in the discussions that follow , various process steps may or may not be described using certain types of manufacturing equipment , along with certain process parameters . it is to be appreciated that other types of equipment can be used , with different process parameters employed , and that some of the steps may be performed in other manufacturing equipment without departing from the scope of this invention . furthermore , different process parameters or manufacturing equipment could be substituted for those described herein without departing from the scope of the invention . these and other details and advantages of the present invention will become more fully apparent from the following description taken in conjunction with the accompanying drawings . some embodiments of the invention address synthetic control over β - phase nayf 4 nanocrystal size utilizing a rare - earth trifluoroacetate decomposition reaction , a 2 - step sequence that first produces β - phase nanocrystals that are then heated to 330 ° c . to form monodisperse 20 - 30 nm β - nayf 4 . attempts to isolate sub 10 - nm β - phase nanocrystals from this embodiment were partially successful , although eliminating oleic acid from the reaction did produce 10 - nm β - nayf 4 in the first step . these particles were strongly prone to aggregation and could not be transferred to water as individual nanocrystals . because trifluoroacetate decomposition requires cleavage of a covalent bond to produce f − , it was understood that this may be inefficient at producing f − and would limit nucleation , leading to fewer , larger nanoparticles . as a more efficient f − source , embodiments of the invention combined ammonium fluoride ( nh 4 f ) with oleylamine and undertook a combinatorial screen varying reaction temperature , time , y 3 + : f − ratio , na + stoichiometry , and surfactant concentrations . in a typical reaction , rare - earth oleates were prepared from their chlorides and heated along with solid nh 4 f , sodium oleate , and other surfactants in 1 - octadecene to 300 - 330 ° c . ( see below for further details ). reactions under these conditions produced either pure β - phase nanocrystals or mixtures of α - and β - phases . phase diagrams of bulk sodium yttrium fluorides suggest that β - phase formation is disfavored under most conditions , except a narrow window in which the 1 : 1 : 4 stoichiometry of na + , y 3 + , and f − is strictly maintained . fig2 illustrates the effect of the addition of increasing oleylamine on the size and phase of the nayf 4 : 2 % er 3 + , 20 % yb 3 + nanocrystals . reactions were heated at 310 ° c . for 45 min , and sizes determined by dynamic light scattering ( dls ) in hexane . β - phase nanoparticles are shown as blue triangles , α - phase or mixed phases as orange circles , and averages as closed black circles . while previous reports have suggested that sub - stoichiometric y 3 + : f − ratios favor the formation of β - phase nayf 4 , it was determined that at reaction temperatures of 310 ° c . or higher , the 1 : 4 ratio was ideal for β - phase formation ( see fig8 ). we observed much stronger effects on nanocrystal size and phase by varying the composition of surfactants , with increasing oleylamine concentrations leading to smaller nanocrystals ( fig1 ). the smallest β - nayf 4 nanocrystals , 5 nm in diameter ( fig2 ), could be synthesized in 750 mm oleylamine at 310 ° c ., consistent with previous observations that oleylamine can modulate nayf 4 size . in all of these reactions , we observed a trade - off between smaller size and β - phase formation , with higher temperatures favoring larger nanocrystals and consistent formation of the desired β - nayf 4 . increasing oleylamine concentrations also favored β - nayf 4 formation , allowing for lower reaction temperatures that produce smaller nanocrystals . surprisingly , at the highest oleylamine concentrations only mixtures were observed ( fig1 and 9 ). the smallest ucnps were then characterized . fig3 illustrates tem images of the β - nayf 4 : 2 % er 3 + , 20 % yb 3 + nanoparticles with an average diameter of 5 . 4 ± 0 . 6 nm . lattice spacing is 3 . 5 å . fig3 illustrates powder xrd of precipitated 5 - nm nanocrystals , with the standard pattern for β - nayf 4 shown as green lines . marked peaks (*) are naf impurities . this window of sub - 10 - nm β - nayf 4 formation could be further refined with changes in reaction time . increasing the reaction time from 15 min to 60 min led to significant increases in the fraction of β - nayf 4 in the presence of oleylamine ( fig1 ), but only small increases in nanoparticle diameter ( fig1 ). the increasing β - phase of the nanoparticles is also shown by an increase in the pl intensity with increasing reaction time ( fig1 ). this increase in β - phase over time is suggestive of a direct α - to β - phase conversion facilitated by heat and oleylamine , although the nature of this transition is not known . we observed some variability in these conditions to consistently produce only β - phase nayf 4 , as determined by xrd , with some reactions yielding mixtures of α and β phases . the percentage of β - phase nanoparticles in the mixed - phase samples increases with addition of oleylamine up to 750 mm ( fig9 ). at temperatures above 310 ° c . the nanoparticles formed are increasingly β - phase ( fig1 ), although this also increases the size of the nanocrystals for a given concentration of oleylamine ( fig4 and 14 ). given these constraints , we identified a window in which β - nayf 4 doped with yb 3 + and er 3 + could be prepared with diameters from 4 . 5 to 15 nm ( fig1 ), and these particles are easily dispersed in organic solvents such as hexane or chloroform in concentrations , up to 50 mg / ml . fig4 illustrates the dependence of nayf 4 nanoparticle size and phase on reaction temperature for 45 - min reactions with 0 . 75m oleylamine . β - phase nanoparticles are shown as blue triangles , α - or mixed phase as orange circles , and average as black closed circles . sizes determined by dynamic light scattering ( dls ). while the optimization of the phase enhances the brightness of these ucnps , we questioned whether reducing their size would make them susceptible to photobleaching or blinking . larger β - nayf 4 : 2 % er 3 + , 20 % yb 3 + nanocrystals ( ca . 25 nm diameter ) can withstand continuous 980 - nm excitation at single - particle powers under ambient conditions for over an hour at without any observable photobleaching or blinking , a remarkable stability for phosphors that may be due to the sequestration of a large fraction of the lanthanides within the nayf 4 matrix . because phosphors exposed to air are prone to quenching and the smaller nanocrystals have a much larger fraction of lanthanides at the nanocrystal surface , we examined whether they share the stability and continuous emission of the larger ucnps . ucnp luminescence was monitored for over an hour under continuous wave 980 - nm excitation at 10 6 w / cm 2 ( fig5 a ), showing that the luminescence from 5 - nm nanoparticles remains photostable after prolonged photoexcitation , similar to larger ucnps . like the larger nanocrystals , on / off blinking is also not observed ( fig1 ). we did observe that reducing the size of ucnps cores reduced their brightness , a phenomenon that others have attributed to the coupling of a larger fraction of lanthanide activators to surface vibrational modes that promote non - radiative relaxation . previous work has shown that addition of a nayf 4 shell without dopants increases the brightness and lifetime of ucnp phosphorescence . a 2 - nm shell was added to the 5 - nm ucnps , with the shell thickness confirmed by tem ( fig1 ) and inductively coupled plasma elemental analysis ( icp ) ( table 1 ). optical characterization of these core / shell heterostructures confirms that the shell dramatically increases their brightness , conferring & gt ; 50 - fold higher quantum yields ( qys ) compared to the 5 - nm cores ( table 2 ), and these heterostructures also do not photobleach or blink ( fig5 and 18 ). the emission of these heterostructures is in fact larger than that of comparable 30 - nm cores , when normalized to the absorbance at 980 nm ( fig6 ). the increased qy of the core / shell heterostructures likely arises from the dampening of high - energy vibrations originating at the surface by the 2 - nm shells , which contain a sufficient number of unit cells (˜ 4 ) of the low - phonon energy nayf 4 lattice . the outermost 2 nm of a 30 - nm core should also passivate the rest of that nanocrystal , but we find that the 30 - nm cores exhibit comparable qys to the smaller core / shell heterostructures . this suggests that energy excited in the yb 3 + sensitizers migrates rapidly via yb 3 + - yb 3 + resonant energy transfer to the surface . these analyses demonstrate that synthetic control over ucnp size can enable the determination of critical length scales for vibrational quenching and energy migration in ucnps . fig5 illustrates ( a ) pl stability and uninterrupted emission of β - nayf 4 : 2 % er 3 + , 20 % yb 3 + core and β - nayf 4 : 2 % er 3 + , 20 % yb 3 + / nayf 4 core / shell heterostructures under 980 nm continuous excitation at powers of 10 6 w / cm 2 , and ( b ) pl intensities ( λ ex = 980 nm ) of small and larger β - nayf 4 : 2 % er 3 + , 20 % yb 3 + nanocrystals in hexane compared to core / shell heterostructures . spectra are normalized to absorbance at 980 nm . embodiments of the invention have used a combinatorial screen to identify reaction conditions that permit the synthesis of lanthanide - doped β - nayf 4 nanocrystals with controlled diameters from 4 . 5 to 15 nm , which are comparable in size to many proteins , making them suitable for a variety of cellular imaging experiments . embodiments of the invention show that nanocrystals less than ¼ th the diameter of previously characterized ucnps retain their continuous emission and extreme resistance to photobleaching , and that 10 - nm core / shell nanocrystals are brighter than 30 - nm cores . these findings show that more biocompatible sizes of ucnp can be synthesized without sacrificing brightness or stability . this synthesis should be useful for nanocrystals to be used in extended single - molecule tracking experiments , as well as for novel lanthanide - doped nanocrystals with varying excitation and emission spectra that will be critical for multi - color upconverting imaging . yttrium ( iii ) chloride ( anhydrous powder , 99 . 99 %), ytterbium ( iii ) chloride ( anhydrous powder , 99 . 99 %), and erbium ( iii ) chloride ( anhydrous powder , 99 . 9 %) were purchased from sigma - aldrich and stored in a n 2 desiccator . sodium oleate ( pfaltz and bauer , 97 %) was purchased from vwr . anhydrous nh 4 f was purchased from sigma - aldrich and stored under n 2 . oleic acid and 1 - octadecene ( tech . grade , 90 %) were purchased from sigma - aldrich . oleylamine ( 80 - 90 %) was purchased from acros . 20 % yb , 2 % er . to a 50 - ml round bottom flask , yttrium chloride ( 0 . 39 mmol , 76 . 1 mg ), ytterbium chloride ( 0 . 1 mmol , 27 . 9 mg ) and erbium chloride ( 0 . 01 mmol , 2 . 7 mg ) were added . oleic acid ( 2 . 7 g ), oleylamine ( 2 g ) and 1 - octadecene ( 3 . 5 g ) were added . ( for reactions without oleylamine , 5 . 5 g of 1 - octadecene was added instead of 3 . 5 g ). the solution was stirred and then placed under vacuum and heated to 110 ° c . for 1 hour . after 1 hour , the reaction was brought under n 2 . solid sodium oleate ( 1 . 25 mmol , 380 mg ) and anhydrous nh 4 f ( 2 mmol , 74 mg ) were added under n 2 . the reaction was then heated to 310 ° c . the reaction was stirred at 310 ° c . for 30 min - 1 hour under n 2 and then cooled rapidly by removal of the heating mantle and air cooling . when the reaction had cooled to 75 ° c ., absolute ethanol ( 9 ml ) was added to the reaction solution to precipitate the nayf 4 20 % yb , 2 % er nanoparticles . the reaction was transferred to a centrifuge tube and allowed to cool to room temperature . the solution was centrifuged at 3000 × g for 2 - 3 min to precipitate the nanoparticles completely . the supernatent was discarded and the white solid (˜ 80 mg ) was suspended in minimal hexanes to break up the pellet . the nanoparticles where then precipitated again with addition of ethanol (˜ 5 ml ) and centrifuged at 3000 × g for 3 min . this washing procedure was repeated 2 more times to ensure washing of the reaction surfactants as well as any naf impurities that were formed . re : a stock solution of rare - earth oleate was prepared , for yb , er doped nayf 4 , by addition of yttrium chloride ( 3 . 51 mmol , 685 mg ), ytterbium chloride ( 0 . 9 mmol , 252 mg ) and erbium chloride ( 0 . 09 mmol , 25 mg ) to a 100 ml round bottom flask . oleic acid ( 24 . 4 g ) and 1 - octadecene ( 14 . 2 g ) were added . the suspension was stirred and then placed under vacuum and heated to 110 ° c . after 1 hour , the stock solution was cooled to room temperature and brought under n 2 in a glove box equipped with the automated nanoparticle synthesis robot . to each reaction vial , solid sodium oleate ( 1 . 25 mmol , 380 mg ) and anhydrous nh 4 f ( 2 mmol , 74 mg ) were added , followed by the rare - earth oleate stock solution ( 4 . 38 g ) and oleylamine ( 0 - 10 mmol ) and additional 1 - octadecene ( such that the total mass of ode + om = 5 . 5 g ). the reaction vials were loaded onto the wanda platform . the reactors were heated at 30 ° c ./ min up to temperatures of 280 - 330 ° c . and held at that temperature for 30 min - 60 min . the reactors were cooled to 75 ° c . after which 9 ml of absolute ethanol was added to precipitate the nanoparticles . aliquots were removed by the robot at appropriate time - points to monitor the reaction . undoped nayf 4 shells were grown on the lanthanide - doped cores using a method modified from that of abel , et al . 27 ycl 3 was heated to 110 ° c . in oleic acid and ode for 1 hour . the solution was cooled to ˜ 60 ° c . and the stock solution of nanoparticle cores in hexane was added . the hexane was removed by vacuum then the solution cooled to room temperature after which nh 4 f ( 2 mmol , 74 mg ) and sodium oleate ( 1 . 25 mmol , 381 mg ) were added . the solution was then heated to 280 ° c . for 30 min , then cooled rapidly and 10 ml of ethanol was added when the solution reached & lt ; 75 ° c . nanoparticles were precipitated and cleaned as described for the ucnp cores . an aliquot ( 1 ml ) of a stock solution of the nanoparticles in hexane was precipitated with addition of ethanol (˜ 2 ml ). the nanoparticle slurry was spotted onto glass coverslips or silicon wafers multiple times until an opaque white film formed . the sample was then allowed to air dry completely . xrd patterns were obtained on a bruker axs d8 discover gadds x - ray diffractometer system with cu kat radiation ( λ = 1 . 5406 å ) from 28 of 15 ° to 65 °. for combinatorial screenings , the reaction mixture ( 250 μl ) was spotted onto a glass crystallization plate ( symyx ). the nanoparticles were precipitated from the reaction mixture onto the plate by addition of ethanol (˜ 700 μl ). the plate was centrifuged to concentrate the precipitated nanoparticles to the bottom of the wells . the supernatant was removed with a pipette and the plate dried in a vacuum desiccator overnight . xrd patterns were obtained on each sample directly on the glass plate from 28 of 15 ° to 65 °. for rietveld refinement , fitting of the xrd patterns to α and β - phase nayf 4 was performed in panalytical x &# 39 ; pert hiscore plus software . due to the peak broadening for the small nanocrystals , fittings of samples containing 8 % or less of each phase may appear identical to that of the pure phase the emission spectra of the nayf 4 : 20 % yb , 2 % er nanoparticles were recorded on a horiba - jobin yvon fluorolog ii modified with a fiber - coupled 1 w continuous wave 980 - nm laser excitation source ( sheaumann ) and a micromax 96 - well plate reader . the photoluminescence was measured in solid - state samples spotted onto either a clear polypropylene 96 - well plate or onto a 96 - well glass crystallization plate ( symyx ). for determination of pl quantum yields , the ucnp stock solutions in hexane ( 500 μl ) were placed in a quartz sample holder , which was inserted into an integrating sphere ( horiba jobin - yvon ). the excitation laser to the integrating sphere and the emission to the fluorolog ii were routed using fiber optics . the excitation intensity was measured after passing through a 2 . 5 % neutral density filter . excitation and emission spectra were corrected for the sensitivity of the detector over the appropriate wavelengths . photostability measurements of ucnp photoluminescence were performed by exciting a thin film of ucnps on a glass coverslip with a 980 nm continuous - wave laser ( thorlabs tcldm9 , 300 mw diode ) at 10 6 w / cm 2 . a high numerical - aperture objective ( nikon plan apo , 100 ×, 1 . 4 oil ) was used to focus the laser and collect pl emission , which was then routed in free space to an avalanche photo diode ( micro photon devices , pdm series spad ) for pl intensity measurements . a 750 nm short pass filter ( thorlabs ) was used to filter residual excitation light after collection . the excitation density was determined from the measured laser power at the back aperture of the objective and the area of the focused excitation spot . pl intensity was recorded over 4000 sec by a 1 mhz digital counter ( rhk technologies ) measuring photon counts from the spad . lifetime measurements . time - resolved measurements of the pl emission from ucnps were performed by modulating the excitation laser with a function generator ( srs , model ds340 ) connected to a voltage amplifier ( srs , model sim983 ). the laser - pulse edge and rep - rate were 1 μs and 250 hz , allowing a 2 ms window for pl decay . the measured photon counts from the spad and the trigger signal from the function generator were recorded simultaneously by a time correlated single photon counter ( tcspc ) ( picoquant , picoharp 300 ). the time - arrival of pl emission referenced to laser - pulse edge was calculated using a software program customized in matlab . the size of the nanocrystals was determined by dls measurements on a malvern zetasizer . samples were prepared from hexane stock solutions of the nayf 4 20 % yb , 2 % er nanoparticles by dilution with hexane and filtered through a ptfe 0 . 2 μm syringe filter ( pall ) into a quartz cuvette . the diameters of the nanoparticles in each sample were determined based on the fitting by volume . for electron microscopy , dilute samples ( 7 μl ) of nanoparticles in hexanes were dropped onto ultrathin carbon film / holey carbon , 400 mesh copper or 300 mesh au grids ( ted pella , inc .). the grids were washed with ethanol and then hexanes . images of the nanoparticles were obtained using a zeiss gemini ultra - 55 analytical scanning electron microscope . dark - field images were collected in transmission ( stem ) mode with 30 kv beam energy . tem images were also obtained using a jeol 2100 - f 200 kv field - emission analytical transmission electron microscope . the amounts of na , y , yb , and er in each sample were determined with icp . samples and standards were analyzed on a varian 720 - es icp optical emission spectrometer . standards ( sigma aldrich ) were diluted in 7 % nitric acid to give standards with a concentrations from 200 ppb to 5 ppm . samples of ucnps ( 1 ml of stock in hexane , ˜ 5 mg / ml ) were digested with concentrated nitric acid ( 1 - 2 ml ) and stirred with gentle heating ( 50 ° c .). the samples were then diluted by addition to 8 ml of water . fig7 illustrates the xrd of samples prepared determined to have 93 % β - phase ( black ) and 98 % β - phase ( blue ) by rietveld fitting . the 5 . 4 nm nanocrystals ( blue ) show more intensity at 2θ = 28 degrees compared to the 7 . 5 nm nanocrystals , yet are determined to have less % β - phase . this shows the error in the determination of % phase using rietveld fitting , as well as peak broadening observed for the smaller nanocrystals . fig8 illustrates xrd of samples prepared with a 1 : 4 ( black ) and 1 : 8 ( blue ) y 3 + to f − ratio at 310 ° c . heated for 45 min . the sample with 1 : 8 ratio shows many other impurities besides the cc or β - phase nayf 4 . fig9 illustrates the percent β - phase nayf 4 in each reaction , as determined by rietveld fitting , with increasing om at 310 ° c . with 45 min reaction time . averages of 5 - 12 runs for each concentration of oleylamine , and error bars show standard deviation . fig1 illustrates the effect of reaction time at 310 ° c . on the % of β - phase nayf 4 in each reaction and fig1 illustrates the effect of reaction time at 310 ° c . on the size of the nanocrystals with ( orange circles ) and without ( blue squares ) 0 . 75 m oleylamine . percent β - phase as determined by rietveld fitting of powder x - ray diffraction and size determined by dls . fig1 illustrates the photoluminescence after 980 nm excitation for 250 - μl aliquots of a reaction in xylene with increasing reaction time from 15 to 60 minutes at 310 ° c . with 0 . 75 oleylamine . fig1 illustrates the percent β - phase nayf 4 in each reaction , as determined by rietveld fitting , with increasing reaction temperature with 750 mm om and 45 min reaction time . averages of 5 - 12 runs for each concentration of oleylamine , and error bars show standard deviation . fig1 illustrates comparison of the dependence of nayf 4 nanoparticle size and phase on reaction temperature for 45 - min reactions with 0 . 75m oleylamine ( black circles ) and 1 . 12m oleylamine ( red squares ). sizes determined by dls . fig1 illustrates a scanning transmission electron microscopy ( stem ) images of representative β - nayf 4 nanoparticle samples at each reaction temperature of a ) 310 ° c . b ) 315 ° c ., c ) 318 ° c . and d ) 320 ° c . and at different oleylamine concentrations e ) 0 . 112m , f ) 0 . 75m , g ) 0 . 37m and h ) no oleylamine . average diameters of the nanoparticle synthesized at these temperatures and oleylamine concentrations are a ) 6 . 0 nm , b ) 6 . 1 nm , c ) 7 . 0 nm , d ) 8 . 0 nm , e ) 6 . 25 nm , f ) 7 . 1 nm , g ) 6 . 0 nm , h ) 14 . 0 nm . scale bar in each image is 10 nm . fig1 illustrates a photoluminescence of 5 . 4 nm core nanoparticles on glass with excitation of 980 nm over 1 s showing the absence of blinking . data points are every 10 ms . fig1 illustrates a tem of the core / shell β - nayf 4 : 20 % yb , 2 % er / β - nayf 4 nanoparticles . average diameter of the nanoparticles is 9 . 5 ± 2 nm . ( b ) powder x - ray diffraction showing that the core / shell nanocrystals remain β - nayf 4 . referring to table 1 , the theoretical values for the core / shell are those based on the amount of core and shell by volume expected for core nanocrystals of 5 . 4 nm with a 2 nm shell as is seen in tem . experimental values suggest a thinner shell of ˜ 1 . 5 nm . given the polydispersity of the core / shell sample , this fits within the expected range . fig1 illustrates the photoluminescence of 9 . 5 nm core / shell nanoparticles on glass with excitation of 980 nm over 1 s showing the absence of blinking . data points are every 10 ms . this invention has been described herein in considerable detail to provide those skilled in the art with information relevant to apply the novel principles and to construct and use such specialized components as are required . however , it is to be understood that the invention can be carried out by different equipment , materials and devices , and that various modifications , both as to the equipment and operating procedures , can be accomplished without departing from the scope of the invention itself .