Reversible Tuning of Ca Nanoparticles Embedded in a Superionic CaF 2 Matrix

Controlling the size and shape of metallic colloids is crucial for a number of nan-otechnological applications ranging from medical diagnosis to electronics. Yet, achieving tunability of morphological changes at the nanoscale is technically diﬃcult and the structural modiﬁcations made on nanoparticles generally are irreversible. Here, we present a simple non-chemical method for controlling the size of metallic colloids in a reversible manner. Our strategy consists on applying hydrostatic pressure on a Ca cationic sublattice embedded in the irradiated matrix of CaF 2 containing a large concentration of defects. Application of our method to CaF 2 along with in situ optical absorption of the Ca plasmon shows that the radii of the Ca nanoparticles can be reduced with an almost constant rate of − 1 . 2 nm/GPa up to a threshold pressure of ∼ 9 . 4 GPa. We demonstrate recovery of the original nanoparticles upon decompression of the irradiated matrix. The mechanisms for reversible nanocolloid-size variation are analyzed with ﬁrst-principles simulations. We show that a pressure-driven increase in the binding energy between ﬂuorine centers is responsible for the observed nanoparticle shrinkage. We argue that the same method can be used to generate other metallic colloids (Li, K, Sr, and Cs) with tailored dimensions by simply selecting an appropriate matrix.


Introduction
Metal nanoparticles (MNP) are the pillar of many technological applications extending from calorimetric sensors and chemical catalysts to in vivo imaging and photothermal therapy 1 .
The success of these technologies strongly depend on the shape and size of the MNP.However, achieving specific modifications on the morphology of MNP can be an arduous and erratic task when chemical methods are used 2,3 .Additionally, the structural changes inflicted on MNP by synthetic methods normally are permanent, which hinders the reutilization of expensive products based on nanocolloids.An extreme case occurs when MNP are embedded in composite materials involving dielectric matrices, which is a common setup in plasmonic applications 4 ; subsequent size tuning of the entreched MNP is unattainable with current methods.
(a) (b) Here we present a simple and effective physical method to reversibly tune the size of Ca MNP.Our method consists of applying hydrostatic pressure on Ca MNP embedded in a dielectric matrix, which are generated by irradiating a crystal; in this way, a large concentration of highly mobile point defects is created.We apply our method to control the size of calcium nanoparticles in CaF 2 (Ca@CaF 2 ).Our starting point is a CaF 2 crystal irradiated with 2.2 GeV 197 Au ions 5 (other irradiation techniques involving x-rays or different types of ions 6 , or simple exposure to ultraviolet light, to metal vapor, or electron beam lithography 7 , should also provide an alternative means to fabricate similar nanostructures [8][9][10] ); the irradiated matrix contains a large number of highly mobile fluorine vacancies and interstitials [11][12][13][14][15][16] , hence calcium nanoparticles with a crystal symmetry compatible with that of CaF 2 naturally appear (Fig. 1a).Here, we show that subsequent application of hydrostatic pressure causes the radii of the so-generated MNP to decrease considerably in a controlled and reversible manner.Specifically, using in situ optical absorption spectroscopy we determine that the radii of the Ca nanoparticles are reduced at an almost constant rate of −1.2 nm/GPa up to a pressure of ∼ 9.4 GPa, when a structural phase transition occurs in CaF 2 (Fig. 1) and the MNP vanish.The proposed MNP modification method red under high pressure exploits the appearance of metallic clusters and color centers in dielectric matrices, which usually are regarded as a drawback for classical-optics applications [17][18][19][20] , to engineer new functional materials.

Experimental Details
Irradiated high-purity CaF 2 single crystals from the Optical Institute (St.Petersburg, Russia) were employed.The irradiation with ions was performed in vacuum at the linear accelerator UNILAC (GSI, Darmstadt, Germany) with 2.2 GeV 197 Au ions at ambient temperature, the ion flux was kept to 10 8 -10 9 ion/cm 2 s with a fluence of 2×10 11 ions/cm 2 .More details can be found in Ref. 5 .For optical absorption in the UV-VIS range, ∼15 µm thick single crystals were cleaved and placed together with a ruby chip for pressure determination 42 into the 200 µm hole drilled in a 50 µm thick stainless steel gasket inserted between two IIA diamonds of a membrane-type diamond anvil cell (DAC).The transmittance measurements were carried out with a confocal optical setup that consisted of a deuterium lamp, fused silica lenses, two Cassegrain objectives, and two UV-VIS spectrometers to cover the measured range.The surface area of the sample was around 80×60 µm 2 and the focused beam spot was of 25 µm in diamater.

Calculations Details
First-principles calculations were performed with the VASP code 43 by using the generalized gradient approximation to the exchange-correlation energy due to Perdew et al. 44 The projector augmented-wave method is used to represent the ionic cores, 45 and the Ca's 6p-2s, and F's 2s-5p electronic states are considered as valence band states.Wave functions are represented in a plane-wave basis truncated at 650 eV.By using these parameters and dense k-point grids for integration within the Brillouin zone (equivalent to a 16 × 16 × 16 mesh employed for the cubic fluorite structure), the resulting energies are converged to within 1 meV per formula unit.In the geometry relaxations, a threshold tolerance of 0.01 eV/Å is imposed on the atomic forces.
The binding energy between F centers has been estimated with the formula where the first term in the rhs of (1) corresponds to the energy of bulk fcc Ca, the second to the energy of bulk fluorite CaF 2 , and the third to the energy of non-stoichiometric bulk fluorite CaF 2 for a given pressure P ; the subscripts indicate the size of the supercells that have been employed to compute each energy term (e.g., Ca 32 F 63 represents a 32-formula unit fluorite CaF 2 supercell in which one F ion has been removed).
The interface energy per unit surface of a fcc Ca nanoparticle embedded in a fluorite CaF 2 matrix can be estimated with the formula 10 where "Ca n/2 F n |Ca m |Ca n/2 F n " stands for a supercell constructed by stacking m fcc Ca unit cells on top of n fluorite CaF 2 unit cells and in which periodic boundary conditions are applied along the three Cartesian directions.The lattice parameter of bulk CaF 2 is constrained along the stacking direction; this can be done because the arrangement of Ca atoms in the nanoparticle and fluorite CaF 2 is the same, and the stiffness of CaF 2 is significantly larger than that of Ca (hence we assume that the colloid completely takes up the mechanical stress).The energy penalty associated to the mechanical strain of the nanoparticle is considered separately (see below).In order to avoid spurious interactions between periodic interface images, the size of the supercell along the stacking direction needs to be sufficiently large.We have performed tests on the convergence of the E Ca n/2 Fn|Cam|Ca n/2 Fn energy with respect to the supercell size and concluded that parameters m = 3 and n = 11 provide sufficiently accurate results converged to within 10 meV/nm 2 .
Finally, the stress energy per unit volume of a fcc Ca nanoparticle embedded in a fluorite CaF 2 matrix is calculated as 10 where B represents the bulk modulus of bulk fcc Ca and ≡ the accompanying lattice strain for a given pressure P .

Results and Discussion
At ambient conditions, the interaction of light with calcium colloids in irradiated CaF 2 produces a broad absorption band located at around 560 nm (Fig. 2), which can be modelled as a function of colloid size by using Mie theory [21][22][23] .In order to in situ monitor the size of the calcium colloids in CaF 2 under high pressure, we employ optical absorption spectroscopy.
This technique is widely used to quantify the number of MNPs in ionic crystals and can be performed inside the diamond anvil cell.The experimental data are analyzed by Mie theory assuming that the calcium nanoparticles are spherical, and ab initio simulations are performed to disclose the atomistic mechanisms causing the MNP size reduction.A summary of the absorption spectra obtained at different pressures is shown in Fig. 2.
The absorbance spectrum of irradiated CaF 2 at ambient pressure is well known and consists of two bands (Fig. 2 (b)).The first band, located at 2.28 eV (545 nm), is a relatively intense broad band that normally is attributed to the presence of Ca colloids 24 .The second band is a narrower and weaker band located at 3.25 eV (382 nm) that is attributed to the presence of F-centers 25 .Under pressure, the overall absorbance reduces and the maximum of the broad band blueshifts at a rate of 0.025 eV/GPa (Fig. 2c).At P = 9.4 GPa, the absorption spectrum changes drastically and the intensity of the first peak drops abruptly.Such an intensity reduction is most probably related to a noticeable decrease in the density of colloids under pressure confirmed by the complete dissapearence of the bands at higher pressures.However, when pressure is released both bands reappear (although their absorbance intensities are much lower).The disappearance of the bands above 9.4 GPa can be associated with the pressure-induced phase transition 26 that CaF 2 undergoes at this pressure from the fluorite (space group Fm 3m) to the contunnite phase (space group Pnma), as shown in Fig. 1.We will elaborate on the causes of this effect latter on when explaining our ab initio calculations.
To a first approximation, and due to their small size, let us assume that the optical properties of the Ca@CaF 2 colloids can be described within the Rayleigh limit, a good approximation when the size of the MNPs is much smaller than the wavelength of light.In this case, the resonance in the total absorption cross-section of the system is expected to occur when where (ω) and m are the dielectric functions of metallic calcium and the surrounding CaF 2 medium, respectively.Considering that the pressure coefficient of the refracive index of CaF 2 is very small (2.44 × 10 −3 GPa −1 ) 28 , m can be assumed to be independent of wavelength and pressure while (ω) can be expressed by using the Drude model, which neglects interband transitions and the finite lifetime of the plasmons, i.e. (ω (where ω 2 p = 4πN e 2 /m * is the plasma frequency of the bulk metal, and N and m * the density and effective mass of the conduction electrons, respectively).According to Rayleigh's condition, the resonance takes place when Using the value m * = 1.9m e for the optical mass of the electrons in bulk Ca, the resulting plasma frequency for Ca is 5.78 eV. 22By using these values and Eq. 5, it is found that the resonance frequency for Ca@CaF 2 nanocolloids should occur at 2.56 eV, which is close to the maximum absorbance measured in our sample at ambient pressure (2.28 eV, see Fig. 2).
Thus, the Rayleigh approximation provides a reasonable estimation of the wavelength of the maximum absorbance in these colloids.
The pressure behavior of the optical properties of the Ca@CaF 2 system can then be obtained analytically from Eq. 5 by taking its pressure derivative where B 0 is the bulk modulus of the Ca nanocolloids (which appears after taking the pressure derivative of N ).The degree of compression of the Ca nanocolloids should be dictated by the less compressible CaF 2 matrix, hence it can be assumed that B 0 is equal to the bulk modulus of CaF 2 , namely, 82 GPa. 27By using this value and Eq. 6, one finds that the pressure coefficient expected for the plasmon resonance within the Rayleigh limit is 0.015 eV/GPa, which is significantly smaller than the experimental value of 0.025 eV/GPa.
The difference between these theoretical results and the experiments becomes even larger when the pressure behavior of the CaF 2 refractive index 28 is taken into consideration in the analysis: the pressure coefficient deduced in this case becomes ∼ 4 meV/GPa larger.In spite of the possible limitations of the presented simple approach based on the Rayleigh's limit, the large differences between theory and experiments suggest that an overlooked effect may be modifying the pressure dependence of the optical absorbance of Ca@CaF 2 colloids.As we will show next, such a difference can be explained in terms of a pressure-induced shrinkage of the colloids.
A better description of the pressure behavior of the optical absorbance of the Ca@CaF 2 colloids can be obtained with Mie theory. 10,22In the present work we employ the software MiePlot, 29 which is based on the classical work by Bohren and Huffman, 30 and closely follow the procedure used by Orera and Alcalá to simulate the optical properties of Ca@CaF 2 spherical colloids at ambient conditions. 22Within this approach, the dielectric function of the metal is modeled through the Drude function, including the finite lifetime of the plasmons and interband terms that, for the sake of simplicity, here are assumed to be independent of pressure.An additional correction on the plasmon damping due to the small particle size of the colloids has been taken into account. 22In the present calculations, the dielectric functions and spherical sizes of metallic Ca nanocolloids were obtained at different pressures by assuming that the pressure dependence of the corresponding dielectric function stems from changes in the electron density, a good approximation within the Drude model; the bulk modulus of CaF 2 was employed, as justified previously.The pressure dependence of the refractive index of CaF 2 is also included in our analysis by following the work of Schmidt and Vedam 28 .It is worth noting that test calculations of the extinction efficiency performed for vanishingly small particle sizes at ambient pressure, Q ext , are in very good agreement with those obtained analytically with the Rayleigh approximation (Eq.5).
Fig. 3 shows the experimental absorbance (solid curves) and Q ext calculated with Mie theory (dashed curves) at two different pressures (1 atm and 6.1 GPa).As can be seen in the figure, the theoretical curves qualitatively follow the wavelength dependence of the absorbance maxima.At ambient pressure, the best agreement between the experimental absorbance and Q ext is obtained by considering a radius R of 31 nm for spherical Ca colloids.
At P = 6.1 GPa, the particle size that is found to better reproduce the experimental curve is 23 nm.These values are of the same order of magnitude as those reported by Rix et al.
for CaF 2 crystals irradiated with intense UV light. 10g. 4 shows the pressure-dependence of the particle size of the Ca colloids as extracted from the analysis of the absorbance curves with Mie theory.As can be seen therein, the size of the nanocolloids is approximately reduced at a constant rate of −1.2 nm/GPa over the entire pressure range.By performing similar calculations at different particle sizes and constant pressure, it can be shown that such a size reduction leads to a ∼ 0.014 eV/nm E n e r g y ( e V ) increase in the absorbance maximum at zero pressure.At around 6 GPa, this value decreases down to ∼ 0.011 eV/nm.Consequently, the pressure coefficient of the absorbance maxima is enhanced by 0.013-0.017eV/GPa due to a pressure-induced size reduction, regardless of the shifts arising from the increase in N under pressure.As shown previously in the description of the optical properties of Ca@CaF 2 colloids within the Rayleigh limit, such an increase can account for around half of the experimental pressure coefficient (0.025 eV/GPa).
The remaining part, as predicted by the Rayleigh limit (∼ 0.011 eV/GPa), is originated by the increase of N upon compression.Hence, our analysis based on Mie theory provides an explanation for the fast blueshift observed in the Ca colloidal band.
In order to analyze the mechanisms of the formation of Ca nanoparticles in irradiated CaF 2 and their pressure-induced shrinkage, we focus on the binding of F centers, since it can be related to the formation of the Ca colloids in CaF 2 .We perform first-principles calculations based on density functional theory (DFT).Following the previous work by Rix et al. 10 , we express the formation energy of a spherical metal nanoparticle as: where the first term in the rhs of Eq. ( 7) accounts for the binding between F centers (or vacancies), the second for the energy associated to the creation of the colloid interface, and the third for the distortion energy resulting from the lattice mismatch between the metal nanoparticle and surrounding CaF 2 matrix.Normally, E bind favors the formation of colloids whereas E interface and E strain prevent it.
Figure 5 shows the dependence of the colloid formation energy and the components E bind , E interface , and E strain on the nanoparticle radius, R, and pressure Calculation Details Section).At equilibrium (Fig. 5a), we compute a binding energy between F centers of −47.35 eV/nm 3 (or, equivalently, of −0.99 eV per fluorine vacancy), an interface colloid energy of 3.24 eV/nm 2 , and a strain colloid energy of 0.002 eV/nm 3 .In this case, the minute- ness of the E strain term is due to the practically coincident equilibrium lattice parameters of bulk fcc Ca and fluorite CaF 2 (Methods Section).The formation of Ca colloids is energetically favorable for radii larger than R min (0) = 0.21 nm owing to the dominant role of the E bind term at such lengths.Under compression (Fig. 5b), the bind and interface colloid energies decrease (e.g., E bind = −56.07eV/nm 3 and E interface = 2.19 eV/nm 2 at P m = 10 GPa) while the colloid strain energy increases due to the increase in the lattice mismatch between the fcc nanoparticle and surrounding fluorite matrix (e.g., E strain = 2.36 eV/nm 3 at P m ).
Nevertheless, the P -driven raise in strain energy is not able to counteract the steadily more attractive binding between F centers and consequently the threshold radius R min decreases under pressure; for instance, we estimate a R min of 0.19 nm at 5 GPa and of 0.13 nm at P m .
The E colloid theory that we employ here assumes an infinite source of F centers, which is a highly idealized picture of the real system (in practice the number of F centers is limited by the amount of received radiation and occurrence of recombination events with F − 2 dimers).
Consequently, we are not able to calculate an optimal or average Ca nanoparticle radius as a function of pressure.Nevertheless, it can be reasonably assumed that such an optimal or average colloid radius, R opt , will follow a similar pressure-induced variation than R min since the average number of F centers per colloid will remain roughly constant owing to the energy barriers involved in ionic diffusion (which typically increase under pressure 31,32 ); therefore, based on our DFT calculations, we estimate that at P t = 8 GPa R opt will shrink by ∼ 25% of its equilibrium value.This theoretical prediction is in good agreement with our experimental observation that the size of Ca colloids decreases by ∼ 30% when increasing pressure from ambient to the fluorite → contunnite transition point (see Fig. 4), which comes to validate our energy arguments explained above.Meanwhile, the likely reasons for the disappearance of Ca colloids at pressures P t < P are (1) the lack of superionicity in the contunnite phase of CaF 2 , 32,33 which prevents the coalescence of F centers, and (2) the large energy penalty involved in the creation of a fcc Ca/contunnite CaF 2 interface owing to the very distinct arrangements of Ca ions in the two structures 34 .
The dissipation of Ca nanoparticles at the pressure point at which CaF 2 undergoes a phase transition from a cubic to an orthorhombic phase, illustrates the fact that our MNP size tuning technique cannot be generalized to any material.In particular, the crystal symmetry of the metallic sublattice within the matrix and the resulting MNP need to be coincident (fcc in the present case).Moreover, in order to guarantee the initial formation of nanocolloids at ambient temperature within the matrix, the lattice mismatch between the metallic sublattice and the MNP must be small.Otherwise, the formation of anion centers dominates and the resulting MNP are amorphous and most likely to be unstable under high pressure 35 .This is the case, for instance, for heavily irradiated NaCl in which metallic Na is bcc and the matrix Na@NaCl is fcc.This forces Na to keep an unstable fcc arrangement.
Figure 6 shows a number of binary ionic compounds in which superionicity has been observed, or is very likely to occur, 32,36 and the structural symmetry requirement explained above is fulfilled.Among those compounds, LiF, SrF 2 and CsF also fulfill the second requirement that a (compound) ≈ a (metal) (in the case of LiF above 7 GPa) 37 .Therefore, Li, Sr, and Cs MNP with customized radii in principle could be also produced with pressure-based techniques.Moreover, pressure-induced quenching could be exploited to accomplish further MNP radius control.For instance, bulk Li crystallizes in a bcc structure whereas in LiF, LiCl, LiBr, and LiI, lithium renders a fcc sublattice; however, at ∼ 7 GPa Li transforms 37 from bcc to fcc with an almost identical lattice parameter to LiF, hence the appearance of Li MNP is expected beyond that point.In this particular case, pressure-induced quenching could be used to achieve control of the Li MNP radius at pressures below ∼ 7 GPa.Exactly the same would occur for KF in which K undergoes a bcc to fcc transition 38 at 12.4 GPa.
Likewise, Sr undergoes a fcc to bcc phase transition 39  In order to fulfill the lattice parameter requirement a (compound) ≈ a (metal), doping strategies based on isoelectronic element substitutions may be used; in this way the electronic features of the system would not be affected while potentially improving their structural and superionic properties 32 .Biaxial and uniaxial stresses could lead to similar control of MNP radii as demonstrated here.An additional feature is that negative stresses, inducing an increase in the dimensions of the nanocolloids formed at equilibrium, can be applied effectively 31 .M e t a l L a t t i c e P a r a m e t e r ( Å) The lattice parameter of binary fcc ionic compounds versus the lattice parameter of the corresponding bulk fcc metals.In bcc or hcp structured binary ionic crystals there is no structural correspondence with the structure of their corresponding metallic cations.The discontinuous line represents an ideal zero lattice strain between both lattice parameters.

Conclusions
In conclusion, we have found a non-chemical method for reversibly controlling the size of metallic colloids embedded in the cationic sublattice of an irradiated crystal.Contrary to conventional synthetic procedures in which the production of size-controlled metallic nanoparticles is non-reversible, the high-pressure method introduced here allows us to reversibly tune the size of Ca MNP at an almost constant rate of −1.2 nm/GPa.At 9.4 GPa, CaF 2 undergoes a structural phase transition from the fluorite to a contunnite phase, which is not superionic and displays an hexagonal cationic structure that is not compatible with the cubic symmetry of Ca nanocolloids 32,33 .Consequently, the formation of MNP is energetically not favourable (that is, the F centers cannot diffuse so to coalescence, and the creation of a sharp fcc Ca/contunnite CaF 2 interface is is not possible due to the incommesurability of the cation sublattices in the two involved structures) and the Ca nanocolloids vanish.This finding highlights the importance of chosing an appropriate ionic compound (i.e., with a cationic sublattice structure that is compatible with the resulting nanocolloid crystal symmetry) when employing our MNP size control method.Examples of materials in which our approach can be applied successfully include LiF, KF, SrF

Figure 1 :
Figure 1: (a) Crystal structure of fluorite CaF 2 in which the Ca cationic lattice coincides with that of fcc metallic calcium.(b) Cystal structure of the high-pressure contunnite CaF 2 structure in which the Ca cations are arranged in a hcp sublattice.Ca and F atoms are represented with white and green spheres, respectively.The cationic lattice is highlighted with solid lines.In (a) the cationic lattice coincides with the unit-cell edges but in (b) they are represented by the rectangle.

Figure 2 :
Figure 2: (a) Optical absorption spectra of CaF 2 at different pressures.(b) Lorentzian fit of the spectrum at ambient pressure.(c) Pressure dependence of the broad and intense absorbance band of CaF 2 due to the absorption of Ca colloids.The experimental data and fits are represented by points and continuous red lines, respectively, in (b) and (c).

Figure 3 :Figure 4 :
Figure 3: Experimetal (continuous line) and calculated by Mie theory (dashed line) absorbance spectra of irradiated CaF 2 at ambient temperature and P = 1 atm and 6.1 GPa.

Figure 5 :
Figure 5: First-principles calculations of the formation energy of Ca colloids in irradiated CaF 2 at (a) zero pressure and (b) 10 GPa.The R-dependence of the different E colloid contributing terms are shown.The vertical black lines in the figures indicate the minimum threshold radii for energetically favorable formation of nanoparticles, R min .
i c C o m p o u n d L a t t i c e P a r a m e t e r ( Å)

2 ,
and CsF, and numerous solid solutions involving similar binary compounds.Hence, our work should stimulate the design of new functional materials containing MNP with tailored dimensions for use in advanced optoelectronic and plasmonic applications.support from the Australian Research Council under the Future Fellowship funding scheme (No.FT140100135).Computational resources and technical assistance were provided by the Australian Government and the Government of Western Australia through the National Computational Infrastructure (NCI) and Magnus under the National Computational Merit Allocation Scheme and The Pawsey Supercomputing Centre.This project has received funding from the European Union's Horizon 2020 research and innovation programme under grant agreement No 829161.
at 4.2 GPa.In this case, the stress due to lattice mismatch could quench Sr MNP in SrF 2 and SrCl 2 at pressures beyond that transition point.Meanwhile, the case of CsF is almost identical to CaF 2 .CsF transforms from fcc to a cubic structure (space group P m 3m) with a simple cubic cationic lattice at 4.8 GPa 40 ; however, at ambient temperature Cs displays a fcc structure that is stable up to 88 GPa 41 hence Cs MNP are likely to vanish at P > 4.8 GPa.