assets-eu.researchsquare.com/files/rs-5272029/v1/7ce192a44f3bc6175b297781.png"},{"id":66921207,"identity":"a516a31c-d847-4187-b681-e759c89cc425","added_by":"auto","created_at":"2024-10-18 04:32:01","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":1456023,"visible":true,"origin":"","legend":"\u003cp\u003e(a)Variation law of thermal conductivity of RE:CaF\u003csub\u003e2\u003c/sub\u003e crystals with doping concentration; (b) Variation law of thermal conductivity of RE:SrF\u003csub\u003e2\u003c/sub\u003e crystals with doping concentration; (c) Variation law of thermal conductivity of RE:BaF\u003csub\u003e2\u003c/sub\u003e crystals with doping concentration.\u003c/p\u003e","description":"","filename":"Figure3.tif.png","url":"https://assets-eu.researchsquare.com/files/rs-5272029/v1/8e95a4b0d31eb022be35c2fd.png"},{"id":66922658,"identity":"d70d31e1-7320-4015-a9eb-2ce65f2bf923","added_by":"auto","created_at":"2024-10-18 05:04:01","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":1024711,"visible":true,"origin":"","legend":"\u003cp\u003e(a)Thermal conductivity of Ce:Ca/BaF\u003csub\u003e2\u003c/sub\u003e crystals with temperature (low doping concentration); (b) Thermal conductivity of Yb:Ca/Sr/BaF\u003csub\u003e2\u003c/sub\u003e crystals with temperature (low doping concentration).\u003c/p\u003e","description":"","filename":"Figure4.tif.png","url":"https://assets-eu.researchsquare.com/files/rs-5272029/v1/ace809e570e725e24efaf2c2.png"},{"id":66921786,"identity":"93946feb-cd20-4a66-8a71-52f963c8c4bc","added_by":"auto","created_at":"2024-10-18 04:48:01","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":765649,"visible":true,"origin":"","legend":"\u003cp\u003e(a)Cluster phonon scattering coefficients of RE:CaF\u003csub\u003e2\u003c/sub\u003e crystals with doping concentration; (b)Cluster phonon scattering coefficients of RE:SrF\u003csub\u003e2\u003c/sub\u003e crystals with doping concentration.\u003c/p\u003e","description":"","filename":"Figure5.tif.png","url":"https://assets-eu.researchsquare.com/files/rs-5272029/v1/d62423eb2ae6711f753d4f09.png"},{"id":66921713,"identity":"4cd1d8e2-b595-42a6-a2c0-19583ea84779","added_by":"auto","created_at":"2024-10-18 04:40:01","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":2024832,"visible":true,"origin":"","legend":"\u003cp\u003e(a)Cluster phonon scattering coefficients of La:Ca/SrF\u003csub\u003e2\u003c/sub\u003e crystals with doping concentration; (b)Cluster phonon scattering coefficients of Nd:Ca/SrF\u003csub\u003e2\u003c/sub\u003e crystals with doping concentration; (c) Cluster phonon scattering coefficients of Gd:Ca/SrF\u003csub\u003e2\u003c/sub\u003e crystals with doping concentration.\u003c/p\u003e","description":"","filename":"Figure6.tif.png","url":"https://assets-eu.researchsquare.com/files/rs-5272029/v1/bd95e2af57a268874f117171.png"},{"id":66921220,"identity":"f4901e34-e706-4377-83e1-7a8e8c0bd756","added_by":"auto","created_at":"2024-10-18 04:32:01","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":2332025,"visible":true,"origin":"","legend":"\u003cp\u003eCluster phonon scattering coefficients of Y:Ca/Sr/BaF\u003csub\u003e2\u003c/sub\u003e crystals with doping concentration.\u003c/p\u003e","description":"","filename":"Figure7.tif.png","url":"https://assets-eu.researchsquare.com/files/rs-5272029/v1/b4b30f46e9c47ed8ff0328e1.png"},{"id":66921213,"identity":"ff596d85-48c1-4570-b10c-cb5fefb1cc31","added_by":"auto","created_at":"2024-10-18 04:32:01","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":1505337,"visible":true,"origin":"","legend":"\u003cp\u003e(a)Thermal conductivity of Ce:Ca/BaF\u003csub\u003e2\u003c/sub\u003e crystals with temperature (high doping concentration); (b) Thermal conductivity of Yb:Ca/Sr/BaF\u003csub\u003e2\u003c/sub\u003e crystals with temperature (high doping concentration); (c) Thermal conductivity of Ca/Sr/BaF\u003csub\u003e2\u003c/sub\u003e crystals with temperature.\u003c/p\u003e","description":"","filename":"Figure8.tif.png","url":"https://assets-eu.researchsquare.com/files/rs-5272029/v1/f6eea9a580595e16b620e4c0.png"},{"id":66921717,"identity":"fb0500ae-ada1-4c0a-b136-2ff0b399824b","added_by":"auto","created_at":"2024-10-18 04:40:01","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":1615206,"visible":true,"origin":"","legend":"\u003cp\u003e(a)Mass phonon scattering coefficients of RE:CaF\u003csub\u003e2\u003c/sub\u003e crystals with low doping concentration; (b)Radius phonon scattering coefficients of RE:CaF\u003csub\u003e2\u003c/sub\u003e crystals with low doping concentration.\u003c/p\u003e","description":"","filename":"Figure9.tif.png","url":"https://assets-eu.researchsquare.com/files/rs-5272029/v1/acb9f56a5325ec98080ee119.png"},{"id":66921718,"identity":"40729ecd-3a4c-4d37-b52d-481fc316922c","added_by":"auto","created_at":"2024-10-18 04:40:01","extension":"png","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":1370012,"visible":true,"origin":"","legend":"\u003cp\u003e(a)Mass phonon scattering coefficients of Y/La/Yb:Ca/Sr/BaF\u003csub\u003e2\u003c/sub\u003e crystals with low doping concentration; (b)Radius phonon scattering coefficients of Y/La/Yb:Ca/Sr/BaF\u003csub\u003e2\u003c/sub\u003e crystals with low doping concentration.\u003c/p\u003e","description":"","filename":"Figure10.tif.png","url":"https://assets-eu.researchsquare.com/files/rs-5272029/v1/c5623c96c8cd5ca383fe1a24.png"},{"id":66921217,"identity":"34dc7e7b-5d84-476e-8fcb-35a9b18cff8a","added_by":"auto","created_at":"2024-10-18 04:32:01","extension":"png","order_by":11,"title":"Figure 11","display":"","copyAsset":false,"role":"figure","size":1048578,"visible":true,"origin":"","legend":"\u003cp\u003e(a) Variation law of thermal conductivity of RE:CaF\u003csub\u003e2\u003c/sub\u003e crystals in mass phonon scattering coefficients with low doping concentration; (b) Variation law of thermal conductivity of RE:CaF\u003csub\u003e2\u003c/sub\u003e crystals in radius phonon scattering coefficients with low doping concentration.\u003c/p\u003e","description":"","filename":"Figure11.tif.png","url":"https://assets-eu.researchsquare.com/files/rs-5272029/v1/f032f385fec712de1c9d3d3c.png"},{"id":66921216,"identity":"24343b8e-3acd-4369-aef7-c2b1beea79be","added_by":"auto","created_at":"2024-10-18 04:32:01","extension":"png","order_by":12,"title":"Figure 12","display":"","copyAsset":false,"role":"figure","size":924342,"visible":true,"origin":"","legend":"\u003cp\u003e(a)Mass phonon scattering coefficients of RE:CaF\u003csub\u003e2\u003c/sub\u003e crystals with high doping concentration; (b)Radius phonon scattering coefficients of RE:CaF\u003csub\u003e2\u003c/sub\u003e crystals with high doping concentration.\u003c/p\u003e","description":"","filename":"Figure12.tif.png","url":"https://assets-eu.researchsquare.com/files/rs-5272029/v1/a29de3994f02b8674242ed72.png"},{"id":66921215,"identity":"9fc4954a-41d3-4be0-82a0-85e908c8f79c","added_by":"auto","created_at":"2024-10-18 04:32:01","extension":"png","order_by":13,"title":"Figure 13","display":"","copyAsset":false,"role":"figure","size":1119491,"visible":true,"origin":"","legend":"\u003cp\u003e(a)Mass phonon scattering coefficients of Y:Ca/Sr/BaF\u003csub\u003e2\u003c/sub\u003e crystals with high doping concentration; (b)Radius phonon scattering coefficients of Y:Ca/Sr/BaF\u003csub\u003e2\u003c/sub\u003e crystals with high doping concentration.\u003c/p\u003e","description":"","filename":"Figure13.tif.png","url":"https://assets-eu.researchsquare.com/files/rs-5272029/v1/371cfc6c9becf5ed9274524e.png"},{"id":66921222,"identity":"d7c40e4b-e9be-49fa-b2e1-b532c7f710d6","added_by":"auto","created_at":"2024-10-18 04:32:01","extension":"png","order_by":14,"title":"Figure 14","display":"","copyAsset":false,"role":"figure","size":215978,"visible":true,"origin":"","legend":"\u003cp\u003e(a) Variation law of thermal conductivity of Y:Ca/Sr/BaF\u003csub\u003e2\u003c/sub\u003e crystals in mass phonon scattering coefficients with high doping concentration; (b) Variation law of thermal conductivity of Y:Ca/Sr/BaF\u003csub\u003e2\u003c/sub\u003e crystals in radius phonon scattering coefficients with high doping concentration.\u003c/p\u003e","description":"","filename":"Figure14.tif.png","url":"https://assets-eu.researchsquare.com/files/rs-5272029/v1/75486f1def02d61bf90a733a.png"},{"id":67559141,"identity":"428bce22-537e-4d27-bcb7-82aacbc43ea1","added_by":"auto","created_at":"2024-10-26 21:46:37","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":18727741,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5272029/v1/0e3d83c5-be39-49ad-9c36-c538790a0416.pdf"},{"id":66921221,"identity":"bae4ffba-97e8-44f9-bbbe-5ddddfcf4167","added_by":"auto","created_at":"2024-10-18 04:32:01","extension":"docx","order_by":16,"title":"","display":"","copyAsset":false,"role":"supplement","size":1496472,"visible":true,"origin":"","legend":"","description":"","filename":"Supplementalmaterial.docx","url":"https://assets-eu.researchsquare.com/files/rs-5272029/v1/29a7cae9eb986998ef464973.docx"}],"financialInterests":"No competing interests reported.","formattedTitle":"Calculating and analyzing the relationship between thermal conductivity and microstructure in rare-earth doped fluoride crystals","fulltext":[{"header":"1 Introduction","content":"\u003cp\u003eRE ion-doped fluoride crystals have garnered significant interest owing to their remarkable capabilities in laser, TBCs, thermoelectric material, and other domains\u003csup\u003e\u003cspan additionalcitationids=\"CR2\" citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e\u003c/sup\u003e. Among these, thermal behavior is a crucial performance that restricts the application of RE ion-doped fluoride crystals. Thermal conductivity equires additional optimization based on the application fields. The thermal conductivity of RE ion-doped fluoride shows abnormal behavior. When RE ions are inserted in fluoride crystals, the thermal conductivity exhibits significant abnormal characteristics. For instance, when Yb\u003csup\u003e3+\u003c/sup\u003e are doped at 0.1 at.%, the thermal conductivity drops by 50% compared to pure CaF\u003csub\u003e2\u003c/sub\u003e crystals\u003csup\u003e\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e, \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e\u003c/sup\u003e. Furthermore, the thermal conductivity of RE ion-doped fluoride single crystal transitions from a crystalline state to an amorphous state as the doping concentration rises.\u003c/p\u003e \u003cp\u003eIn previous work\u003csup\u003e\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e\u003c/sup\u003e, RE ions replace calcium ions in RE ion-doped fluoride crystal structures to form interstitial fluoride ions, which cause point defects. The number of RE ion clusters rises as the doping concentration increases because of the dipole action that aggregates the RE ions into clusters. The thermal conductivity eventually drops and the thermal conductivity behavior is similar to that of glass. Among them, the primary reason for the continuous change in thermal conductivity between crystalline and amorphous with concentration is that in RE ion-doped fluoride, disordered structures like point defects and clusters coexist with the original fluoride lattice order structure, which leads the competition between defect phonon scattering and phonon-phonon scattering with concentration \u003csup\u003e\u003cspan additionalcitationids=\"CR8 CR9\" citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eTherefore, based on the point defects and cluster structure transformation, the effects of various cluster structures generated by RE ion-doped fluoride crystals at different doping concentrations on the thermal conductivity are explored by phonon scattering coefficient calculation. The influences of different doping ions and fluoride matrices in RE ion-doped fluoride crystals on the thermal conductivity are provided\u003csup\u003e\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e, \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e\u003c/sup\u003e. In different RE ion-doped fluoride systems, the calculated results of the phonon scattering coefficient have a favorable correlation with the variation of thermal conductivity of RE ion-doped fluoride crystals, providing a qualitative explanation for the abnormal thermal behavior of RE ion-doped fluoride crystals\u003csup\u003e\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eIn addition, the differences between RE ions and lattice ions in RE ion-doped fluoride are analyzed by using the intrinsic characteristics of various cluster structures. The impact of variations in mass and radius on thermal conductivity is thoroughly discussed. The refinement and classification of mass field and strain field on the glass state transition of thermal conductivity are explored, and the factors influencing the transition from a crystalline to an amorphous state of RE ion-doped fluoride crystal are provided with a detailed explanation.\u003c/p\u003e"},{"header":"2 Microstructure influences the thermal conductivity of RE ion-doped fluoride crystals","content":"\u003cp\u003eThe insertion of RE ions into fluoride crystals significantly alters the system's microstructure, leading to the abnormal variation in thermal conductivity. According to the variation trend of thermal conductivity with doping concentration, it can be divided into two stages. With lower doping concentrations (\u0026lt; 1 at.%), the RE ion-doped fluoride systems mainly generate point defects and exhibit a transition in thermal conductivity between a crystalline state and a crystalline-like state. At high doping concentrations (\u0026gt; 1 at.%), the complex cluster structure predominantly influences the thermal conductivity of RE ion-doped fluorides, displaying thermal behavior comparable to that of glass. The influences of point defects and clusters on the thermal conductivity of RE ion-doped fluoride crystals are discussed.\u003c/p\u003e \u003cp\u003eA parameter called phonon scattering coefficient is introduced to describe the thermal behavior of RE ion-doped fluorides\u003csup\u003e\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e\u003c/sup\u003e. The decisive factor of phonon scattering is the structure modification of RE ion-doped fluorides, that is, the variation trends of the mass and radius with doping. The phonon scattering coefficient is calculated by Eq.\u0026nbsp;(\u003cspan refid=\"Equ1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). The thermal conductivity of the fluoride crystals is related to the scattering of phonons, as shown in Eq.\u0026nbsp;(2)\u003csup\u003e13\u003c/sup\u003e. Hence, the phonon scattering coefficient reveals the relationship between the microstructure and the thermal conductivity variation in RE ion-doped fluorides.\u003c/p\u003e\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\Gamma ={x_i}\\left[ {{{\\left( {\\frac{{{M_i} - \\overline {M} }}{{\\overline {M} }}} \\right)}^2}+\\varepsilon {{\\left( {\\frac{{{\\delta _i} - \\overline {\\delta } }}{{\\overline {\\delta } }}} \\right)}^2}} \\right]$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$$\\:\\kappa\\:\\propto\\:{{\\Gamma\\:}}^{-0.5}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e\u003cp\u003e\u003c/p\u003e \u003cp\u003eWhere i represents element species of RE ion-doped fluorides; x stands for the proportion of elements; M represents the atomic mass of RE ion-doped fluorides; δ stands for the ion radius of RE ion-doped fluorides.\u003c/p\u003e \u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1 Point defects influence RE ion-doped fluorides' thermal conductivity with low doping concentration\u003c/h2\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eWhen doping a modest amount of RE ions, the doped fluoride systems produce point defects, which cause progressive disorder, intense phonon scattering, and diminished thermal conductivity. The relationship between the point defect phonon scattering coefficients of doped with CaF\u003csub\u003e2\u003c/sub\u003e, SrF\u003csub\u003e2,\u003c/sub\u003e and BaF\u003csub\u003e2\u003c/sub\u003e for different kinds of RE doped with concentration is calculated according to Eq.\u0026nbsp;(\u003cspan refid=\"Equ1\" class=\"InternalRef\"\u003e1\u003c/span\u003e), as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, to investigate the variation of the point defect phonon scattering coefficients in fluoride crystals with doping RE ions. Figure\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ea shows that the point defect phonon scattering coefficients change approximately as a linear function relation with the concentration when the doping concentration is less than 0.1 at.%. Next, the increasing trends of point defect phonon scattering coefficients steadily slow down as the doping concentration increases. When reaching a certain doping concentration, the point defect phonon scattering coefficients are close to a maximum value. In other words, the point defects significantly impact the RE:CaF\u003csub\u003e2\u003c/sub\u003e systems' thermal conductivity at this concentration. The point defects caused by the doping of RE ions start to transform into clusters under the influence of dipole interaction, and the factors of clusters on the thermal conductivity then start to dominate\u003csup\u003e\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eFurthermore, the point defect phonons scattering coefficients increase with the number of doped RE atoms rising, as indicated by the curve variation rule in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ea. This phenomenon may be due to the gradual increase in the difference between the mass and radius of RE ions and the lattice calcium ions. As a result, the system's mass field and strain field fluctuations enhance, lattice distortion and disorder degree surrounding RE ions increase, and the phonon scattering becomes intense\u003csup\u003e\u003cspan additionalcitationids=\"CR15\" citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e–\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e\u003c/sup\u003e. By comparing the point defect phonon scattering coefficients with the atomic number of different fluoride crystals doped with RE ions, similar conclusions can also be obtained in RE ion-doped SrF\u003csub\u003e2\u003c/sub\u003e crystal systems (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eb). Whereas, the scattering coefficients of point defect phonons of RE ion-doped BaF\u003csub\u003e2\u003c/sub\u003e crystals are slightly opposite to that of CaF\u003csub\u003e2\u003c/sub\u003e and SrF\u003csub\u003e2\u003c/sub\u003e systems (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ec). Among them, the point defect phonon scattering coefficient of the Y:BaF\u003csub\u003e2\u003c/sub\u003e system is significantly larger than that of the BaF\u003csub\u003e2\u003c/sub\u003e crystals doped with lanthanide RE ions \u003csup\u003e\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e\u003c/sup\u003e. The main reason is the mass and radius difference between Y\u003csup\u003e3+\u003c/sup\u003e and Ba\u003csup\u003e2+\u003c/sup\u003e is greater than that of the lanthanide RE ions and Ba\u003csup\u003e2+\u003c/sup\u003e, while the mass and radius difference between Y and Ca/Sr ions is smaller than that between lanthanide RE ions and Ca/Sr ions.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe variation trends and maximum values of the point defect phonon scattering coefficient differ for various fluoride systems. According to Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e, the point defect phonon scattering coefficient in RE ion-doped CaF\u003csub\u003e2\u003c/sub\u003e crystals changes sharply with doping concentration. Compared with the SrF\u003csub\u003e2\u003c/sub\u003e and BaF\u003csub\u003e2\u003c/sub\u003e systems, the RE ion-doped CaF\u003csub\u003e2\u003c/sub\u003e systems have higher peak values of the point defect phonon scattering coefficients. Moreover, the doping concentration of CaF\u003csub\u003e2\u003c/sub\u003e crystal is the lowest when it reaches the peak of the point-defect phonon scattering coefficient (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). In other terms, CaF\u003csub\u003e2\u003c/sub\u003e crystal embedded with RE ions is more likely to produce point defect to cluster transformation, resulting in more severe phonon scattering.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe relationship between the point defect phonon scattering coefficient and thermal conductivity of RE ion-doped fluorides can be semi-quantitatively analyzed\u003csup\u003e\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e\u003c/sup\u003e by a functional relationship (Eq.\u0026nbsp;(\u003cspan refid=\"Equ2\" class=\"InternalRef\"\u003e2\u003c/span\u003e))\u003csup\u003e\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e\u003c/sup\u003e. Figure\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e illustrates the variation rule of thermal conductivity that can be derived by the point defect phonon scattering coefficient of RE ion-doped Ca/Sr/BaF\u003csub\u003e2\u003c/sub\u003e (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). At the doping concentration of ≤ 1 at.%, the thermal conductivity rapidly decreases, and then is stable with the doping concentration rising\u003csup\u003e\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e, \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eThe increasing doping atomic number leads to an obvious changing trend of thermal conductivity and inferior thermal conductivity values. At low concentrations, the thermal conductivity of RE ion-doped fluorides varies dramatically due to the change in atomic types. However, as the doping concentration increases, the difference in fluoride systems’ thermal conductivity with different atomic types becomes less noticeable. For different fluoride systems, the changing trend of thermal conductivity of CaF\u003csub\u003e2\u003c/sub\u003e crystals is more significant and the thermal conductivity value reduces drastically. Additionally, the glass-like thermal conductivity transition of RE ion-doped fluorides is qualitatively explored by contrasting the calculated and measured thermal conductivity values.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFirstly, by comparing the doping of different kinds of RE ions, the 0.5 at.%Yb:CaF\u003csub\u003e2\u003c/sub\u003e has been transformed into glass-like thermal conductivity, while the glass-like thermal conductivity of 1at.%Ce:CaF\u003csub\u003e2\u003c/sub\u003e is not distinct. Therefore, RE ion-doped fluoride systems with large atomic numbers are prone to glass-like thermal conductivity behavior. It is consistent with the previous conclusion that fluoride crystals with large atomic numbers have low thermal conductivity and considerable phonon scattering.\u003c/p\u003e \u003cp\u003eThe CaF\u003csub\u003e2\u003c/sub\u003e crystal system has strong point defect phonon scattering, the thermal conductivity value decreases rapidly, and the transition from crystalline to amorphous thermal conductivity is more likely to occur under the same doping concentrations and types of doping atoms when only evaluating the doping concentration without taking the influence of the fluoride matrix on thermal conductivity. The variation of thermal conductivity is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e (red dotted lines). The thermal conductivity data drop substantially with large point defect phonon scattering coefficient in the RE ion-doped CaF\u003csub\u003e2\u003c/sub\u003e systems, which also has a similar relationship with the above-mentioned\u003csup\u003e\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e, \u003cspan additionalcitationids=\"CR22 CR23\" citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e–\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.2 Clusters influence RE ion-doped fluorides' thermal conductivity with high doping concentration\u003c/h2\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eIt is assumed that the configurations of clusters change to the highest order under extremely high doping concentrations. According to Eq.\u0026nbsp;(\u003cspan refid=\"Equ1\" class=\"InternalRef\"\u003e1\u003c/span\u003e), the variation laws of cluster phonon scattering coefficient with concentration are calculated, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e. The cluster phonon scattering coefficient in RE ion-doped fluoride crystals grows progressively and shows a great tendency as concentration increases. This phenomenon indicates that cluster phonon scattering has an additive effect as the number of clusters rises, which causes extreme changes in thermal conductivity and the transition from a crystalline to an amorphous state. In addition, the cluster scattering coefficient increases with the atomic number of doped RE ions, which exerts enormous influences on the thermal conductivity of crystals (according to Eq.\u0026nbsp;(\u003cspan refid=\"Equ2\" class=\"InternalRef\"\u003e2\u003c/span\u003e))\u003csup\u003e\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e, \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eDepending on the difference in doping atomic types, the thermal conductivity is connected to the phonon scattering coefficients of highest-order cluster configurations. For the lanthanide RE elements with small atomic numbers, the highest-order clusters of the RE ion-doped fluoride systems have relatively small order and simple configurations. As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003ea, the highest-order clusters are a tetramer, and the cluster phonon scattering coefficients are low when the doped RE ions are La, Ce, Pr, and other low atomic number elements, which has little influence on the change trend and value of thermal conductivity. However, the highest-order cluster is hexamer when the doped RE ions are Ho, Er, Yb, and Lu. The increase of cluster phonon scattering coefficients causes the thermal conductivity to transition into an amorphous state\u003csup\u003e\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e, \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eAs illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e, the influences of various cluster structure types on the cluster phonon scattering and thermal conductivity are examined. In La/Nd/Gd:Ca/SrF\u003csub\u003e2\u003c/sub\u003e crystal systems, the cluster phonon scattering coefficients of all kinds of cluster configurations are gradually enhanced with doping concentration, and the growth rate accelerates dramatically at high concentrations. It is demonstrated that the increase of doping concentration has a beneficial effect on the cluster phonon scattering coefficient, aggregation degree increases rapidly, thermal conductivity exhibits a significant amorphous change, and thermal conductivity values fall abruptly. Furthermore, under the same concentration of RE ions doping, the cluster configuration progressively becomes more complex, indicating that the cluster phonon scattering coefficient increases. The cluster configuration gradually transforms from a monomer to a higher-order configuration, such as a dimer, trimer, tetramer, or pentamer, and the cluster phonon scattering steadily enhances. In a word, the doping concentration of RE ions and intricate cluster configuration result in phonon scattering, which leads to the enhancement of thermal resistance and the decrease of thermal conductivity.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eTo further study the influence mechanism of different kinds of fluoride matrices on thermal conductivity in RE ion-doped fluorides, Y:CaF\u003csub\u003e2\u003c/sub\u003e, Y: SrF\u003csub\u003e2,\u003c/sub\u003e and Y:BaF\u003csub\u003e2\u003c/sub\u003e are taken as examples, as illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e. It further proves the impact of doping concentrations and cluster types on thermal conductivity. The thermal conductivity declines abruptly in complex clusters and high doping concentrations. For various fluoride matrices, the cluster phonon scattering coefficient of the Y:CaF\u003csub\u003e2\u003c/sub\u003e system changes strongly with doping concentration and doping has an obvious negative effect on heat transfer behavior. The relationship between the scattering coefficient of cluster phonons and thermal conductivity will not be demonstrated again, since the relationship between phonon scattering and thermal conductivity is already provided in Eq.\u0026nbsp;(\u003cspan refid=\"Equ2\" class=\"InternalRef\"\u003e2\u003c/span\u003e) and explained in 2.1 above. Next, the heat transfer of glass-like thermal conductivity in fluoride systems is analyzed by comparing the calculated thermal conductivity values with the measured thermal conductivity data\u003csup\u003e\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e, \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eInitially, the system's thermal conductivity transitions into a glass-like thermal behavior when the doping concentration is ≤ 1at.%. The 1 at.% Ce:BaF\u003csub\u003e2\u003c/sub\u003e and 1 at.% Yb:BaF\u003csub\u003e2\u003c/sub\u003e both show crystalline thermal conductivity behavior, however the thermal conductivity of 1 at.% Ce:CaF\u003csub\u003e2\u003c/sub\u003e and 1 at.% Yb:CaF\u003csub\u003e2\u003c/sub\u003e has started to change to a glass-like state. Among them, 1 at.% Yb:CaF\u003csub\u003e2\u003c/sub\u003e has a more apparent glass-like thermal conductivity than 1 at.% Ce:CaF\u003csub\u003e2\u003c/sub\u003e, as demonstrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003ea,b (purple dotted lines). The thermal conductivity behavior is negatively impacted by atomic number and it is relatively easy to obtain a thermal conductivity behavior similar to that of glass. It is deduced that the thermal conductivity of RE ion-doped fluoride systems can transition from a crystalline state to a non-crystalline state within a critical value, which is approximately 1at.%. It is also confirmed that the cluster phonon scattering coefficients of RE ion-doped CaF\u003csub\u003e2\u003c/sub\u003e systems are higher in each cluster configuration than those of the SrF\u003csub\u003e2\u003c/sub\u003e systems. RE ions doping on CaF\u003csub\u003e2\u003c/sub\u003e crystals are more likely to produce a transition from crystalline thermal conductivity to amorphous thermal conductivity.\u003c/p\u003e \u003cp\u003eAs illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003ea and b (yellow dotted lines), the thermal conductivity of Ce/Yb:CaF\u003csub\u003e2\u003c/sub\u003e in the high-temperature region is greater than that of Ce/Yb:BaF\u003csub\u003e2\u003c/sub\u003e, despite the system's thermal conductivity changing to a glass-like thermal conductivity with high doping concentration. The impact mechanism of the fluoride matrix on thermal conductivity is necessary and the effect of RE ions doping on thermal conductivity cannot be considered only. Pure crystals of BaF\u003csub\u003e2\u003c/sub\u003e have a lower thermal conductivity than CaF\u003csub\u003e2\u003c/sub\u003e, as Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003ec illustrates. The direct effect of the fluoride matrix on the thermal conductivity trend cannot be entirely reversed by doping RE ions, even though the thermal conductivity declines through doping RE ions. As a result, the thermal conductivity of La/Yb:BaF\u003csub\u003e2\u003c/sub\u003e is lower\u003csup\u003e\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e, \u003cspan additionalcitationids=\"CR22 CR23\" citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e–\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003c/div\u003e "},{"header":"3 Influence of different concentration mass and radius phonon scattering on thermal conductivity of RE ion-doped fluoride crystals","content":"\u003cp\u003eThe phonon scattering coefficient primarily includes radius scattering and mass scattering in the system structure, as shown in Eq.\u0026nbsp;(\u003cspan refid=\"Equ1\" class=\"InternalRef\"\u003e1\u003c/span\u003e), which states that the thermal conductivity values of RE ion-doped fluoride crystals are closely related to the difference of mass and radius in the microstructure, such as point defects and clusters. The mass/radius scattering of the point defect and cluster phonon scattering coefficient mechanism of RE ion-doped fluoride crystals are researched, and the relationship between the variation of thermal conductivity of RE ion-doped fluoride and the microstructure of mass and radius is described \u003csup\u003e\u003cspan additionalcitationids=\"CR28 CR29 CR30 CR31\" citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e–\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e\u003ch2\u003e3.1 Influence of low-concentration mass and radius phonon scattering on thermal conductivity\u003c/h2\u003e\u003cp\u003e \u003c/p\u003e\u003cp\u003eThe RE ions replacement and interstitial fluoride ions compensation appear in the doped calcium fluoride system at low doping concentrations, resulting in a high concentration of point defects. The formation of point defects causes the shortwave phonon scattering of RE ion-doped fluoride to rise, and the thermal conductivity values reduce. The impact of radius and mass scattering on the thermal conductivity of RE ion-doped fluoride is concretely studied based on the point defect phonon scattering in 2.1 above. As illustrated in Figs.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003e and \u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ea, the mass scattering and total scattering of RE ion-doped CaF\u003csub\u003e2\u003c/sub\u003e exhibit comparable variation tendencies and approximately equal values. The mass scattering values of RE ion-doped CaF\u003csub\u003e2\u003c/sub\u003e are significantly greater than the radius scattering values. Therefore, the mass difference between RE ions and lattice Ca ions is dominant. The mass phonon scattering of RE ion-doped CaF\u003csub\u003e2\u003c/sub\u003e influences the heat conduction behavior, the system's thermal conductivity changes from a crystalline to a crystal-like state, and the thermal conductivity value reduces but the changing trend does not significantly alter. Furthermore, when the doping concentration of RE ions increases, the mass scattering of the doped CaF\u003csub\u003e2\u003c/sub\u003e growth trend gradually slows down, and the radius scattering growth trend steadily increases. The radius scattering of RE ion-doped CaF\u003csub\u003e2\u003c/sub\u003e could have a significant impact on the thermal conductivity from a crystal-like state to a glass-like state with high doping concentration\u003csup\u003e\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e, \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e, \u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e\u003c/sup\u003e. For different RE ions doping, both mass and radius scattering increase with the increase of atomic number, which is consistent with the variation rule of the total phonon scattering coefficient. As demonstrated in the supplemental information, comparable results have also been reached for SrF\u003csub\u003e2\u003c/sub\u003e and BaF\u003csub\u003e2\u003c/sub\u003e systems doped with RE ions (Figs. S1 and S2).\u003c/p\u003e\u003cp\u003e \u003c/p\u003e\u003cp\u003eThe mass and radius phonon scattering coefficients of low doping Y/La/Yb:Ca/Sr/BaF\u003csub\u003e2\u003c/sub\u003e systems are extracted, and the thermal conductivity of various fluoride matrices is proved, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003e. For the different fluoride matrices, the CaF\u003csub\u003e2\u003c/sub\u003e inset with RE ions has the highest mass phonon scattering coefficients (Fig.\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003ea). However, the largest radius scattering coefficient is seen in the RE ion-doped BaF\u003csub\u003e2\u003c/sub\u003e, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003eb. The radius and mass scattering coefficients are opposite influences on the fluoride matrices with low doping concentrations. Compared to the radius scattering coefficient, the mass scattering coefficient is substantially greater. Hence, the mass scattering coefficient displays a profound impact on thermal conductivity. In the low doping concentration, the calcium fluoride systems’ thermal conductivity diminishes, resulting in heat transfer behavior that is similar to that of the crystal.\u003c/p\u003e\u003cp\u003e \u003c/p\u003e\u003cp\u003eThe contribution of mass scattering and radius scattering of RE ion-doped fluoride to the thermal conductivity at low doping concentration is investigated, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig11\" class=\"InternalRef\"\u003e11\u003c/span\u003e, as the thermal conductivity can be calculated using Eq.\u0026nbsp;(2) \u003csup\u003e19\u003c/sup\u003e. When the doping concentration is less than 1 at.%, the impact of mass and radius phonon scattering on thermal conductivity is noticeable. The variation trend of thermal conductivity is steadily stable with doping concentration when the doping concentration is more than 1at.%. Similar to the total defect phonon scattering, mass phonon scattering has a considerable influence on thermal conductivity, leading to the decline of thermal conductivity. The thermal conductivity is barely impacted by radius phonon scattering\u003csup\u003e\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e, \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e\u003c/sup\u003e. In addition, the thermal conductivity estimated by mass and radius scattering coefficients is low when various RE ion species have large RE atomic numbers. For RE ion-doped SrF\u003csub\u003e2\u003c/sub\u003e and BaF\u003csub\u003e2\u003c/sub\u003e systems, there is a comparable variation tendency (see supplementary information Figs. S3 and S4).\u003c/p\u003e\u003ch2\u003e3.2 Influence of high-concentration mass and radius phonon scattering on thermal conductivity\u003c/h2\u003e\u003cp\u003e \u003c/p\u003e\u003cp\u003eUnder high-concentration doping, the point defects of RE ions gradually gather to form clusters, leading to the scattering of long-wavelength phonons, which reduce the thermal conductivity and further transform into an amorphous state. Based on the cluster phonon scattering coefficients in 2.2 above, the specific influence factors and value ranges of cluster mass scattering and radius scattering on the thermal conductivity of RE ion-doped fluoride are investigated, for example, the CaF\u003csub\u003e2\u003c/sub\u003e systems. Due to the high doping concentrations, the crystal systems form several different kinds of clusters. The mass and radius scattering coefficients are calculated by taking the highest-order cluster as an example. Figure\u0026nbsp;\u003cspan refid=\"Fig12\" class=\"InternalRef\"\u003e12\u003c/span\u003e illustrates mass and radius phonon scattering steadily enhance as high doping concentration and atomic number, which exerts the opposite influence on the doped fluoride systems’ thermal conductivity. Moreover, the changing trend of both the mass and radius scattering coefficients with doping concentration are comparable to total defect phonon scattering (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003ea). The cluster radius phonon scattering coefficients are larger than the cluster mass phonon scattering coefficients. Then, the cluster radius phonon scattering coefficients vary considerably more than that of point defects. Consequently, the radius scattering is sensitive to cluster generation behavior. The impact of radius scattering on the trend change in the thermal conductivity of RE ion-doped fluoride (from crystalline to amorphous thermal conductivity) is necessary, and it plays a major role\u003csup\u003e\u003cspan additionalcitationids=\"CR38\" citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e–\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e\u003c/sup\u003e. The mass and radius scattering of the highest-order clusters grows with the increasing atomic number for various RE ions doping. The system of SrF\u003csub\u003e2\u003c/sub\u003e doped with RE ions exhibits the same conclusions (supplemental information Fig.S5).\u003c/p\u003e\u003cp\u003e \u003c/p\u003e\u003cp\u003eNext, fluoride systems that generate various types of clusters are analyzed to further demonstrate the effects of mass phonon scattering and radius phonon scattering of clusters on the thermal conductivity of different crystal systems (Fig.\u0026nbsp;\u003cspan refid=\"Fig13\" class=\"InternalRef\"\u003e13\u003c/span\u003e). The mass and radius phonon scattering increase and the heat transfer reaction decreases as cluster complexity (from monomer to highest-order cluster) rise. Conversely, with SrF\u003csub\u003e2\u003c/sub\u003e and BaF\u003csub\u003e2\u003c/sub\u003e crystals, CaF\u003csub\u003e2\u003c/sub\u003e crystals possess larger cluster mass and radius scattering values. The RE ion-doped CaF\u003csub\u003e2\u003c/sub\u003e crystal is easier to alter to the glass-like state further demonstrating the critical role that cluster phonon scattering plays in reducing thermal conductivity and achieving glass-like thermal behavior.\u003c/p\u003e\u003cp\u003e \u003c/p\u003e\u003cp\u003eUsing Eq.\u0026nbsp;(\u003cspan refid=\"Equ1\" class=\"InternalRef\"\u003e1\u003c/span\u003e), the effect of cluster mass and radius differences on thermal conductivity is further evaluated. Figure\u0026nbsp;\u003cspan refid=\"Fig14\" class=\"InternalRef\"\u003e14\u003c/span\u003e shows the trend of Y:Ca/Sr/BaF\u003csub\u003e2\u003c/sub\u003e thermal conductivity with doping concentration. The considerable changes in thermal conductivity induced by radius phonon scattering coefficient with doping concentration, and radius difference affects positively on the thermal conductivity of RE ion-doped fluoride at high doping concentrations. Among them, the radius scattering of various cluster types has a regular influence on the thermal conductivity of RE ion-doped fluoride. The highest-order cluster has a more substantial impact on thermal conductivity. The difference in radius scattering of various fluoride matrices on thermal conductivity is not easily observed. It is further demonstrated that radius phonon scattering makes the thermal conductivity transition to an amorphous state during the generation of clusters. Moreover, the mass and radius phonon scattering rise as the cluster combination degree increases. Under mass scattering and radius scattering, RE ion-doped fluoride's thermal conductivity exhibits abnormal thermal behavior. For different fluoride matrices, the thermal conductivity results due to mass and radius scattering of calcium fluoride are at the lowest value\u003csup\u003e\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e, \u003cspan additionalcitationids=\"CR39 CR40 CR41 CR42\" citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e–\u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e43\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e"},{"header":"4 Conclusion","content":"\u003cp\u003eIn conclusion, the investigation of RE ion-doped fluoride's abnormal thermal conductivity has been conducted, accompanying a thorough examination of the interaction between phonon scattering and thermal conductivity. Firstly, under different RE ions and fluoride matrices, the impact of diverse point defects and cluster structures at varying concentrations on thermal conductivity is explored. The relationship between the calculated thermal conductivity of phonon scattering and the actual measured thermal conductivity data has been analyzed. Furthermore, the influence of phonon scattering caused by the difference in mass and radius on the abnormal thermal properties of RE-doped fluoride has been systematically explored.\u003c/p\u003e \u003cp\u003eThe phonon scattering coefficient calculation has demonstrated that the thermal conductivity of fluoride crystals diminishes with increasing doping concentration and atomic number, which can rapidly transition into a glass-like state. The complexity and superposition of the clusters also lead to a decline in the thermal conductivity of RE ion-doped fluoride at high concentrations. Next, for various fluoride crystals, it has been discovered that CaF\u003csub\u003e2\u003c/sub\u003e crystals doped with RE ions are more susceptible to the formation concentration of clusters, leading to a transition of the glass-like thermal conductivity. Due to the large mass of Ba atoms in BaF\u003csub\u003e2\u003c/sub\u003e crystal, the thermal conductivity of RE ion-doped BaF\u003csub\u003e2\u003c/sub\u003e is not easy to transition to a glass-like state, but the thermal conductivity value is always at the lower value. Moreover, the calculated thermal conductivity of phonon scattering matches well with the actual measured thermal conductivity data.\u003c/p\u003e \u003cp\u003eAdditionally, it has been discovered that the thermal characteristics of RE ion-doped fluoride crystals are influenced by the mass and radius discrepancies between RE-doped ions and lattice ions in a variety of point defects and cluster structures. Among them, under the different concentrations, the variation in mass and radius causes the RE ion-doped fluoride's thermal conductivity to decrease. However, after the generation of clusters in high doping concentration, the radius scattering coefficient's variation degree is more than the mass scattering coefficient compared to the point defect with low concentration. It is mainly that radius disorder caused by the alteration in ionic radius, and this distortion of the lattice exhibits an association with the amorphous transformation of thermal conductivity. For various fluoride systems, the CaF\u003csub\u003e2\u003c/sub\u003e crystal has the highest mass scattering coefficient. Whereas CaF\u003csub\u003e2\u003c/sub\u003e has the biggest radius scattering coefficient at high concentrations, BaF\u003csub\u003e2\u003c/sub\u003e has the largest at low concentrations. These factors cause the system structure to become disorder, which finally causes the thermal conductivity of RE ion-doped fluorides to change to an amorphous state.\u003c/p\u003e \u003cp\u003eThus, the thermal behavior of RE ion-doped fluoride can be universality calculated and analyzed using the phonon scattering coefficient, which also offers theoretical support for other research fields on RE ion-doped fluoride systems. Consequently, further research on the heat conduction of RE ion-doped fluoride will better integrate theoretical simulations with experimental tests, creating the way for thorough thermal analyses of the RE ion-doped fluoride crystals and extending the range of applications. Nonetheless, additional investigation and validation are necessary due to the lack of intuitive structural characterization.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e \u003ch2\u003eConflicts of interest\u003c/h2\u003e \u003cp\u003eThere is no conflict of interest in this manuscript.\u003c/p\u003e \u003c/p\u003e\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eInvestigation, data curation, validation, formal analysis, and writing \u0026ndash; original draft (Kexin Liu); resources, supervision, funding acquisition, project administration, and writing \u0026ndash; review \u0026amp; editing (Dapeng Jiang, Gang Bian, Zhen Zhang, Zhonghan Zhang and Liangbi Su). All authors participated in discussing and editing the manuscripts.\u003c/p\u003e\u003ch2\u003eAcknowledgements\u003c/h2\u003e \u003cp\u003eThis work has been financially supported by the National Key Technologies R\u0026amp;D Program (2023YFB3507403), the National Natural Science Foundation of China (61925508), the Science and Technology Commission of Shanghai Municipality (23511102700), CAS Project for Young Scientists in Basic Research (YSBR-024).\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eJ. Zhou, G. Chen, E. Wu, G. Bi, B. Wu, Y. Teng, S. Zhou and J. Qiu, Nano Letters, 2013, 13, 2241\u0026ndash;2246.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eQ. Y. Zhang and X. Y. Huang, Progress in Materials Science, 2010, 55, 353\u0026ndash;427.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eM. Runowski, N. Stopikowska, D. Szeremeta, S. Goderski, M. Skwierczynska and S. 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Wang, Journal of Alloys and Compounds, 2022, 918.\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"RE ions, fluoride crystal, thermal conductivity, phonon scattering, mass and radius","lastPublishedDoi":"10.21203/rs.3.rs-5272029/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5272029/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eRare earth (RE) ion-doped fluoride crystals have shown great application potential in various fields, attracting the attention of many researchers. The abnormal thermal transformation behavior of RE ion-doped fluoride crystals leads to the singularity and weakness of their application fields. Here, the influence of different structural characteristics of RE ion-doped fluoride crystals on the variation of thermal conductivity is further analyzed using phonon scattering calculation. Firstly, based on the effect of the phonon scattering mechanism on the thermal conductivity of RE ion-doped fluoride, a comprehensive analysis examines the diverse factors that affect the abnormal thermal behavior of different doping types and fluoride crystals. The actual thermal conductivity characteristics are predicted to optimize the crystal performance in various application fields of RE ion-doped fluoride crystals. Next, the influence mechanism of mass and radius difference caused by RE ion doping structure on the thermal conductivity of RE ion-doped fluorides is deeply investigated. Ultimately, a theoretical foundation for behavior and influence of disorder crystals' thermal conductivity is established.\u003c/p\u003e","manuscriptTitle":"Calculating and analyzing the relationship between thermal conductivity and microstructure in rare-earth doped fluoride crystals","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-10-18 04:31:56","doi":"10.21203/rs.3.rs-5272029/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"c678e7e6-22a4-46d7-9123-3d62836652c8","owner":[],"postedDate":"October 18th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":39015877,"name":"Physical sciences/Engineering"},{"id":39015878,"name":"Physical sciences/Materials science"}],"tags":[],"updatedAt":"2024-10-26T21:38:15+00:00","versionOfRecord":[],"versionCreatedAt":"2024-10-18 04:31:56","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-5272029","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-5272029","identity":"rs-5272029","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}