Understanding the Shell Passivation in Ln3+‐Doped Luminescent Nanocrystals

Surface quenching is the main reason limiting the luminescence performance of Ln3+‐doped nanocrystals and their practical applications. Although the shell passivation strategy effectively improves the luminescence efficiency, the understanding of the relevant passivation mechanisms remains elusive and contradictory explanations are often proposed. Herein, the context of debates on this topic is reviewed emphasizing that the discordant viewpoints are probably due to the lack of consideration of chemical disorders such as shell inhomogeneity, core–shell element intermixing, and inhomogeneous dopant distribution in the crystals. A clear awareness of the extent of these chemical disorders and their deleterious impact on the luminescence properties of the nanocrystals (intensified by the energy migration process) is crucial to avoid misinterpretations of the experimental findings.


Introduction
Due to a series of intriguing features, [1] trivalent lanthanide ions (Ln 3þ )-doped luminescent materials have attracted considerable attention for a long time. [2] Given that the 4f orbitals are shielded by filled 5s and 5p orbits, [3] Ln 3þ ions possess intriguing 4f-4f luminescence properties, making Ln 3þ -doped materials indispensable in disparate domains, e.g., the lighting industry. [4] Beginning at the turn of this century, the rapid progress of nanotechnology put forward large demand for luminescent nanomaterials. This urgent need brought new challenges and opportunities, [5] and tremendous efforts have been made to develop Ln 3þ -doped luminescent nanocrystals with unique properties, [6] Because of the size advantage, these nanocrystals show potential for small-scale applications. [7] Unlike its bulk counterpart, the luminescence signal of Ln 3þ -doped nanocrystals can be used as a probe to monitor the characteristic fluctuations of the environment and trigger the designed function of integrated components. [8] Therefore, the use of these nanocrystals provides a unique opportunity to investigate the nature of scientific phenomena, [9] for instance, Brownian motion, [9a] heterogeneous catalysis, [9b] and photon avalanche. [9c] Yet, the widespread application of Ln 3þdoped nanocrystals is still limited because of the inferior luminescence efficiency in comparison with commercial luminescent materials. Taking Ln 3þ -doped hexagonalphase (β) NaYF 4 (abbreviated as β-NaYF 4 ) as an example, the upconversion luminescence (UCL) quantum yield (QY) of β-NaYF 4 :Yb 3þ , Er 3þ nanocrystals is typically less than 1% upon 980 nm excitation, [10] in contrast to the 10% value of its bulk counterpart [11] and high luminescence QY of commercial phosphors. [12] The large surface-to-volume ratio (SVR) of nanocrystal leads to the generation of surface-related quenching process which results in the poor luminescence performance of Ln 3þ -doped nanocrystals. [13] The epitaxial growth of luminescent-inert material on the luminescent nanocrystal is one facile way to alleviate the impact of surface quenchers, [14] which is termed as "shell passivation." Its effectiveness has long been approved, [15] while the explicit understanding of the passivation mechanism is still ambiguous. The surface-related quenching is attributed to the interaction of luminescent centers with quenchers located at the particle surface (as adhesive ligands and surface lattice defects) or floating in the medium (as solvent molecules). The essence of "shell passivation" is to increase the distance between luminescent centers and surface quenchers by intentionally inserting a layer of luminescent-inert shell between them, which diminishes the quenching effect consequently. Based on this understanding, various attempts have been made to establish a set of paradigms to assess the effectiveness of shell passivation in the general case, [16] while the paradoxes (as proposed by different works) perplex the understanding of this issue instead. [17] Even worse, little effort is made to sort out the reasons behind these inconsistencies. The interpretation of the shell passivation effect is generally based on the simple read-out of experimental observations, including sometimes the analysis of the bulk material, which are many times inconsistent. For instance, regarding the luminescence performance dependence of the Ln 3þ -doped nanocrystals to environmental variations, [18] it is impossible to generalize its commercialization without a thorough understanding of their luminescence properties.
To address this issue, this article provides a detailed discussion on the topic of shell passivation. Beginning with the concept interpretation, the context of debates on the extent of quenching alleviation as observed in Ln 3þ -doped core-shell nanocrystals DOI: 10.1002/sstr.202100194 Surface quenching is the main reason limiting the luminescence performance of Ln 3þ -doped nanocrystals and their practical applications. Although the shell passivation strategy effectively improves the luminescence efficiency, the understanding of the relevant passivation mechanisms remains elusive and contradictory explanations are often proposed. Herein, the context of debates on this topic is reviewed emphasizing that the discordant viewpoints are probably due to the lack of consideration of chemical disorders such as shell inhomogeneity, core-shell element intermixing, and inhomogeneous dopant distribution in the crystals. A clear awareness of the extent of these chemical disorders and their deleterious impact on the luminescence properties of the nanocrystals (intensified by the energy migration process) is crucial to avoid misinterpretations of the experimental findings.
is reviewed. Efforts are subsequently made to survey the reasons behind inconsistent viewpoints assessing the impact of chemical disorders (such as shell inhomogeneity, [19] element intermixing, [20] and inhomogeneous dopant distribution [21] ) on the interpretation rationality of the shell passivation effect. Next, the origins of these disorders are explored from the aspect of formation behavior of nanocrystal, [22] and the effects of thermodynamic and kinetic processes are evaluated. Finally, the profound effect of these chemical disorders on the luminescence properties of Ln 3þ -doped nanocrystals is demonstrated, and a comprehensive understanding of shell passivation is provided.

Concept Interpretation
Surface-related quenching is one of the most deleterious effects reducing the performance of Ln 3þ -doped nanocrystal. (Figure 1a) The large SVR of nanocrystal results in a high density of surface quenchers, and the interaction between these quenchers and luminescent centers in the nanocrystal controls the luminescence performance. It is well-known that the features of the luminescent centers residing in the outer region of the nanocrystal are more susceptible to the impact of surface quenchers, regarding the distance proximity. This susceptibility becomes more significant with the decrease of the particle size. The concept of "dark layer" was proposed by Zhao et al., [23] and defined by Gargas et al. afterward [16a] (Figure 1b), to represent the nearsurface region of the crystal in which the luminescent centers strongly interact with surface quenchers thus showing no luminescence. This concept was employed by Hossan et al. to study the luminescence quenching mechanism of Ln 3þ -doped β-NaYF 4 nanocrystals, [17b] and a phenomenon of thermally enhanced luminescence was reported by Zhou et al. by reactivating the centers residing in this region. [24] To eliminate the impact of surface quenchers, restoring the luminescence of the nanocrystal, a strategy of "shell passivation" was proposed by growing a layer of luminescent-inert material on the nanocrystal surface, thus nominally forming a "core-shell" geometry. Kömpe et al. pioneeringly grew a LaPO 4 shell of 1.1 nm on 5 nm-sized CePO 4 :Tb 3þ nanocrystals, [14] which resulted in a Tb 3þ luminescence enhancement (Figure 1c). Based on this strategy, it is commonly reported that the luminescence intensity of Ln 3þ -doped nanocrystals increases by several orders of magnitude after the inert-shell passivation nowadays [13,15a,c] (Figure 1d  heterogeneity in Ln 3þdoped nanocrystals. Green dots denote the particle size-dependent luminescence intensity of a single nanoparticle normalized to its volume. The top inset presents an ideal nanocrystal in which all luminescent centers are active, while the bottom one shows the luminescence quenching of the centers residing in the "dark layer." Adapted with permission. [16a] Copyright 2014, Springer Nature. c) Emission spectra of CePO 4 :Tb 3þ and LaPO 4 shellpassivated nanocrystals upon 277 nm excitation. Adapted with permission. [14] Copyright 2003, Wiley-VCH. d) Luminescence improvement of a β-NaGdF 4 :Yb 3þ , Tm 3þ nanocrystal after β-NaGdF 4 shell coating. Adapted with permission. [13a] Copyright 2010, Wiley-VCH. e) Shell thickness-dependent luminescence of a β-NaErF 4 @β-NaLuF 4 nanocrystal upon 980 nm excitation. The luminescence enhancement with the increase of the shell thickness and the corresponding photographs are also shown. Adapted with permission. [ Despite the success, the understanding of the passivation mechanism is still ambiguous and contradictory results are often reported. Here, the dependence of luminescence quenching alleviation on the inert-shell thickness of Ln 3þ -doped nominal core-shell nanocrystals is exemplified. Qian et al. denoted that a β-NaYF 4 shell of 3 nm was sufficient to prevent the surface quenching on the luminescence of 11 nm-sized β-NaYF 4 :Yb 3þ , Er 3þ nanocrystal, [25] and a 15-fold luminescence enhancement was detected. (Figure 2a) Su et al. paraphrased this result later [26] and claimed that the interaction between Ln 3þ dopant in β-NaGdF 4 nanocrystal and surface quenchers could be largely blocked with a β-NaYF 4 shell of 2.5 nm (as termed as the critical shell thickness). An analogous trial was conducted by Gargas et al., [16a] and a β-NaYF 4 shell of 1.8 nm was denoted Figure 2. a) Shell thickness-dependent luminescence intensity of β-NaYF 4 :Yb 3þ , Er 3þ nanocrystals after a β-NaYF 4 shell coating. The inset shows the emission spectra of core and core-shell nanocrystals. Adapted with permission. [25] Copyright 2009, Springer Nature. b) Luminescence intensity and decay time of Er 3þ in single β-NaYF 4 :Yb 3þ , Er 3þ nanocrystals with different β-NaYF 4 shell thicknesses. Adapted with permission. [16a] Copyright 2014, Springer Nature. c) Shell thickness-dependent QY of Er 3þ 4 I 13/2 ! 4 I 15/2 emission in β-NaGdF 4 :Yb 3þ , Er 3þ @β-NaYF 4 nanocrystals upon 980 nm excitation. Adapted with permission. [16b] Copyright 2018, American Chemical Society. d) Shell thickness-dependent decay time of the Yb 3þ 2 F 5/2 ! 2 F 7/2 transition in β-NaYF 4 : Yb 3þ , Er 3þ @β-NaLuF 4 nanocrystals and the model simulation result (orange dash line). The dependence of the intrinsic decay rate is also depicted. Adapted with permission. [17a] Copyright 2016, American Chemical Society. e) Shell thickness-dependent UCL internal QY of β-NaYF 4 :Yb 3þ , Er 3þ @β-NaYF 4 nanocrystals and the simulation result. Adapted with permission. [17b] Copyright 2017, American Chemical Society. f ) The luminescence intensity of β-NaYF 4 :Yb 3þ , Tm 3þ @β-NaYF 4 nanocrystals for different shell thicknesses. Adapted under the terms of the CC-BY license. [28] Copyright 2019, The Authors. Published by AIP Publishing. g) Shell thickness-dependent Er 3þ 4 I 13/2 ! 4 I 15/2 emission intensity of β-NaYbF 4 :Er 3þ , Ce 3þ @β-NaYF 4 nanocrystals as dispersing in different media upon 980 nm excitation. Adapted under the terms of the CC-BY license. [29] Copyright 2017, The Authors. Published by Springer Nature. h) The external QY of β-NaYF 4 :Er 3þ @β-NaLuF 4 nanocrystals upon 1500 nm excitation. Adapted with permission. [30] Copyright 2019, American Chemical Society. i) Shell thickness-dependent decay time of Yb 3þ 2 F 5/2 ! 2 F 7/2 luminescence in β-NaGdF 4 :Yb 3þ , Er 3þ @β-NaGdF 4 nanocrystals and the simulation result (red line). Adapted with permission. [17c] Copyright 2019, American Chemical Society.
In summary, these critical shell thicknesses are simply readout based on experimental observations, not considering, thus, the interferences arising from differences in sample features (e.g., the synthesis method, preparation route, doping concentration, and particle size), data collection conditions (e.g., the dispersion medium, sample dispersibility, ambient temperature, and apparatus setup), variation of electronic transition probability, energy transfer dynamics, [15a,16b,31] and local-field effects. [32] Taking the results of Zhong et al. as an example [29] (Figure 2g), the distinct effectiveness of shell passivation on Er 3þ 4 I 13/2 luminescence was observed when dispersing the nanocrystals into different media. Also, the lack of a standard analysis scheme limits the rational assessment of shell passivation efficiency when different types of luminescence features such as emission intensity, QY, decay times, and transition rates are used, and different data analysis criteria are employed ( Figure 2). Apart from these, additional uncertainties originate from the ambiguous understanding of the surface quenching effect. Surface quenching is the generic term for quenching processes attributed to the interaction of luminescent centers with quenchers located at the particle surface or floating in the medium (Figure 1a). Depending on the coupling mechanism (such as electron transfer and multipole and exchange interactions), the correlation between the quenching rates and the spatial distance is different. Even for the same coupling mechanism, the shell passivation efficiency on various types of luminescent centers can be distinct because of the difference in coupling strength. [15a,17a] For instance, because of a higher energy resonance of the OH stretching vibration mode with the Er 3þ 4 I 13/2 ! 4 I 15/2 transition, compared to the Yb 3þ 2 F 5/2 ! 2 F 7/2 transition, a 20 times stronger coupling for the OH vibration to the 4 I 13/2 level was recorded, [33] resulting in a dramatic de-excitation of the Er 3þ emission. [15a,34] Yet, the experimentally recorded quenching and the corresponding shell passivation efficiency represent the overall contribution of the inert shell to the quenching alleviation of the entire nanocrystal, rather than the feature depiction of a certain individual center. Standing on this point, these critical shell thicknesses as reported, strictly speaking, cannot be used as the metrics to produce a role of thumb to assess the passivation efficiency on a particular surface quenching process, but merely denotes the extent of validity of the shell passivation strategy. Hence, the shell passivation efficiency should be cautiously interpreted requiring the development of new perspectives for comprehension.

Shell Inhomogeneity
The proximity in distance between luminescent centers and surface quenchers determines the extent of the surface quenching in the nanocrystals and the inert-shell coverage increases the distance between them, diminishing, thus, the coupling efficiency. Provided that the quenchers are located at (or beyond) the particle surface, the isotropic shell growth is one prerequisite for the interpretation of the shell passivation effect with an explicit "core-shell" geometry because the distance between luminescent centers (residing in the outmost region of core) and their nearest surface quenchers remains constant in any orientation ( Figure 3a). However, evidence from different resources showed that this condition was not easily fulfilled, and the shell thickness inhomogeneity appeared more generally.
Using electron microscopy, Abel et al. analyzed the shell feature of 21 nm-sized β-NaYF 4 @β-NaGdF 4 nanocrystals as prepared by a one-pot heating-up (OPH) method. [19a] The results showed the uneven shell thickness of most particles (Figure 3b), indicating an anisotropic shell growth. Similar observations were reported by Zhang et al., [19b] revealing also an anisotropic shell growth in 20 nm-sized β-NaYF 4 :Yb 3þ , Er 3þ @β-NaGdF 4 nanocrystals ( Figure 3c). An anisotropic shell growth was reported in β-NaGdF 4 :Er 3þ @β-NaYF 4 nanocrystal as well, [35] which was attributed to the kinetically controlled growth process. More common shell growth was accompanied by a change in morphology, [36] which generated a thinner shell thickness in certain regions of the nanocrystal, and luminescent centers residing in these regions would suffer severer surface quenching. [37] For instance, a weaker luminescence was collected in β-NaYF 4 :Yb 3þ , Er 3þ with an anisotropic β-NaGdF 4 shell growth, compared to an isotropic shell growth, and its luminescence was more susceptible to quenching effects by water molecules. [19b] Liu et al. showed the quenching aggravation in the region of β-NaGdF 4 :Er 3þ nanocrystal which failed to be covered by the β-NaYF 4 shell. [35] The fact that the overall shell passivation efficiency is restricted by the thinnest part of the shell was also stated by Fischer et al., [38] Zhang et al., [37] Kwock et al., [30c] and Arboleda et al. [39] (Figure 3d). The incorporation of large amounts of Nd 3þ ions (>50%) into the shell changed the morphology of the β-NaYF 4 @β-NaGdF 4 nanocrystals decreasing the shell thickness in the middle. As a result, the interaction between the luminescent centers in the core and the surface quenchers is strengthened in these regions, resulting in a severe quenching (Figure 3e,f ).
Valuable evidence was provided by Wang as well. [40] By regulating the shell growth route, a change in the morphology of β-NaYF 4 :Yb 3þ , Er 3þ @β-NaYF 4 nanocrystals (from sphericalto rod-like) was obtained (Figure 4a). In contrast to nanospheres, the thin shell of the nanorods in the short-axis direction was insufficient to suppress the surface quenching, even though the loss in the long-axis direction was fully suppressed (Figure 4b), and a weak UCL from the high-energy excited state of Er 3þ was observed. Kang et al. provided a more indicative demonstration of the anisotropic shell passivation effect [36c] ( Figure 4c). In comparison to the luminescence enhancement of β-NaYF 4 :Yb 3þ , Er 3þ @β-NaYF 4 nanorods, as rising the dosage of the shell precursor, a larger enhancement was collected in nanospheres with the same chemical composition, and a longer 4 S 3/2 lifetime was observed (Figure 4d), indicating the better suppression of the surface quenching. Based on these results, the necessity of isotropic shell growth in the nanocrystals for the rational interpretation of shell passivation in Ln 3þ -doped nanocrystals is undisputed. . a) Normalized emission spectra of β-NaYF 4 :Yb 3þ , Er 3þ @β-NaYF 4 nanocrystal with different morphologies upon 975 nm excitation and b) the energy loss pathway in the nanocrystals with different shell features. Adapted with permission. [40] Copyright 2019, Royal Society of Chemistry. c) TEM images of β-NaYF 4 :Yb 3þ , Er 3þ and β-NaYF 4 :Yb 3þ , Er 3þ @β-NaYF 4 nanocrystals with different morphologies. d) The photographs of shell thickness-dependent brightness of nanocrystals and the corresponding Er 3þ 4 S 3/2 luminescence decay dynamics. Adapted with permission. [36c] Copyright 2019, IOP Publishing. Figure 3. a) Graphic representation of isotropic and anisotropic shell growth. b) High-angle annular dark-field (HAADF) transmission electron microscopy (TEM) images of different β-NaYF 4 @β-NaGdF 4 nanocrystals as prepared in the same batch and the corresponding electron energy loss spectroscopy (EELS) line scan on the Gd 3þ signal. Adapted with permission. [19a] Copyright 2011, American Chemical Society. c) Cryo-highresolution (HR) TEM images of β-NaYF 4 :Yb 3þ , Er 3þ @β-NaGdF 4 nanocrystals as prepared in the same batch and the corresponding element-dependent EELS mapping. Adapted with permission. [19b] Copyright 2012, American Chemical Society. d) Morphology evolution of β-NaYF 4 :Yb 3þ , Er 3þ @β-NaLuF 4 :Nd 3þ nanocrystal as rising Nd 3þ concentration in the shell; e) the corresponding emission spectra upon 800 nm excitation; and f ) the variation of the Er 3þ luminescence intensity arising from different excited states. Adapted with permission. [39] Copyright 2019, American Chemical Society.

Core-Shell Element Intermixing
Besides the shell inhomogeneity, element intermixing confounds the interpretation of shell passivation as well. Ideal shell growth requires the formation of an explicit "core-shell" geometry in which a rigid shell covers uniformly the core of the crystal, without destructing its integrity, and an infinite concentration gradient of elements is generated at the boundary between the core and shell regions (Figure 5a, left). Even if the isotropic shell growth is not assured, the effectiveness of the shell passivation is still preserved to some extent. Yet, recent reports showed that the strict segregation of elements within the designed region of the nanocrystal was unlikely in the nominal core-shell system, and the occurrence of element intermixing in the entire nanocrystal was more likely (Figure 5a, right).
One relevant report was the study of Eu 3þ distribution in β-NaEuF 4 @β-NaGdF 4 nanocrystals. [20a] This designed geometry of Eu-based core/Gd-based shell permits probing the Eu 3þ distribution in the nanocrystals ( Figure 5b). The basis of this strategy is that the Eu 3þ 5 D 1 ! 7 F 0-4 luminescence is quenched by the severe Eu 3þ -Eu 3þ cross-relaxations in the core and this impact will diminish as the Eu 3þ ions are immersed into the shell (due to the concentration dilution), resulting in the re-emergence of the 5 D 1 ! 7 F 0-4 emissions. Relying on this strategy, the authors found that the mean concentration of leaked Eu 3þ in the Gd 3þ -based shell reached 3.6% (or 6.7%) when the cubic-phase (α)-NaGdF 4 (or trifluoroacetic acid [TFA]-based salts) was used as the shell precursor during the OPH reaction ( Figure 5c). These levels of leakage should not be overlooked because 6% Eu 3þ doping of β-NaGdF 4 shell requires the dissolution of 42% original β-NaEuF 4 core volume due to a large difference between the core and shell volumes (mean size of 7.6 nm for core and 14 nm for nominal core-shell nanocrystals). Besides, depending on the choice of the shell precursors, the concentration of leaked Eu 3þ on the particle surface was estimated to be 0.7% and 5.6% relying on the ligand (2-naphthoate)-sensitized experiments (Figure 5b, d). Hence, the strong element intermixing occurred in all cases, and different concentration gradients of leaked Eu 3þ in the Gd 3þ -based shell were detected ( Figure 5e).
Similar efforts were made to study the element intermixing in β-NaGdF 4 :Ln 3þ @β-NaYF 4 nanocrystals by Hudry et al. [41] ( Figure 6a). The mean size of the core was 5 nm, and the size of nominal core-shell nanocrystals increased gradually to 7, 9, and 12 nm by increasing the dosage of the shell precursor during the reaction. The energy-dispersive X-ray spectroscopy (EDX) was employed to probe the element distribution in these nanocrystals after signal reconstruction. [42] Different from a solid-solution as generated in the core sample (Figure 6a1), the element distribution in the nominal core-shell nanocrystals was complex. Instead of forming the "core-shell" geometry with a clear component boundary, the Gd 3þ -based core was mixed with the shell element, generating a "core-interface" geometry. The increase in shell precursor dosage resulted in severe element intermixing, with Y concentration in the "interface" region reaching 28%, 45%, and 76%, respectively, in the 7 nm- (Figure 6a2), 9 nm- (Figure 6a3), and 12 nm-sized nanocrystals ( Figure 6a4). Meanwhile, the chemical feature of the core was altered. While for 7 and 9 nm-sized nanocrystals the Gd 3þ chemically Figure 5. a) Illustration of an explicit "core-shell" geometry and element intermixing. b) Illustration of the luminescence and energy transfer pathway in β-NaEuF 4 @β-NaGdF 4 nanocrystals. c) Eu 3þ concentrationdependent intensity ratio of the Eu 3þ 7 F 0 ! 5 L 6 (394 nm) and Gd 3þ 8 S 7/2 ! 6 I J (272 nm) transitions in the excitation spectra of Eu 3þ -doped β-NaGdF 4 nanocrystals by monitoring the Eu 3þ 5 D 1 ! 7 F 2 emission (555 nm). The mean leaked Eu 3þ concentration in the β-NaGdF 4 shell can be determined by comparing the intensity ratios of the doped particles with those of the β-NaEuF 4 @β-NaGdF 4 nanocrystals (as prepared using different shell precursors). d) Eu 3þ concentration-dependent luminescence intensity of Eu 3þ -doped NaGdF 4 nanocrystals upon 331 nm excitation before (black dots) and after (red dots) photosensitive ligand exchange. The Eu 3þ concentration on the surface of β-NaEuF 4 @β-NaGdF 4 nanocrystals can be determined based on this variation tendency. Adapted with permission. [20a] Copyright 2015, American Chemical Society. e) Illustration of distinct Eu 3þ concentration gradients in the Gd 3þ -based shell of nanocrystals, as prepared using different precursors. pure core was preserved, although its size shrank to around 1 nm, it completely vanished in the 12 nm-sized crystals, being replaced by a 39% Y containing component. The region outside of this "core-interface" region was composed of a Y 3þ -based shell, while its chemical purity was not assured because the immersion of a slight amount of core elements into the shell could not be excluded.
Later in 2019, Hudry et al. evaluated the extent of element intermixing in large-sized nanocrystals [20b] (Figure 6b). The 21 nm-sized β-NaEr 0.8 Yb 0.2 F 4 nanocrystals was selected as the core, and nominal core-shell nanocrystals were prepared by three shell growth methods, 1) TFA-salts hot-injection ( Figure 6b1); 2) OPH coprecipitation (Figure 6b1); and 3) α-phase hot-injection ( Figure 6b3). Although identical conditions were used in the reactions, different morphologies of β-NaEr 0.8 Yb 0.2 F 4 @NaYF 4 nanocrystals were obtained. While isotropic growth was observed for methods (1) and (3), an anisotropic growth was detected for method (2). More diversities were found in the analysis of components. The volume of pure core decreased to 22% (1), 8% (2), and 36% (3) of its original value after shell growth (Figure 6b, bottom). Pure cores were enveloped by the "interface" regions with variable compositions (core elements richer toward the particle center while Y richer toward the surface). Depending on the shell growth method, different elemental composition variation trends were found in this region, but in either case, the "interface" regions accounted for roughly 70% of the total nanocrystal. Efforts were also devoted to assessing the element intermixing in the multishell nanocrystals (as prepared by method (1)) ( Figure 7a). A second-round shell growth increased the particle size to 42 nm, and the element distribution in the nanocrystals was reset. The size of pure core shrank to 8 nm in the current case accompanied by the thickening of the "interface" (7.5-9 nm) with a variable extent of intermixing between core elements and Y. This "interface" was covered by a second "interface" of 2.5 nm as mainly composed of Y and Gd with various compositions, and the presence of all used Ln 3þ was detected within an ultrathin (1 nm) inner layer of this second "interface" region. It was noted that the pure core in this sample only accounted for 1% of the nanocrystal and that of "interfaces" reached 34%. Another trial was conducted in 51 nm-sized triple-shell nanocrystals. The size of the pure core in this sample was still far smaller than the original 21 nm. The residual component of the nanocrystals was composed of various "interfaces" with distinct elemental compositions and the chemically pure shell vanished. Core elements immersed in outer regions and strongly mixed with Y and Gd and forming an "interface" of 8 nm, and elements supposed to be confined in the second and third shells were mixed forming a solid-solution shell of 10 nm located at the outmost region of the nanocrystals.
All the above results prove that the traditional shell growth strategy has a limited effect on the element segregation in the designed region. Support for this viewpoint can be found in the study of element distribution in β-NaGdF 4 :Er 3þ @β-NaYbF 4 @β-NaGdF 4 :Tm 3þ @β-NaYF 4 as well [43] (Figure 7b). Highly diverse intermixing between various types of Ln 3þ ions was observed, and the strict boundaries between different regions were undiscerned (Figure 7b, bottom). Relevant element intermixing study in nominal core-shell nanocrystals can be found elsewhere. [44] Very recently, Hudry et al. employed the corrected HR ADF-STEM to analyze the interfacial properties of core-shell Ln 3þ -doped nanocrystals and discussed the susceptibility of the characteristics of the nanocrystals to the variation of experimental parameters. [45] A similar study was carried out in β-NaErF 4 @β-NaYF 4 nanocrystal [46] to assess the intermixing of core Er 3þ into the Y-based shell under postannealing conditions (Figure 8), with the variation of Er 3þ luminescence intensity used to monitor the extent of intermixing. Surface quenching becomes active if core Er 3þ immerses into the shell, resulting in the luminescence decrease of the material (Figure 8a). Less extent of Er 3þ intermixing was observed in the sample with the thicker shell coating (Figure 8b), Figure 6. a) HAADF-scanning transmission electron microscopy (STEM) images and element analysis results based on EDX-based line scan of (a1) β-NaGdF 4 :Ln 3þ and (a2-a4) β-NaGdF 4 :Ln 3þ @β-NaYF 4 nanocrystals. The bottom diagrams show the element distributions. Adapted with permission. [41] Copyright 2017, American Chemical Society. b) HAADF-STEM images and EDX element analysis of β-NaEr 0.8 Yb 0.2 F 4 @β-NaYF 4 nanocrystals as prepared by different shell growth methods: (b1) TFA-salts hotinjection; (b2) OPH coprecipitation; and (b3) α-phase hot-injection. Adapted with permission. [ while in cases of high annealing temperature and high Er 3þ concentration (Figure 8c,d), the intermixing was aggravated.
The intermixing extent was also influenced by the core size, and a significant Er 3þ diffusion was found when using a smaller-sized core ( Figure 8e). Moreover, the intermixing of Er 3þ was somehow controlled by the shell component ( Figure 8f ). The occurrence of element intermixing in the nominal core-shell nanocrystal was reported by Alvares et al. as well, [47] and an independent demonstration was provided by using nuclear magnetic resonance (NMR). As denoted in the work, the strong coupling between Dy 3þ and water molecule was the reason for making Dy-based nanocrystals as contrast agents for magnetic resonance imaging (MRI). [48] The 1 H NMR longitudinal relaxivity of water is correlated with the proximity of Dy 3þ to water molecules, and its relaxivity value is mainly contributed by the coupling of water molecules and Dy 3þ residing in the outermost region of the nanocrystal. Therefore, the distribution of Dy 3þ ions in the nanocrystal can be roughly deduced by monitoring 1 H relaxivity. Four sets of similar-sized nanocrystals (β-NaDyF 4 @β-NaDyF 4 , β-NaDyF 4 @β-NaYF 4 , β-NaYF 4 @β-NaDyF 4 , and β-NaYF 4 @β-NaYF 4 ) with different nominal geometries were prepared ( Figure 9a). The 1 H NMR relaxivity of water in aqueous dispersions of these nanocrystals was 1791, 959, 747, and 40 s À1 mmol À1 , respectively (Figure 9b). If the element segregation within the designed core-shell geometry was strictly abided by in these nanocrystals, the essentially matching 1 H relaxivity should have been obtained for Dy@Dy and Y@Dy because of  . a) HR-TEM, HAADF-STEM images and EDX element analysis of β-NaEr 0.8 Yb 0.2 F 4 @β-NaYF 4 @β-NaGdF 4 and β-NaEr 0.8 Yb 0.2 F 4 @β-NaYF 4 @β-NaGdF 4 @β-NaYF 4 nanocrystals. Adapted with permission. [20b] Copyright 2019, Royal Society of Chemistry. b) HAADF-STEM images and element analysis of β-NaGdF 4 :Er 3þ @β-NaYbF 4 @β-NaGdF 4 : Tm 3þ @β-NaYF 4 nanocrystals with different sizes and illustrations of element distributions. Adapted with permission. [43] Copyright 2019, Royal Society of Chemistry.
www.advancedsciencenews.com www.small-structures.com the similar Dy 3þ abundance on the particle surface, and vice versa the relaxivity should not have been detected in cases of Dy@Y and Y@Y. The disagreement between experimental findings and predictions reveals the deviation from designed geometries in Y@Dy and Dy@Y, and core-shell element intermixing probably occurs. The impact of element intermixing on the luminescence properties of the nanocrystals should not be overlooked. [16b] Ning et al. reported that the substantial core element Mn 2þ immersed in the ZnS shell in KMnF 3 :Yb 3þ , Er 3þ @ZnS during shell growth generated a 3 d-3 d broadband emission arising from Mn 2þ incorporated into ZnS [49] (Figure 9c,d). The occurrence of element intermixing has been accepted in semiconductor [50] and noble-metal nanocrystals, [51] and the term "alloying" has been adopted to depict the complex element distribution in the materials. [51b,52] In contrast, there is a lack of attention to this issue in Ln 3þ -doped luminescent nanocrystals. Some researchers also hold different opinions on the extent of element intermixing. For instance, Chen et al. [53] claimed that Ce 3þ , Tb 3þ were confined in the designed regions of β-NaYF 4 :20%Ce 3þ @β-NaYF 4 :20%Tb 3þ nanocrystal ( Figure 9e) and no intermixing was detected unless the sample was annealed at high temperature (>350 C) (Figure 9f ).

Inhomogeneous Dopant Distribution in the Core
Apart from these factors, the distribution of luminescent dopants in the core affects the shell passivation efficiency as well ( Figure 10a). It is straightforward that the determination of the distance between the core dopant and surface quenchers becomes difficult if the spatial distribution of core elements deviates from the statistical manner, making the interpretation of shell passivation intricate. Unfortunately, experimental findings in various works indicate that this concern is not nonsense.
One associated study was conducted in Ln 3þ -doped β-NaGdF 4 nanocrystals by Dong et al. [21a] (Figure 10b,c,d). Three sets of samples with similar doping concentrations (around 20%) were adopted: (1) Y 3þ , Tb 3þ -doped nanocrystals (9 nm) as prepared by a thermal decomposition method; (2) Nd 3þ -and (3) Tb 3þ -doped nanocrystals (5-6 nm) as prepared by a coprecipitation method. Dopant distributions in these samples were derived by using the technique of energy-dependent X-ray photoelectron spectroscopy (XPS). Given that the penetration depth of X-ray photon can be adjusted by tuning its excitation energy, the signal of elements residing in different radial depths of the nanoparticle can be read-out to a first approximation, and its distribution can be roughly deduced. [54] In this case, the signal of Gd 3þ 4 d peak (I Gd ) was used as the reference, and the I Gd /I Ln intensity ratio was used to probe the Ln distribution in the nanocrystal. With the increase of excitation energy, the variation of I Gd /I Ln showed various trends in different samples. In sample 1, Gd was richer toward the particle center and Y slightly richer toward the particle surface with a subtle concentration gradient (Figure 10b, inset). In contrast, a steep concentration gradient of Nd was detected in sample 2 with Nd richer toward the surface and Gd richer toward the center (Figure 10c, inset). The situation was opposite in sample 3 where Tb was richer toward the center with a steep concentration gradient and Gd richer toward the surface (Figure 10d, inset). None of them followed the statistical distribution which should have shown an excitation energy-independent I Gd /I Ln variation trend.
Similar research was carried out in NaYF 4 :20%Yb 3þ nanocrystals of different sizes, [21b] and the I Yb /I Y ratio was used to probe the Yb distribution in these nanocrystals (Figure 10e). With the increase in excitation energy, I Yb /I Y increased similarly in all samples. This measurement was also conducted in a series of Figure 9. a) Schematic of composition and size of different Y, Dy-based nanocrystals, and b) the 1 H NMR longitudinal relaxivity of water in aqueous dispersions of various nanocrystals. Molar relaxivity data were normalized with respect to the concentration of nanocrystals and expressed relative to the value of β-NaDyF 4 @β-NaDyF 4 , with absolute values (s À1 mmol À1 ). Adapted with permission. [47] Copyright 2017, American Chemical Society. c) HR-TEM image of KMnF 3 :Yb 3þ , Er 3þ @ZnS nanocrystal, and d) the emission spectra of KMnF 3 :Yb 3þ , Er 3þ before and after shell coating under 325 nm excitation and the excitation spectrum by monitoring Mn 2þ 3d-3d emission. The inset gives the luminescence photograph of nanocrystals-dispersed solution. Adapted with permission. [49] Copyright 2020, American Chemical Society. e) Emission spectrum of β-NaYF 4 :20% Ce 3þ @β-NaYF 4 :20%Tb 3þ nanocrystal upon 264 nm excitation. The inset gives the enlargement of the spectrum showing the absence of Tb 3þ 5 D 3 ! 7 F 6-0 emission, which indicates limited Tb intermixing into the core. f ) Emission spectra of nanocrystals after annealing at different temperatures, and Tb 3þ 5 D 3 ! 7 F 6-0 emission emerges, indicating the occurrence of Tb 3þ intermixing in the material. Adapted with permission. [53] Copyright 2015, Wiley-VCH.
www.advancedsciencenews.com www.small-structures.com Yb 3þ -doped samples with different sizes and Yb concentrations (20-60%). The rising in excitation energy caused the increase of I Yb /I Y , and a more significant signal increase was observed in the sample with higher doping concentrations. The distribution manner of Yb 3þ ions was also studied by EDX line scan, which showed Yb richer toward the center. Depending on the doping concentration, the variation trend of the Yb signal in the nanocrystals was different. In 43 nm-sized 20%Yb 3þ -doped nanocrystals, the Yb signal started at 14.25% of the left edge of the particle and reached its maximum at 24.35% before dropping to 15.5% of the right edge (Figure 10f ). In contrast, a less symmetrical variation of the Yb signal was observed in 51 nm-sized 60% Yb 3þ -doped nanocrystals, and the value varied between 40% and 58% (Figure 10g). These results showed that Yb preferably gathered at the particle center, instead of following the statistical distribution. Regarding that these nanocrystals are synthesized by using different methods, the above observations indicate that this type of distribution deviation is probably ubiquitous in Ln 3þ -doped nanocrystals, which immediately raises the question of whether the shell thickness-oriented criterion as currently used to assess the effectiveness of shell passivation is still valid.

Contention
The above review shows that the effectiveness of inert-shell passivation is controlled by various factors, and most of them have not received enough attention. The essence of passivation is to reduce the coupling strength between luminescent centers and surface quenchers by increasing the distance between them, while chemical disorders such as anisotropic shell growth, element intermixing, and inhomogeneous dopant distribution disturb the effectiveness of this strategy. Therefore, the interpretation of shell passivation in Ln 3þ -doped nanocrystals cannot be simply based on the experimental read-out but should rely on more rigorous analysis. Besides, the reason behind the emergence of these disorders ought to be clarified. Some attempts have been made to deal with this issue. As inspired by the work of Mai et al., [55] Dong et al. suggested that the reactivity difference between precursors during material synthesis could be the inducement of these disorders in the nanocrystal.
[21a] A similar view was proposed to explain the intricate formation behavior of InP@ZnS [56] and CdSe(Te) [51a] nanocrystals. Thus, the analysis of the formation of Ln 3þ -doped nanocrystals is a feasible way to identify the origins of these disorders. Here, the classic crystallization mechanism of the nanocrystals is briefly introduced to facilitate the comprehension of later discussions. [22,57]

Formation of Nanocrystal
One of the most prestigious interpretations of crystallization is the LaMer mechanism, as proposed dating back to the 1940s. [58] Stemming from the formation behavior of sulfur sol as prepared by the decomposition of Na 2 S 2 O 3 , LaMer et al. concluded that the process of crystallization underwent several stages: 1) monomer releasing and accumulation; 2) nucleation by consuming monomers; and 3) nucleus growth. Monomers are initially released by the decomposition of reaction precursors and accumulate in the system proceeding along with the reaction, resulting in the condition of supersaturation. Next, the process of "burst nucleation" generates numerous nuclei simultaneously, which is the key to forming uniform colloidal particles. [58b,59] The LaMer plot (Figure 11a) was proposed to describe the variation of monomer saturation degree in the reaction, which denoted the essential role of monomer supersaturation in the nucleation process. This phenomenological explanation is validated from the aspect of thermodynamics by considering the variation of Gibbs free energy (ΔG) of the nucleus (Figure 11b), and the crystallization features of the nucleus (as the critical radius, r c , and nucleation rate) are closely correlated with the thermodynamic parameters of the system, such as the surface free energy per unit area of nuclei (γ) and the supersaturation degree of monomer in the reaction medium. After the "burst nucleation," the nucleus grows by consuming the rest of the monomers, and the growth rate is controlled by the monomer flux through the interface between nucleus and reaction medium (Figure 11c). Reiss developed a model to depict this growth dynamics of the nucleus by using a classic diffusion theory, [60] and a "self-focusing" mechanism of the size distribution of the nanocrystals was established. [61] Unfortunately, this model overlooked the reaction kinetic effect. Precipitation and dissolution are two opposite processes that control the monomer flux (Figure 11c), while the dependences of reaction rate constants of these processes on particle size are different. [58a] Considering the reaction kinetics, a complex nucleus growth mechanism was derived which showed that the growth behavior was correlated with the nucleus size and type of growth reaction (monomer diffusion-controlled or reaction-controlled), and the final size distribution of nanocrystal was controlled by a trade-off between the "self-focusing" effect and the defocusing effect as brought about by the Gibbs-Thomson effect (also termed as Ostwald ripening [62] and Lifshitz-Slyozov-Wagner theory [63] ) (Figure 11d). This issue was studied by Talapin et al. later using a numerical simulation approach, [64] and the results perfectly reproduced the trend as previously predicted (Figure 11e,f ). The LaMer mechanism and its derivations were also used to study the nucleation and growth behaviors of fluoride-based nanocrystals due to widespread acceptance. [65] Yet the deviation of experimental observation from the predicted manner was frequently detected. Attention is also worthy of being paid to the impact of element mobility on the formation of nanocrystals which are composed of various types of cations, such as cases of impurity-doping and heterogeneous growth. Different from the situation of singletype monomer flux, a complex merging of cation monomers occurs in these cases, resulting in a more intricate formation mechanism. As one of the typical representatives, the process of cation exchange has been studied over the field, [66] and the exchange approach has been widely used for material development and viewpoint verification. An ultrafast Cd↔Ag exchange in Cd-Ag-Se nanocrystals was reported by Son et al., [67] showing the high utilization potential of cation exchange to develop novel nanomaterials (Figure 12a). By using the exchange approach, Han et al. achieved the incorporation of multiple types of Ln 3þ ions into 17 nm-sized β-NaGdF 4 nanocrystals dispersed in an aqueous medium [68] (Figure 12b). The exchange approach was also adopted by Lehmann et al. to study the luminescence properties of Eu 3þ -doped LaPO 4 nanocrystals, confirming the surface site occupation of Eu 3þ ions [69] (Figure 13a). In addition, the use of the exchange approach accomplished the Gd 3þ substitution on the surface of β-NaYF 4 :Yb 3þ , Er 3þ nanocrystals, [70] illustrating its potential in MRI.
In comparison, little is known about the detailed influence of the cation exchange process on the crystallization of heterogeneous nanocrystal. Because cation exchange is essentially a kinetic process, its feature details can be roughly studied by using Figure 11. a) LaMer plot, representing the time-dependent supersaturation degree (S) of monomer concentration. The insets illustrate different stages of the crystallization process. b) Plot of particle radius (r)-dependent crystallization ΔG variation of nanocrystal (solid line). [87] The dash-dot line denotes the variation of nucleus surface energy (ΔG surface ), and the dashed line shows the contribution of the free energy change when the monomer in the reaction medium or merging into the bulk crystal (ΔG bulk ). r c defines the minimum radius of a nucleus that can grow spontaneously in the supersaturated medium, and the corresponding critical free energy is given as ΔG c , denoting the free energy necessary to form a stable nucleus. c) Graphic representation of nucleus growth, dominated by monomer precipitation, nucleus dissolution, and monomer diffusion in the reaction medium. The net outcome of the former two processes is defined as the monomer flux. A comparison of the effectiveness of monomer flux to the monomer diffusion in the reaction medium determines the type of growth reaction, either monomer diffusion-controlled or reaction-controlled. d) Illustration of Ostwald ripening. e) Numerical simulations of nanocrystal size evolution. The temporal evolution of size distribution of nanocrystal at high monomer supersaturation (S ¼ 900) under the diffusion-controlled growth reaction, and f ) the dependence of the standard deviation of particle size distribution on the mean particle size at different S of monomer in the reaction medium. Adapted with permission. [64] Copyright 2001, American Chemical Society. Fick's laws of diffusion. Dong et al. concluded that a high diffusivity of La 3þ ions was responsible for the rapid exchange in 5 nm-sized GdF 3 nanocrystals with a hopping mechanism through vacancies. [71] While other researchers held different opinions on this point, for example, Chen et al. claimed that Ln 3þ diffusion in β-NaYF 4 nanocrystals was sluggish because of the insufficient motion of the Ln 3þ ions and the vacancy absence in the lattice. [53] Exchange activity is also correlated with other factors [52a] and particle size-dependent cation exchange in the nanocrystal has been reported. [67] The effect of temperature is proved to be significant and a more efficient Gd 3þ exchange was detected in Ln 3þ -doped β-NaYF 4 nanocrystals at 100 C than at 25 C. [72] Besides, evidence shows the correlation of exchange activity to the cation concentration, [68] and a high degree of exchange is generally accomplished in the case of a steep concentration gradient. [72] The influence of reaction medium on the exchange process cannot be neglected as well, and a more efficient Tb 3þ exchange in β-NaGdF 4 :Yb 3þ , Er 3þ was observed in the organic solvent than in the aqueous medium [73] (Figure 13b,c). The impact of cation exchange on the formation of the nanocrystals also needs to be understood thermodynamically. Wang et al. denoted that a more thermodynamically stable β-NaLnF 4 than KLnF 4 triggered the KLnF 4 !NaLnF 4 transformation even under the condition of Na insufficiency. [74] Based on a thermodynamic cycle calculation, Dong et al. obtained a very slight variation of ΔG value in LnF 3 before and after cation exchange, [71] which explained the reversible exchange process Figure 13. a) HR emission spectra of Eu 3þ -doped LaPO 4 nanocrystal. These emission lines are composed of two sets of the Eu 3þ 5 D 0 ! 7 F 0-4 transitions which are attributed to Eu 3þ residing on the surface and interior of the nanocrystals, respectively. The spectral feature of surface Eu 3þ ions is recorded by using the sample as prepared by the exchange approach. Adapted with permission. [69] Copyright 2004, American Chemical Society. b) Luminescence photographs of β-NaGdF 4 :Yb 3þ , Er 3þ nanocrystals before and after Tb 3þ exchange in different media and c) concentration-dependent emission spectra of Tb 3þ after exchange routes. Adapted with permission. [73] Copyright 2018, Royal Society of Chemistry. Figure 12. a) Cation exchange in Cd-Ag-Se nanocrystals. The forward CdSe!Ag 2 Se transformation is rapidly accomplished (less than 1s) with Ag þ concentration slightly larger than the necessity, while the reverse process can be only triggered with 50-100 times excessive Cd 2þ concentration in the solution containing tributylphosphine. TEM images of the material at different stages prove the maintaining of nanocrystal morphology. The accomplishment of exchange can be verified by X-ray diffraction (XRD), emission, and absorption spectra. Adapted with permission. [67] Copyright 2001, The American Association for the Advancement of Science. b) Cation exchange in a β-NaLnF 4 nanocrystal. TEM images of β-NaGdF 4 :Yb 3þ , Tm 3þ @β-NaGdF 4 nanocrystals before and after Tb 3þ exchange, demonstrating that the morphology of nanocrystal is preserved. The emergence of 4f-4f luminescence of incorporated cations confirms the occurrence of exchange and the corresponding luminescence color changes of the material is shown. Adapted under the terms of the CC-BY license. [68]  in the system because of a low exchange energy barrier. Some even reported the opposite propensities of the exchange process as controlled by the rules of kinetics and thermodynamics, [75] which led to the temporal evolution of the material composition. [76] Hence, it is safe to conclude that the formation of the nanocrystals is essentially controlled by multiple mechanisms. [77] Keeping these in mind, the origins of chemical disorders in Ln 3þ -doped nanocrystal are discussed below.

Inhomogeneous Distribution of Dopant
The LaMer mechanism and its derivations can be used to survey the formation of fluoride-based nanocrystals, while the analysis should be done with caution. [78] Compared to that of elemental sulfur, the crystallization of fluoride-based ionic compounds (such as NaLnF 4 ) is more complex, and the reaction kinetics should be primarily considered ( Figure 14). Multiple types of monomers exist in the reaction medium and the formation of the nanocrystal requires the participation of all monomers. Even in the stage of monomer accumulation, a more intricate situation is expected regarding distinct supersaturations for various types of monomers [79] (Figure 15a). The study of monomer flux in the stage of nucleation is difficult as well.
The difference in diffusivities of various types of monomers makes the analysis of monomer aggregation and coalescence cumbersome [36e,80] (Figure 15b). Similar attention should be paid during the analysis of nucleus growth as well [81] (Figure 15c). Apart from these, more intractability will be brought by the issue of phase stability of nanocrystal. Taking NaLnF 4 as an example, there are two crystallographic phases of material (α and β) and it has been approved that the sequential emergence of these phases occurs during the wet synthesis of β-NaLnF 4 . Although tremendous efforts have been made to explore the origin of this phenomenon [80,82] (Figure 16a,b), the α!β phase transition mechanism is still unclear. Standing on this point, the crystallization of Ln 3þ -doped nanocrystals can be affected by any fluctuation of thermodynamic parameters and reaction kinetics during the reaction [83] which consequently alters the intrinsic features of the material. As denoted by Mai et al., [55] distinct crystallization routes of β-NaLnF 4 nanocrystals were observed depending on the type of Ln 3þ ion, which were related to the difference in the free energy variation of the system (Figure 16c). Hasse's group made great efforts to study the nucleation and growth features of different types of β-NaREF 4 nanocrystals (RE ¼ Sm, Eu, Gd, Tb; [81] RE ¼ La, Ce, Pr, Nd; [84] and RE ¼ Y [82e] ), and a unique crystallization route was observed in each case. In addition, the phenomenon of doping-induced phase transition was reported. Yu et al. showed that the α!β phase transition of NaYF 4 nanocrystals was achieved by doping 10%Ln 3þ owning a larger ionic radius than that of Y 3þ . [85] In the meantime, Wang et al. reported that the synthesis of small-sized β-NaYF 4 nanocrystals could be achieved by incorporating a certain amount of Gd 3þ in the system under some mild reaction conditions [6b] (Figure 16d). They explained that Gd 3þ incorporation increased the electron charge density on the particle surface, slowing down the diffusion of F À and increasing the polarizability of the system, which finally resulted in the size and phase control of the nanocrystal.
These results reveal that the formation of the nanocrystals is ascribed to the equilibrium between multiple processes. In this regard, the statistical distribution of dopants can be acquired only when the feature difference between dopant and host monomers does not affect the progress of every stage crystallization of the material, which cannot be assured in practical cases. Therefore, the dopant distribution in the nanocrystal ought to be inhomogeneous, and the concentration gradient of dopants is perhaps generated in the system containing different types of cations because of the reactivity difference.

Anisotropic Shell Growth
Shell growth is essentially a type of crystallization process occurring in the third stage of LaMer route; [86] only in this case the nucleation and nucleus growth are separated. Hence, shell growth is controlled by the thermodynamic properties of the system and reaction kinetics as well. [87] Compared to homogeneous nucleation, the shell growth process only requires overcoming a smaller energy barrier (Figure 17a). Given that the homogeneous nucleation and shell growth are dominated by the same mechanism, useful knowledge can be obtained from Figure 14. Graphic representation of the formation of β-NaLnF 4 nanocrystals. The whole process is divided into five different stages and fluctuations in any of these stages will alter the formation of the materials. previous reports on the anisotropic crystallization of nanocrystals to explore the origin of anisotropic shell growth. The generation of anisotropic morphology of NaLnF 4 nanocrystals was analyzed by Mai et al., [55] which was attributed to the thermodynamiccontrolled crystallization. Li et al. found that the morphology of β-NaLnF 4 :Yb 3þ , Er 3þ nanocrystals was associated with the chemical composition of the reaction medium, [88] and different morphologies were obtained when various dosages of the surfactant agent were used. This issue was also addressed by Shan et al. [36e] and the impacts of surfactant and concentration ratio of various types of monomers on the nucleus growth were discussed. Wang et al. reported the anisotropic crystallization of Ln 3þ -doped β-NaGdF 4 and discussed the relation of the nanocrystal morphology to the reaction conditions. [89] Liu et al. provided a comprehensive study on the controllable growth of β-NaLnF 4 nanocrystals [36g] and the relations of nanocrystal morphology to various factors (such as facet-dependent ligand adsorption, thermodynamic features of ligands, reaction temperature, pH, monomer concentration, and concentration ratio of different surfactants) were analyzed. They claimed that the growth of β-NaLnF 4 was mainly controlled by the facetdependent ligand adsorption (Figure 17b), and the morphology of nanocrystal could be facilely modulated by adjusting the reaction conditions. An analogous statement was proposed by Kang et al., [36c] showing that the shell growth behavior of β-NaYF 4 : Yb 3þ , Er 3þ @β-NaYF 4 nanocrystals could be altered by adjusting the dosage of OA ligand during the reaction (Figure 4c,17c). The variation of the experimental procedure can influence the shell growth feature as well [20b] (Figure 6b). Fisher et al. found that the isotropic shell growth of β-NaYF 4 :Yb 3þ , Tm 3þ @β-NaYF 4 was achieved by the fast sequential injection of the shell precursor into the reaction medium, while the anisotropic shell growth was obtained by dropwise injecting of the precursor into the reaction under identical conditions [38] (Figure 18a). They stated that monomers were energetically favorable to grow on the facet of the nanocrystals possessing a weaker ligand binding in a low monomer concentration condition, and the isotropic shell growth was preferable if the monomer concentration was sufficient. This finding shows that even a simple change in the experimental procedure can induce a dramatic change in the shell growth process, demonstrating the importance of methodology standardization in nanocrystal preparation. Recent reports have shown that the lattice mismatch between core and shell components also affected the shell growth [90,91] (Figure 18b) and the morphology of the nanocrystals could be influenced by the extent of interfacial strain [92] (Figure 18c). The isotropic shell growth was observed in the case of shell-to-core tensile strain and the anisotropic growth was detected in the case of shell-to-core compressive strain even under the same magnitude of lattice mismatch [90] (Figure 18b). Very recently, Chen et al. showed that the shell growth of β-NaYbF 4 @β-NaYF 4 nanocrystals could be significantly altered by delicately selecting the injection rate of shell precursor and demonstrated that the difference in growth was mainly controlled by the interplay between the core/shell lattice mismatch and the chemical potential of the shell precursor in the reaction system. [93] These observations reveal that the shell growth can be easily affected and the interpretation of shell passivation can be accomplished only if sufficient efforts are made to ensure isotropic shell growth in the studied system.

Element Intermixing
Although the phenomenon of element intermixing has been detected in Ln 3þ -doped nominal core-shell nanocrystals, the Figure 15. a) TEM images and XRD patterns of nanocrystals prepared in media with different compositions. Compared to the NaF insolubility in pure 1-octadecene (ODE), its solubility increases in the medium containing oleic acid (OA) because of the increase of polarity. Besides, Ln(oleate) 3 is more easily dissolved in an OA-containing medium which reaches a higher monomer concentration. Adapted with permission. [79e] Copyright 2009, Royal Society of Chemistry. b) Temporal evolutions of formation of α-NaGdF 4 nanocrystals as prepared at different temperatures as presented by TEM images and the variation in luminescence intensity. A phenomenon of "delayed nucleation" is observed, which is related to the insufficient accumulation of a certain type of monomer in the system. Adapted with permission. [80] Copyright 2007, American Chemical Society. c) Time-dependent size growth of α-NaGdF 4 nucleus, verified by TEM images. Adapted with permission. [81] Copyright 2013, Royal Society of Chemistry.
www.advancedsciencenews.com www.small-structures.com origin of this process is intricate. As a type of crystallization, the process of shell growth is controlled by the equilibrium of monomer precipitation and nucleus dissolution as well. Here, the integrity of the core of the nanocrystals during shell growth is worthy of note particularly (Figure 19). In fact, evidence has been shown that this integrity could not be assured [20b,41] and a substantial dissolution of core was more likely (Figure 6 and 7). This issue can be better understood from different perspectives. As it is known, the biosecurity assessment of Ln 3þ -doped nanocrystals for bioapplications has attracted great attention in recent years, [94] and material stability is one of the research hotspots. [95] The crux of the matter is the integrity of the material in biocompatible media [96] and different results have shown strong correlations between material stability, the type of medium, and the surface feature of the nanocrystal. [97] Several groups investigated the chemical stability of Ln 3þ -doped β-NaYF 4 in the aqueous   (Figure 20a,b), and disintegration appeared to be unavoidable but only partially alleviated. [99] Although these works used a variety of experimental conditions and setups, the concept of solubility equilibrium was commonly used to understand the disintegration effect. When the ionic compound disperses into a blank medium, some fractions of material dissociate into the forms of constituent ions to reach the solubility equilibrium of the system. The crystallization of fluoride-based nanocrystal follows an analogy equilibrium mechanism. Back to the process of shell growth (Figure 19), whichever growth method (OPH or hot-injection) is adopted the core nanocrystals are initially put into the reaction medium for the purpose of subsequent shell growth and the dissolution of core takes place immediately regarding the monomer-free condition of the medium. The rising in reaction temperature increases the core monomer concentration in the medium due to the aggravation of core  Adapted with permission. [38] Copyright 2017, American Chemical Society. b) Impact of lattice mismatch on the shell homogeneity. Adapted with permission. [90] Copyright 2014, American Chemical Society. c) Morphology of β-NaYF 4 :Yb 3þ , Tm 3þ nanocrystals after shell growth with different compositions. As increasing the core/shell lattice mismatch, a gradual change in growth manner (from isotropic to anisotropic) is observed. Adapted with permission. [92] Copyright 2019, Wiley-VCH. dissolution, which is also along with the monomer supply escalation from the decomposition of shell precursor. The net-zero core dissolution reaches once the monomer concentration in the medium is beyond the condition of supersaturation, and the shell starts to grow on the rest of core by consuming the mixed-composition monomer. Hence, core-shell element intermixing is essentially induced by the complex shell growth process, and the extent of intermixing is associated with the actual composition of shell monomer in the system. A similar explanation was proposed by Dühnen et al., [20a] showing that distinct monomer supply efficiencies and reactivities of various types of shell precursors (α-phase or TFA-based salts) during shell growth reaction were the reasons behind the observations of different concentration gradients of Eu 3þ in the Gd 3þ -based shell (Figure 5e). Following this idea, Hudry et al. explained the element intermixing in Ln 3þ -doped nominal core-shell nanocrystals and rationalized its dependence on different growth methods [20b,41] (Figure 6b). The verification of this viewpoint can be found in the work of Halimi et al. [79a] (Figure 20c), which denoted the difference in monomer supply efficiency during the decomposition reaction of precursor to form β-NaLnF 4 nanocrystals. The impact of element mobility needs to be considered as well. When the core nanocrystal is put into the medium as filled by shell cations, the exchange process can be easily triggered on the surface of the core particle. [37,70b,72,100] These released core cations will mix with the rest of shell cations in the medium and grow on the core subsequently, [77a] resulting in the core-shell element intermixing. The fundamental principle of this process is analogous to the crystallization equilibrium, yet the difference is that the flux in the current case is on the level of cation, and the integrity of core nanocrystal is maintained, in contrast to the substantial core dissolution as denoted before.
The influence of element diffusion should not be neglected. Instead of the localization of atoms in the lattice of the nanocrystal, the process of atom diffusion can be active once the diffusion energy barrier is overcome by thermal assistance. Depending on the involved mechanism, different atom diffusion efficiencies are expected, and vacancy-participated diffusion is generally regarded as the most efficient one (Figure 20d). Although some researchers held different opinions on the effectiveness of element diffusion in inorganic compounds, for example, the observation of a less 1 nm diffusion length of Mn in CdTe after 1 h duration [101] and undetectable Eu 3þ diffusion in Ce x Zr 1-x O 2 after high-temperature treatment, [102] the element diffusion in β-NaLnF 4 nanocrystal has been confirmed [46] (Figure 8). The vacancy abundance in β-NaLnF 4 lattice [103] is probably the reason to prompt the element diffusion, which is also responsible for the ionic conduction of β-NaYF 4 , as reported before. [104] It should be kept in mind that the current understanding of element intermixing is still in the preliminary stage. The above analyses are merely qualitative and the quantitative evaluation of intermixing extent in the nanocrystal is challenging because necessary efforts should be made to assess not only the impact of these individual processes but also the synergy effect between them. From the aspect of experimental guidance, one thing that is worth exploring is to find a way to minimize the influence of element intermixing on the interpretation of shell passivation, yet progress in this direction has largely stagnated. Some results in the report of Liu et al. deserve special attention, [46] showing that the diffusion extent of core Er 3þ decreased as changing the shell component β-NaYF 4 > β-NaLuF 4 > β-NaGdF 4 in sequence (Figure 8f ). Regarding a gradual increase in the ionic radius difference between Er 3þ and Y 3þ (1.2% radius difference, with the ninefold coordination), Lu 3þ (2.8%), and Gd 3þ (4.2%), they suggested that the intermixing might favorably occur between Ln 3þ ions with similar radii. Given that the work of Liu et al. aims to study the element intermixing in the nanocrystal as prepared in advance, perhaps this criterion of radius difference can be used to conjecture the probability of element intermixing in the nanocrystal through the process of diffusion. Unfortunately, conflicting results can be found as Figure 19. Illustration of core-shell intermixing from the perspective of crystallization equilibrium. The extent of element intermixing in the nanocrystal is determined by the synergy of core dissolution, monomer accumulation, and mixed-composition monomer precipitation. well [105] (Figure 20e), showing a significant diffusion of Yb 3þ and Er 3þ in β-NaGdF 4 in spite of large radius differences of Yb 3þ /Gd 3þ (6.2%) and Er 3þ /Gd 3þ (4.2%). Inspired by these observations, one may speculate if the radius difference can be used as the criterion to assess the probability of element intermixing through other pathways, for instance, cation exchange, yet no significant correlation can be found because of the observations of both almost complete exchange in the systems containing La 3þ cation and GdF 3 (EuF 3 ) nanocrystals (La 3þ /Gd 3þ , 9.0%; La 3þ /Eu 3þ , 7.9%) [71] and Ln 3þ -exchange in β-NaGdF 4 nanocrystals (Ln ¼ Ce 3þ (7.4%), Tb 3þ (1.1%), Eu 3þ (1.2%), Dy 3þ (2.2%)) in the aqueous [68] (Figure 12b) and organic media [73] ( Figure 13c). Besides, element intermixing becomes elusive during the shell growth reaction at high temperatures because the final observation is the consequence of multiple factors, not only from the kinetic processes as currently discussed but also from the contribution of crystallization thermodynamics, as denoted above. Hence, the strong intermixing was both detected in cases of Dy 3þ /Y 3þ (0.7%) [47] and Eu 3þ /Gd 3þ (1.2%) [46] with small radius differences and in cases of Yb 3þ / Gd 3þ (6.2%) and Gd 3þ /Y 3þ (2.9%) with large differences. [43] Interestingly, Tm 3þ behaved as if it were highly confined in Adapted with permission. [105] Copyright 2017, American Chemical Society.
www.advancedsciencenews.com www.small-structures.com the designed region of β-NaGdF 4 :Er 3þ @β-NaYbF 4 @β-NaGdF 4 : Tm 3þ @β-NaYF 4 and no intermixing with other Ln 3þ ions abundant in neighboring regions was detected, even if those ions owned similar radii (Tm 3þ /Yb 3þ , 1.0%; Tm 3þ /Y 3þ , 2.2%). [43] This anomaly was reported elsewhere as well, [106] showing a strong Yb 3þ /Gd 3þ (6.2%) intermixing in β-NaGdF 4 :Yb 3þ , Er 3þ , while no Er 3þ /Gd 3þ (4.2%) intermixing was detected in the same system. Additional attention should be paid to the work of Dong et al. [105] (Figure 20f ), showing the suppression of Yb 3þ (Er 3þ ) outward (inward) diffusion in β-NaGdF 4 :Yb 3þ @CaF 2 : Er 3þ . They stated that it was due to the large difference in core and shell components. These results indicate that the element intermixing is probably universal in Ln 3þ -doped nanocrystals with complex geometries. The understanding of intermixing process is still limited and more efforts should be made in the future not only to uncover this mystery but also to find a way to regulate its behavior.

Impact on Luminescence Properties of Nanocrystal
The abovementioned discussions show that the stereotyped understanding based on statistics and homogeneity fails to interpret the shell passivation properly in Ln 3þ -doped nanocrystals. A large number of chemical disorders are generated due to the variation in experimental conditions and reactivity differences of precursors during the synthesis, making the intrinsic feature of nanocrystal strongly deviate from its nominal feature. One consequence of this is that the luminescence performance of the nanocrystals will be deteriorated by these chemical disorders, as it is discussed below (Figure 21).
Taking nanocrystals with a nominal core-(single) shell geometry as an example (Figure 21a,b), some core luminescent centers immerse in the inert shell during the synthesis (Figure 21c) shorten the distance to surface quenchers, increasing, then, the probability of quenching. In this case, the apparent effectiveness of shell passivation is diluted because of the excitation energy dissipation of these leaked centers, in contrast to the situation of the ideal "core-shell" case with strict element segregation (Figure 21b). Here, one opinion is held in the previous discussion that the shell passivation is still valid for the centers residing in the interior of the nanocrystals (red solid circles) and only those leaked luminescent centers suffer from the aggravation of surface quenching (Figure 21c, blue solid circles). Unfortunately, this viewpoint overlooks the strong ion-ion interaction that occurs in the system, particularly at high doping concentrations (Figure 21d,e). Energy migration, as a typical representative, plays a crucial role in bridging the excitation energy flow in Ln 3þ -doped materials which makes the energy transfer between luminescent centers more rapid. [26,107] Despite its versatility, its contribution to the luminescence performance of material still requires clarification and the quantification of energy migration length is the crux of the matter. To address this issue, Fischer et al. studied the impact of Er 3þ -Er 3þ ( 4 I 13/2 , 4 I 15/2 ! 4 I 15/2 , 4 I 13/2 ) energy migration on the luminescence of β-NaYF 4 :Er 3þ nanocrystals. [27b] The migration length of this channel under different irradiances at 1523 nm excitation was derived by a 3D random walk simulation model. As the irradiance increased from 0.1 to 150 W cm À2 , the mean migration length of this channel changed from 17 to 3.2 nm. In the subsequent work, [17a] they investigated the dependences of the migration length of Yb 3þ -Yb 3þ ( 2 F 5/2 , 2 F 7/2 ! 2 F 7/2 , 2 F 5/2 ) channel Figure 21. Illustration of the aggravation of surface quenching in Ln 3þ -doped nanocrystals as induced by energy migration in the case with element intermixing. Different from the understanding of a) a "dark layer"-defined surface quenching of a core nanocrystal and b) the ideal shell passivation, c) strong element intermixing occurs in practical accompanying with the outward immersion of core luminescent centers, resulting in the insufficient shell passivation. Taking the process of energy migration into consideration, significant luminescence dissipation occurs in d) the bare core and e) the nominal core-shell nanocrystals, making the effectiveness of shell passivation feebler.
www.advancedsciencenews.com www.small-structures.com ( Figure 22a1) on the excitation irradiance of 980 nm ( Figure 22a2) and the concentration of Yb 3þ (Figure 22a3) in β-NaYF 4 :Yb 3þ , Er 3þ nanocrystal, and a mean migration length of 28 nm was derived for this channel under 33% Yb 3þ doping and 100 W cm À2 irradiance conditions. Hence, the impact of energy migration on the luminescence properties of Ln 3þ -doped nanocrystals is acquired immediately ( Figure 21). As denoted by Fischer et al., 70% of the Er 3þ substitutable sites resided in the region 3.2 nm inward from the surface of 19 nm-sized β-NaYF 4 nanospheres. Thus, Er 3þ ions residing in this region could transfer their excitation energy through a 3.2 nm-long Er 3þ -Er 3þ migration to the particle surface and quenched. [27b] The situation deteriorated when a long-range migration was active, and the length of Yb 3þ -Yb 3þ migration (28 nm) was even longer than the employed diameter of the β-NaYF 4 nanocrystals (e.g., 24 nm) [17a] (Figure 22a2, inset), implying that most of the Yb 3þ luminescence was affected by surface quenchers. Based on these results, a more realistic understanding of the impact of chemical disorders on the luminescence properties of Ln 3þ -doped nanocrystal is acquired. Element intermixing occurs during the synthesis, resulting in a nonzero residing probability of core luminescent center in the surface region of the nanocrystal. [20a,41] In this regard, the luminescent centers have a high probability of combining together through energy migration and sharing properties including quenching behavior with each other. That is to say, these leaked centers virtually serve as the "breach" in the whole energy flow (Figure 22b). Once the network of energy migration is established, the overall excitation energy of the system will be eventually transferred to luminescent centers located nearest the particle surface and dissipated accordingly, [34b,108] even if only a small number of such centers exist. As a result, the aggravation of surface quenching spreads across the entire nanocrystal, which severely deteriorates the luminescence performance of the material. It can be figuratively comprehended as the implementation of percolation of excitation energy dissipation in the system. Hence, the effectiveness of shell passivation will be seriously diluted in Ln 3þ -doped nominal core-shell nanocrystals and the passivation efficiency is essentially controlled by the leakage extent of core luminescent centers in the shell and the number of centers nearest to the particle surface, rather than the apparent shell thickness. This point agrees with the previous statement that the passivation efficiency of inert shell was always controlled by the thinnest shell thickness in the system. [27c,38,40] Figure 22. a) Energy migration in β-NaYF 4 :Yb 3þ , Er 3þ . (a1) Scheme of excitation energy flow and the Yb 3þ -Yb 3þ ( 2 F 5/2 , 2 F 7/2 ! 2 F 7/2 , 2 F 5/2 ) migration channel. (a2) The likelihood of migration length of this channel in the nanocrystal with 33%Yb 3þ doping upon 980 nm excitation of different irradiances. The inset gives a TEM image of the nanocrystal. (a3) The likelihood of migration length in the nanocrystal with different Yb 3þ concentrations upon a 100 W cm À2 excitation. Adapted with permission. [17a] Copyright 2016, American Chemical Society. b) Graphic representation of the role of "breach" as played by the leaked luminescent centers residing near the particle surface, and the excitation energy of the system will be severely dissipated as intensified by the energy migration.
The serious influence of these chemical disorders can be reflected in other aspects. For instance, Hudry et al. [41] argued that the occurrence of element intermixing raised doubts about the notion of total decoupling for various types of Ln 3þ ions as nominally segregated in different regions of the multishell nanocrystals [109] and hence questioned the authenticity of the "interfacial energy transfer" mechanism based on this decoupling notion. [110] Furthermore, the significance of intentionally introducing luminescent centers into the inert shell of Ln 3þdoped nanocrystals should be reconsidered. The strategy of "Yb 3þ active shell" [111] has been approved to boost the brightness of Ln 3þ -doped luminescent nanocrystals by increasing the absorption rate of 980 nm photons. [112] However, the incorporation of Yb 3þ into the inert shell creates the Yb 3þ -Yb 3þ energy migration channel at the same time, which will bridge the core luminescent centers and surface quenchers and reactivate the surface quenching. A clear demonstration of this point can be found in the work of Hu et al., [113] showing that surface quenching is significant in Yb 3þ active-shell-coated Ln 3þ -doped-NaGdF 4 nanocrystals than in the case of inert-shell passivation. Johnson et al. [13b] also denoted that the incorporation of Yb 3þ in the inert shell caused the re-emergence of surface quenching on the luminescence of β-NaErF 4 nanocrystal which should have been largely suppressed by the inert shell. The discussion on true contribution of active shell in Ln 3þ -doped nanocrystals can be found elsewhere, [114] and very recently, Zhang et al. [37] reported that the deposition of Yb 3þ shell on β-NaErF 4 luminescent nanocrystal had little effect on the surface quenching alleviation, which was attributed to the ineffective blocking of core Er 3þ to surface quenchers due to the efficient Yb 3þ -Yb 3þ energy migration.
In brief, these disorders are probably the fundamental reason behind the contradictory observations and explanations of shell passivation as previously reported (Figure 2), which are essentially brought about by tremendous uncertainties during material synthesis. Future research on the luminescence properties of Ln 3þ -doped nanocrystal should fully consider these profound effects to avoid any misinterpretation of observations.

Remarks and Perspectives
Retrieving the topic of this work, the current understanding of the shell passivation effect is proved to be inadequate, and the corresponding analysis may lead to the misinterpretation of results. The root of the problem is manifold. Initially, the acquirement of criterion-normalized experimental data is not assured, which hinders the cross-checking of results from different resources. Next, the understanding of the passivation mechanism is still insufficient, causing the interpretation of shell passivation in most studies stemming only from a narrow perspective which makes the corresponding explanations less persuasive. More importantly, it lacks the clear recognition of intrinsic features of the studied nanocrystal. The analysis of the shell passivation effect generally follows the understanding based on statistics and homogeneity, while the rationality of this paradigm to describe the luminescence quenching of Ln 3þdoped nanocrystals is pending. In fact, results have shown that the intrinsic features of the nanocrystals deviate from their nominal features. Strong chemical disorders, such as shell inhomogeneity, element intermixing, and inhomogeneous dopant distribution, are present and the potential interference brought by these disorders will significantly impede the interpretation of shell passivation in Ln 3þ -doped nanocrystals with nominal core-shell geometries. Up to now, this issue has not received enough attention.
More obstacles will be faced when tracking the origin of these chemical disorders. Here, a deliberate attempt is pursued from the perspective of crystallization. Stemming from the LaMer mechanism, the formation of Ln 3þ -doped nanocrystals is deconstructed and the contributions of thermodynamic and kinetic processes evaluated. Results demonstrate that these disorders are mostly generated during the process of synthesis. The intricate formation of the nanocrystals creates significant uncertainties in component geometry and element distribution in the system, which makes challenging the assessment of the shell passivation efficiency. In addition, the impact of these disorders on the luminescence properties of Ln 3þ -doped nanocrystals will be intensified by the process of energy migration. Hence, it raises a concern about the rationality of shell thickness-oriented understandings of the passivation effect, which deserves more attention.
The importance of this topic can be understood from a more general perspective. In contrast to the case of bulk optical materials in which relevant investigations are focused on their overall characteristics, such as luminescence color and brightness, the size advantage of luminescent nanocrystals makes them seize application potential in the research frontiers which require a high degree of accuracy. Under this circumstance, any variation in the luminescence signal of the materials is regarded to be meaningful, which represents a certain feature change in the system, and the reason behind this variation needs to be very clear. In the matter of shell passivation, without explicit knowledge of the passivation mechanism, versatile strategies cannot be established to suppress the surface quenching, which will hinder the practical application of Ln 3þ -doped nanocrystals. Future efforts should be made to establish rational paradigms for studying the features of luminescent nanocrystals and to permit the development of Ln 3þ -doped nanomaterials with superior properties, capable of meeting the application requirements in various frontier fields, such as visual enhancement, [115] biomedicine, [116] and molecular logic. [117]