ge2sb2te5 ( gst ) , one of the prototypical 
 phase - change materials ( pcms ) , enables rapid and reversible switching 
 between its amorphous and crystalline phases , which is accompanied 
 by large optical and electrical contrast .
this unique feature makes 
 gst attractive for data - storage applications and a strong 
 contender for emerging applications , such as solid - state displays , optical modulators , neuromorphic computing , on - chip photonic circuitry , and plasmonic - based circuits .
crystallization lies at the heart of the switching in phase - change 
 technology ; thus , a solid understanding of the crystallization kinetics 
 entails a crucial aspect of designing phase - change memory .
conventional 
 measurements are only able to investigate crystallization 
 kinetics within a relatively low temperature range ( near the glass 
 transition temperature ) . however , in actual applications , crystallization 
 generally takes place at higher temperatures . despite its scientific 
 and technologic relevance
, the analysis of the crystallization kinetics 
 at these high temperatures has remained for a long time highly challenging 
 due to the ultrashort time and length scales ( ns and nm ) involved . 

this situation persisted until very recently , where ultrafast differential 
 scanning calorimetry ( dsc ) was utilized to explore the crystallization 
 process of gst films with heating rates up to 40  000 k s. using subsequent extensive 
 modeling , growth rates ranging from the glass transition temperature 
 to the melting temperature were derived for the film structures , showing 
 a remarkable breakdown of arrhenius behavior in the viscosity at heating 
 rates beyond 500 k s. non - arrhenius thermal 
 dependence of the viscosity at high temperatures has lately been widely 
 observed in both nucleation - dominated and growth - dominated pcms . for 
 instance , for gst confined in memory cells it was demonstrated that 
 non - arrhenius thermal dependence of crystallization at high temperatures 
 crosses over to a wide temperature range at lower temperatures where 
 still arrhenius behavior prevails . in recent years , also 
 for other pcms , such as gete films , supercooled 
 and melt - quenched aginsbte films , and gesb films , the crystallization kinetics have been determined based on nonconventional 
 techniques with measurements spanning relatively wide temperature 
 ranges .
all these works confirm the breakdown of arrhenius dependence 
 for amorphous pcms at high temperatures .
however , a question that 
 remains is whether this breakdown can be described on the basis of 
 a model for viscosity with a single value for the fragility . in parallel ,
down - scaling the gst into ( sublithographic ) nanostructures 
 generates tremendous advantages for pcm - based memory including ultrafast 
 switching , low switching power , and ultrahigh density .
therefore , 
 many efforts have been devoted to enter this promising field . in this context , the fabrication of monodisperse gst nanoparticles 
 ( nps ) with good size and composition control has been a great challenge 
 for a long time .
we achieved a breakthrough by exploiting a technique 
 based on gas - phase condensation and magnetron sputtering , which is 
 capable of meeting the requirements of gst np fabrication .
size - dependent crystallization was observed 
 through in situ heating in a transmission electron 
 microscope .
yet this previous work mainly focused on the crystallization 
 at relatively low temperatures because of the limitation inherent 
 to the in situ tem heating method .
therefore , the 
 crystallization kinetics of gst nps remains unknown for the high - temperature 
 regime . in this manuscript
we present a facile method to synthesize 
 size- and composition - controlled ge2sb2te5 nanoparticles via gas - phase condensation , followed by the 
 unprecedented exploration of crystallization kinetics of gst nps via 
 ultrafast dsc . by varying the heating rate more than 3 orders of magnitude , 
 the temperature - dependent viscosity and growth rate of the crystallization 

have been unraveled , providing evidence for a fragile - to - strong crossover 
 in as - deposited amorphous gst nps .
moreover , it is shown that methane 
 addition during np production is advantageous for application of nps 
 in pcm - based devices due to the fact that it increases the amorphous 
 phase stability near the glass transition temperature , whereas the 
 maximum switching speed at high temperature is not reduced .
the ge2sb2te5 ( gst ) nanoparticles ( nps ) were directly deposited 
 on a precleaned glass substrate without capping layer , utilizing a 
 home - modified nanocluster system nanogen50 from mantis deposition 
 ltd .
the substrate was put close to the aperture of the aggregation 
 chamber in order to synthesize a large amount of nps .
the main chamber 
 ( to collect the nps ) is evacuated to a pressure of 10 mbar .
amorphous gst nps were directly synthesized by sputtering 
 the gst target ( purity of 99.99% ) , employing a low current ( 0.105 
 a ) to avoid the formation of crystalline nps . the ar gas flow ( purity 
 99.9999% )
used for the two types of samples analyzed in the present 
 work is 35 sccm , with h2/ch4 ( purity 99.99% ) 
 as extra gas to facilitate the development of nascent clusters in 
 the plasma . in this manuscript
, we show the ability of preparing nanoparticles 
 with a large yield , as shown in the figure s1 in supporting information ( si ) .
the morphology of the as - deposited 
 nps was subsequently characterized by transmission electron microscopy 
 ( jeol 2010 ) at 200 kv .
the composition of the nps was characterized 
 by energy - disperse x - ray spectrometry ( thermo instruments ) attached 
 to the tem , as shown in figure s2 of the si .
the phase transitions of the samples were subsequently measured by 
 ultrafast differential scanning calorimetry ( dsc , mettler - toledo flash 
 dsc 1 ) , with the sensor chips ( usf-1 ) each containing the actual sensor 
 and reference area .
the gst nps were scraped off from the glass substrate 
 and then were deposited on the effective area of the chip sensor . 
 instead of the loose powder / multiflakes we used for ge 
sb pcms , 
 a single planar flake consisting of gst nps parallel to the sensor 
 surface was adopted here to run the measurements .
the approximate 
 area that was subjected to ultrafast heating is roughly 60  
 60 m and 20  20 m for 
 nps ( h2 ) and nps ( ch4 ) , respectively .
this methodology 
 remarkably increases the thermal contact between the materials and 
 the chip sensor , as shown in figure s3 of the si with much less scattering of the crystallization temperature 
 in the kissinger plot .
actually , our results show that all previously 
 published ultrafast dsc work employing loose powder or multiflakes 
 ( of pcms ) can contain erroneous results for the higher heating rate 
 ( and thus temperature ) regime .
the heating rates (  ) adopted 
 in this manuscript vary from 10 to 40  000 k s. at each  , measurements were repeated at least 3 times for 
 low  and 510 times for high  , as the values 
 of the crystallization temperature become more scattered .
thermal 
 lag and temperature calibration of the flash dsc are discussed in 
 detail in section 2 of the si .
similar to our previous work , numerical 
 modeling utilizing jmak theory has 
 been performed to interpret the data from the ultrafast dsc measurements . 
 the viscosity model ( myega model ) we employed successfully for the 
 ge 
sb alloy turned out inadequate to explain the arrhenius 
 behavior persisting for such a large temperature range in the kissinger 
 plot presented in the present work .
note 
 that in all the fittings performed in this manuscript the fractional 
 stokes 
einstein relation between viscosity and growth rate 
 has been used , with  = 0.65 suggested by previous work .
the details of jmak modeling can be found in 
 the si of our previous work .
for this jmak model , descriptions of nucleation 
 and growth are required . for the description of nucleation
it is assumed 
 that it is independent of time and temperature ; i.e. , we assume a 
 constant nuclei density ( site saturation ) , analogous to what was adopted 
 for the modeling of gst films .
however , 
 in the si of the present work , we show 
 that the results hardly change when we adopt a more intricate steady - state 
 nucleation model . for the description of the growth ( rate ) eq
2 has been used , in which 
 the viscosity is described by the generalized myega model .
apart 
 from the ultrafast dsc data presented in the kissinger plot , also 
 two relevant data points , one for gst nps ( h2 ) and one 
 for gst nps ( ch4 ) , were added for very low heating rates 
  ( 0.03 k s ) based on our previous in situ 
 tem work . the data point for gst nps 
 ( h2 ) is reliable , but it is not precise for gst nps ( ch4 ) .
the reason is that it is hard to accurately control for 
 different sample batches the amount of methane incorporated in the 
 gas phase during the np sample production .
therefore , this single 
 data point for gst nps ( ch4 ) in the kissinger plot is not 
 used when fitting the jmak - based model to the experimental data .
size - dependent crystallization 
 has been observed for ge2sb2te5 ( gst ) 
 nanoparticles ( nps ) , where the size , 
 morphology , structure , and crystallization temperature of the as - deposited 
 nps have been characterized by transmission electron microscopy ( tem ) . 
 as shown in figure 1 ,
relatively monodisperse gst nps have been synthesized , with average 
 diameters of 16.0  1.3 and 16.8  1.7 nm for nps synthesized 
 with either h2 or ch4 added to the base ar gas , 
 hereafter named nps ( h2 ) and nps ( ch4 ) .
detailed 
 size distributions of these two samples can be found in figure s4 
 of the supporting information ( si ) .
the 
 similar sizes and narrow size distribution of the two gst np ( ch4 ) and ( h2 ) samples exclude size effects on the 
 crystallization observed in the present work . although the nps were 
 produced with a relatively high coverage , they are not coalesced but 
 only aggregated , as can be seen clearly in figure 1 .
the spherical morphology is an indication 
 of the amorphous nature of the nps , which is further confirmed by 
 selected area electron diffraction ( saed ) . as manifested by the insets 
 of figure 1 ,
the saed 
 patterns demonstrate that the nps are amorphous due to the lack of 
 sharp crystalline rings .
the composition of these nps is ge : sb : te 
 = 19:24:57 ( 1 ) at.% , as determined by energy - dispersive x - ray 
 spectrometry ; see the spectrum in figure s2 of the si .
note that the tem grids were located at the periphery 
 of the np cluster beam during production , retaining a lower coverage 
 in comparison to the center part ; see the large amount of nps in figure 
 s1 of the si .
high yield synthesis of gst 
 nps has been achieved by gas - phase condensation in order to obtain 
 a good signal - to - noise ratio when performing differential scanning 
 calorimetry ( dsc ) with ultrafast heating .
moreover , we have demonstrated 
 that the nps do not coalesce during thermal heating in a transmission 
 electron micscope ; see the si of our previous 
 work .
therefore , the above factors enable 
 and ensure the thermal analysis of well - characterized nps via ultrafast 
 dsc .
( a ) , ( b ) bright - field image of the gst nps produced 
 with h2 ( nps ( h2 ) ) and ch4 ( nps ( ch4 ) ) , respectively .
the average diameters of the nps in these 
 two samples are 16.0  1.3 and 16.8  1.7 nm , respectively . 

insets show the selected area electron diffraction patterns of the 
 corresponding nps , clearly demonstrating the amorphous nature of the 
 as - deposited nps .
the obtained ultrafast 
 dsc traces for the two gst np ( h2 ) and np ( ch4 ) samples are shown in figure 2a , b .
the heating rates (  ) used to obtain the data of 
 the present work vary more than 3 orders of magnitude , from 10 to 
 40 000 k s. note that a detectable signal of crystallization 
 only appears for  beyond 50 k s for the 
 nps ( ch4 ) .
the temperatures for the amorphous to rock - salt 
 transition ( tp1 ) drastically 
 increase when higher  are applied to both samples ; e.g. , tp1 of nps ( h2 ) shifts 
 from 440 at 10 k s to 542 k at 40 000 k s , as shown in table s1 .
figure 2 also shows that 
 nps ( ch4 ) have an ( expected ) higher tp1 than nps ( h2 ) , particularly 
 at low . for example , tp1 for nps ( ch4 ) is 20 k higher than that 
 of nps ( h2 ) at 50 k s. in a previous 
 work , we have revealed by in situ heating in a tem 
 that methane addition during gst np production remarkably increase 
 the tp1 at relatively 
 low heating rates .
nevertheless , here 
 we observe that this gap of tp1 gradually decreases when  becomes higher and finally 
 vanishes when  reaches 40 000 k s. surprisingly , 
 at high  we observe a big divergence in tp1 for gst nps ( h2 ) compared to 
 gst films as reported in earlier work ; see detailed data in table s1 .
while 
 the tp1s are very similar 
 at 50 k s , the tp1 of gst films becomes 90 k higher than that 
 of the nps ( h2 ) at 40 000 k s. this 
 gap can ( at least partly ) stem from two origins : ( 1 ) the thermal lag 
 between the thin film and the ultrafast chip sensor , as is discussed 
 in detail in section 2 of the si , and ( 2 ) 
 it is still very well likely that the kinetics of nps differs from 
 that of thin films .
we did not have the appropriate thin - film samples 
 to verify this , and these tests are beyond the scope of the present 
 work ; however , they are of interest for future research .
( a ) , ( b ) ultrafast dsc traces 
 for gst nps ( h2 ) and nps ( ch4 ) , respectively , 
 for heating rates (  ) ranging from 10 to 40  000 k s. insets of ( a ) and ( b ) show the close - up of the crystallization 
 peaks at lower . ( c ) zoomed - in ultrafast dsc traces of rock - salt 
 to rhombohedral structural transition in nps ( h2 ) at  
 ranging from 250 to 20  000 k s. ( d ) evolution 
 of the structural relaxation temperatures with  for nps ( h2 ) and nps ( ch4 ) .
the blue and red curves in the 
 figures hold for nps ( h2 ) and nps ( ch4 ) , respectively .
furthermore , the rock - salt to 
 trigonal structural transition is 
 also unambiguously observed for the nps ( h2 ) in the ultrafast 
 dsc traces when  is above 250 k s. the 
 signal of this transition is unexpected but intriguing as it was not 
 detected for gst films via ultrafast dsc measurement in previous work .
this transition temperature ( denoted hereafter 
 as tp2 ) displays a clear 
 dependence on  as well , where it increases when  rises , 
 even with a more drastic increment compared to tp1 .
locating at around 553 at 250 k s , tp2 moves to 633 k at 20 000 k s , as depicted in figure 2c .
it is noticeable 
 that tp2 is invisible 
 in the dsc signal at the lowest  because of the small heat 
 release involved compared to the amorphous to rock - salt transition . 

interestingly , the rock - salt to trigonal structural transition is 
 unobservable in nps ( ch4 ) in the present work ( figure 2b ) .
several explanations 
 could correlate to this feature : ( i ) the addition of methane alters tp2 to too high temperature 
 which is beyond the upper limit of ultrafast dsc ( 450 c ) ; ( ii ) 
 the incorporation of methane suppresses this structural transition 
 completely ; ( iii ) with methane the transition can still occur but 
 with reduced latent heat ( or spread over a larger temperature range ) 
 such that it is not detected by the ultrafast dsc .
more systematic 
 research is necessary before drawing conclusions on this second transition , 
 and this is out of the scope of the present work .
however , the appearance 
 of this specific transition also indicates good thermal contact between 
 the chip sensor and the np flake , as the heat release involved in 
 this transition is much smaller than that of the amorphous to rock - salt 
 transition .
the obtained tp2 for gst nps is much lower than that of the gst films due 
 to the expected strong size dependence of tp2 , where it has been observed to reduce sharply with 
 decreasing thickness of gst films . in the ultrafast dsc traces ,
a heat release prior to the amorphous 
 to rock - salt transition is also observed , indicated as t1 in figure 2d .
this exothermic heat flow was ascribed to structural relaxation 
 of the amorphous phase by previous researchers , as the temperature is too low for crystallization .
for 
 instance , for gst nps ( h2 ) at a heating rate of 100 k s the temperature t1 is 
 120 c compared to the crystallization temperature tp1 of 180 c . at this t1 temperature ,
for example , for gst nanowires with a width of 60 
 nm , the amorphous phase can remain present for 10 s. therefore , with high heating rate 
 ( 100 k / s ) , the heating process from 25 to 125 c takes only 1 
 s that is way below the time required to start crystallization at 
 120 c .
therefore , no signal for crystallization should be observed 
 at these temperatures indicated by the arrows in figure 2d .
this structural relaxation 
 has been found in other amorphous materials , such as silicon and germanium , 
 and it is attributed to the presence of a spectrum of activation energies 
 for the sites where relaxation takes place .
for both the gst np ( ch4 ) and np ( h2 ) samples , t1 moves toward the onset of the amorphous to 
 rock - salt transition as  rises . to further understand the crystallization 
 kinetics of the nps , kissinger analysis is employed . for crystallization
, 
 the activation energy can be obtained using the following equation 
 proposed by kissinger1with q being the activation 
 energy for crystallization , r the gas constant ,  
 the heating rate , and tp the peak temperature in the dsc signal . for a crystallization process 
 complying with arrhenius behavior , the ( constant ) activation energy 
 can be derived straightforwardly . figure 3a shows the crystallization data for gst 
 nps obtained by ultrafast dsc at different  , with the blue 
 and red solid circles signifying tp1 data for nps ( h2 ) and nps ( ch4 ) , respectively . 

the single flake methodology ( instead of an ensemble of loose flakes ) 
 utilized in running the ultrafast heating here effectively improves 
 the thermal contact between the chip sensor and the np flake , inducing 
 clearly less scatter in tp1 in comparison with the employment of loose powder or multiflakes ; 
 see more details in figure s3 of the si . at low 
, the arrhenius behavior is maintained , as indicated 
 by the kissinger plot ( figure 3 ) .
surprisingly , the arrhenius behavior for the nps persists 
 for a considerably larger  range ( up to 10 000 k s ) in contrast to gst films previously studied where arrhenius behavior 
 was reported to break down already at 500 k s , as shown figure 3a by the black stars .
it is also observable 
 that nps ( ch4 ) have a higher activation energy for crystallization 
 than nps ( h2 ) within the arrhenius behavior range .
the 
 kissinger plot at lower  has been zoomed in and linearly fitted 
 ( figure 3b ) , with an 
 activation energy for crystallization determined as 2.22 and 2.43 
 ev at for nps ( h2 ) and nps ( ch4 ) , respectively .
these values coincide well with the reported 
 values for gst films , in a range between 2 and 3 ev by conventional 
 dsc or electrical resistance measurements .
the increase of activation energy induced by ch4 incorporation 
 is similar to the enhanced activation energy by carbon doping of gst 
 films .
( a ) kissinger 
 plot for nps ( h2 ) and nps ( ch4 ) .
blue solid 
 circles and blue open circles denote the amorphous to rock - salt transition 
 temperatures ( tp1 ) and 
 rock - salt to rhombohedral transition temperatures ( tp2 ) of nps ( h2 ) .
the blue and red triangles correspond to the tp1 of nps ( h2 ) and 
 nps ( ch4 ) , respectively , as obtained using in situ heating 
 in the tem .
( b ) linear fit to the kissinger 
 plot at lower  ( up to 10 000 k s ) , leading 
 to crystallization activation energy of 2.22 and 2.43 ev at for nps ( h2 ) and nps ( ch4 ) , respectively .
nevertheless , further increase 
 in  ( beyond 10  000 
 k s ) prompts the breakdown of the arrhenius behavior , 
 generating a curvature in the kissinger plot . as a result
, the activation 
 energy for crystallization diminishes with the increment of temperature 
 and vanishes at higher temperatures . in order to appropriately interpret 
 these data , johnson  mehl 
avrami  kolmogorov ( jmak ) 
 theory has been adopted to fit the kissinger plot , analogous to our 
 previous work on gesb alloy .
the growth 
 rate of crystallization is vital to utilize the jmak theory , which 
 can be written as2with u(t ) as the growth rate , ratom the atomic 
 radius ( 1.5  ) ,  the diffusional jump distance 
 ( 2.99  ) , rhyd the hydrodynamic 
 radius ( rhyd = ratom ) , kb the boltzmann constant , 
 (t ) the temperature - dependent viscosity ,  
 the decoupling parameter of the stokes  einstein equation (  
  1 ) , and g(t ) the 
 change of gibbs free energy , which can be described , according to 
 thomson and spaepen , as3where hm is the latent heat of melting , approximately 0.152 ev at , and tm is set to 890 k. note that 
 fractional 
 stokes 
einstein equation ( u   with   1 ) is intrinsically included 
 in eq 2 , as the breakdown 
 of stokes  einstein relation has been observed in a large number 
 of supercooled glass forming liquids and in particular pcms and it 
 is attributed to dynamical heterogeneities . for the gst nps we set  = 0.65 , a value similar to gst films .
an appropriate viscosity model is required 
 to determine the growth 
 rate in eq 2 .
although 
 the model proposed by mauro et al . ( myega 
 model hereinafter ) provides , as we proved , a much better description of the viscosity of ge  sb phase - change 
 materials as compared to the one from cohen and grest , it yields inferior fits to the present data 
 for gst nps owing to its inability to afford arrhenius behavior in 
 a large temperature range .
if the myega model ( with a single fragility 
 value ) is adopted , it provides very high values of fragility for the 
 nps ( h2 ) , m = 203 , which is higher than 
 the theoretical value for kinetic fragility for glass forming liquids 
 ( m = 176 ) .
furthermore , 
 this model leads to very high crystallization temperatures at low 
 heating rates , resulting in a large mismatch to the data obtained 
 by in situ heating in tem , as shown in figure s5 of the si .
furthermore , for nps ( ch4 ) , it 
 only fits well in the low heating rate range .
note that the quality 
 of the fits using either the myega model or the cohen and grest model 
 remains poor even using more sophisticated models for nucleation instead 
 of the simple constant nuclei density ( site saturation ) adopted initially . 

therefore , we tested a generalized myega model since it enabled a 
 successful description of the complex viscosity in metallic glass - forming 
 liquids4with ( ) being viscosity at 
 infinite temperature ( here it is taken as 10 pa 
 s ) , t the temperature , and w1 , c1 , w2 , and c2 the fitting parameters .
this 
 model illustrates that two intrinsic terms of viscosity subsist in 
 the liquid , and these two terms can transfer to each other upon cooling 
 or heating .
the blue and red dotted curves in figure 3a denote the modeled kissinger plots utilizing 
 the generalized myega model ( eq 4 ) , showing excellent fits to the corresponding experimental 
 data , with fitting quality evaluated by adjusted r ( 0.973 and 0.984 , respectively ) .
the derived fitting 
 parameters are w1 = 6921.8 , c1 = 7490.2 , w2 = 6.63  
 10 , and c2 = 517.2 
 for nps ( h2 ) and w1 = 8259.3 , c1 = 8091.9 , w2 = 
 5.27  10 , and c2 = 510.2 for nps ( ch4 ) .
note that the data become more 
 scattered when  becomes high , particularly for  above 
 10  000 k s. therefore , only three data 
 points at the most right side for  beyond 10  000 k s are weighted to be the most representative data , 
 as they exemplify the best thermal contact between the chip sensor 
 and the np flake .
a non - arrhenius 
 behavior is evidently 
 revealed in this figure , inferring a temperature - dependent activation 
 energy for this structural transition . without a proper growth rate 
 model for this transition , it is currently not possible to model the 
 kissinger curve via jmak theory .
viscosity is of fundamental and practical 
 relevance for glass forming liquids as it is directly associated with 
 the glass transition and relaxation process , indicating the mobility 
 of the atoms , and therefore it is coupled to the growth rate of crystallization . 

as the unknown parameters in eq 4 have been determined through fitting , the viscosity of the 
 as - deposited amorphous nps as a function of temperature can be derived 
 straightforwardly ; see the red and blue solid curves in the angell 
 plot of figure 4 , where 
 the temperature - dependent viscosity of gst films reported previously 
 by orava et al .
unlike the myega model , eq 4 does not directly provide the value of glass 
 transition temperature ( tg ) and fragility . 

here we set tg as the temperature at which 
 the viscosity equals 10 pa s , and then tg values are determined as 373 and 403 k for nps ( h2 ) and nps ( ch4 ) , respectively .
this value for the 
 nps ( h2 ) is close to the reported values for the gst films 
 ( 373383 k ) .
as indicated in a previous work , the crystallization temperature for nps ( h2 ) is slightly lower than that of gst films ( 10 k ) , 
 therefore the akin tg is plausible as 
 the glass transition usually takes place 10 k lower than tp1 at a  of 40 k min for gst films .
the increase 
 of tg caused by the ch4 incorporation 
 is 30 k , which agrees excellently with the rise of tp1 , as shown here by the ultrafast 
 dsc measurements and by the in situ tem characterization 
 of our earlier work .
the fragility , defined 
 as , is determined from the 
 angell plot for 
 these nps as well .
the fragility of nps ( h2 ) is 57 , consistent 
 with the value from a previous work ( m = 47 for nondoped 
 gst films ) .
these values for fragility 
 are considerably lower compared to the value obtained earlier for 
 gst films ( m = 90 ) .
the blue and red solid curves represent 
 the modeled viscosity for nps ( h2 ) and nps ( ch4 ) , respectively .
the black open circles are the viscosity data for 
 sio2 in order to show a strong ( undercooled ) liquid
. the black open triangles and the corresponding 
 fitting curve are the experimental data and fitting 
 curve utilizing eq 4 for 
 ge15te85 .
the blue stars are the viscosity data 
 for nitrogen - doped gst films , with corresponding 
 fitting curves adopting eq 4 .
black dotted curve shows the viscosity for gst films explored 
 by ultrafast dsc . in the angell plot , an 
 arrhenius behavior results in a fragility approaching 15 , 
 such as holds for sio2 , categorized 
 as a strong ( supercooled ) liquid ( cf .
larger values of fragility lead to non - arrhenius 
 behavior , classified as fragile , such as has been presented for the 
 gst films .
however , in some ( undercooled ) 
 liquids a single fragility model is not able to describe the temperature 
 dependence of viscosity .
then , the coexistence of arrhenius behavior 
 at low temperature and non - arrhenius behavior at high temperature 
 has been successfully explained by a fragile - to - strong ( fs ) crossover , which is a ubiquitous feature in glass formers . 

first discovered in water , this phenomenon 
 has thereafter been observed in glass - forming liquids , chalcogenides , and ag  in  sb  te 
 pcms .
for instance , figure 4 portrays the experimental 
 viscosity data for ge15te85 ( black open triangles ) 
 at temperatures near tg(48 ) and melting temperature ( tm ) , fitted with the corresponding dashed 
 curve utilizing eq 4 , 
 where a distinct fs crossover is illustrated .
the fs crossover in 
 ge15te85 is confirmed by another work employing 
 the adam  gibbs equation to fit the viscosity . for gst nps ,
the fs crossover is likewise discerned , demonstrated 
 by the red and blue solid curves in figure 4 . with the strong segment near tg ,
the viscosity drops exponentially with the increment 
 of temperature with an intermediate fragility ( strong ) , whereas a 
 further increase in temperature yields a nonexponential decline of 
 viscosity ( fragile ) .
the fs crossover in gst nps is weaker than that 
 of ge15te85 , where the two segments of viscosity 
 are clearly distinguished .
still , as we explain in the next paragraph , 
 there are strong arguments that the fs crossover actually occurs in 
 gst nps and that it is not a misinterpretation of a ( more ordinary ) 
 glass transition .
a similar temperature dependence of the growth 
 rate as in the present work was also observed for aginsbte pcms , where 
 the arrhenius dependence of viscosity was found at lower temperatures , 
 while the myega model ( non - arrhenius dependence ) was obtained at higher 
 temperatures . at that time
it was proposed 
 that the arrhenius behavior correlates to the glassy state , whereas 
 the non - arrhenius behavior is associated with the supercooled liquid 
 state . in this scenario ,
this divergence in temperature dependence 
 of viscosity appears at the junction between glass and supercooled 
 liquid .
if our observed ( fs transition ) behavior is explained as a 
 glass transition , that would lead to a tg of 438 k for gst nps ( h2 ) . taking this value 
 for tg ,
we then obtain a viscosity at tg of 10 pa s. it is obvious that 
 this viscosity is in conflict with the definition of glass transition 
 temperature ( where the viscosity is 10 pa s ) .
moreover , 
 we also observed crystallization at a temperature about 20 k lower 
 than this supposed tg of 438 k , which is also inconsistent with the notation 
 that crystallization is only possible above tg .
clearly , with the fragile - to - strong crossover model , these 
 conflicts are avoided .
therefore , the fs crossover is a more plausible 
 explanation of our observations than the ( supercooled liquid to ) glass 
 transition .
the present results therefore show the presence 
 of the fs crossover , 
 which already was signified by the large arrhenius region shown in figure 3b .
it occurs for 
 both samples approximately at 0.85 tg / t , a tg - scaled temperature lower 
 than that of ge15te85 and aginsbte .
the ch4 addition has negligible influence 
 on this crossover . for gst films reported by orava et al .
, however , 
 the fs crossover was not observed , and a viscosity model with a single 
 fragility value ( cohen and grest model ) was adopted to fit the kissinger 
 plot obtained through ultrafast dsc , denoted 
 as the black dotted curve in figure 4 .
the high fragility of gst films results in a sharp 
 reduction of viscosity at temperatures just above tg . yet
, the lower fragility for gst nps , caused by the 
 fs crossover , yields a less acute decline in viscosity .
consequently , 
 the gst nps exhibit a higher viscosity at lower temperature in comparison 
 to the gst films , as distinguished at 0.91 tg / t in figure 4 .
these results thus suggest that nps are 
 advantageous in phase - change memory as higher viscosity correlates 
 to lower atomic diffusivity and therefore longer data retention time . in a previous work , the growth rate 
 of nitrogen - doped gst ( n - gst ) in memory cells
was directly measured 
 in a large temperature regime ( from 420 to 530 k ) , 
 where the overall growth rate of the n - gst deviates in temperature 
 dependence : arrhenius behavior at low temperature and non - arrhenius 
 behavior at high temperature .
the experimental data for growth rate 
 were transposed to viscosity using eq 2 , with decoupling parameter  = 0.72 and other 
 parameters ( viz .
tm , ratom ,  , and rhyd in eq 2 ) from this article .
 
 is adjusted to make (tg ) = 10 pa s , and this value of  is close to that for gst 
 films reported previously .
the transposed 
 viscosity is presented as blue stars in figure 4 . the myega model for viscosity with one 
 fragility
can not fit these data when specifying (tm ) as 1.2  10 pa s. in contrast , the generalized myega model ( eq 4 ) yields a good fit to 
 the viscosity of n - gst , providing a strong indication that the fs 
 crossover also occurs in these n - doped gst films employed in memory 
 cells . in another work , a similar temperature 
 dependence in the growth rate of gst is observed , and two terms of 
 temperature dependence were utilized to fit the kissinger plot for 
 gst confined in a memory cell . yet , the fs crossover was not proposed 
 to explain the observed behavior , but in light of the present work 
 it has thus been generally observed for gst in memory cells .
it has been suggested that fs crossover exists only in growth - dominated 
 pcms but not in nucleation - dominated pcms .
melt - quenched gst pcms confined in a cell are considered ( by their 
 nanoscale volume ) as growth - dominated pcms .
while gst films are considered as nucleation - dominated pcms , gst 
 nps , on the other hand , also possess growth - dominated crystallization 
 ascribed to the extremely small volume for crystallization caused 
 by down - scaling .
for instance , in our previous work we found by high - resolution 
 tem only single crystalline nps .
nevertheless , 
 small crystal domains are generally expected for surface - induced heterogeneous 
 nucleation dominated crystallization of gst pcms . however , the nps in the present work are apparently that 
 small that they still form single crystals
. therefore , it might be 
 possible that the presence of the fs crossover in gst nps compared 
 to its absence in gst films can be attributed to the down - scaling 
 induced change in the crystallization mechanism from nucleation dominant 
 to growth dominant .
the overall growth rate 
 of the crystallization 
 for the gst nps is of technological relevance , e.g. , for pc memories , 
 as it is associated with data retention at the lower temperatures 
 and the switching speed at higher temperatures .
the blue and red solid 
 curves in figure 5 show 
 the overall growth rate , as derived using eq 2 , ranging from tg to tm for both nps ( h2 ) and 
 nps ( ch4 ) , respectively . in comparison , the growth rate 
 of gst films obtained by orava et al .
the maximum growth rate ( um ) for these 2 types of nps is very similar , 1.7 and 1.6 
 m s , with um taking 
 place at approximately 0.7 t / tm . these values for nps are reasonably close to um of gst films , as can be observed in figure 5 by comparing the blue and 
 red solid curves for the gst nps with the black dashed curve holding 
 for gst films . in a previous work , the growth rate of ge 
sb 
 alloy reaches a maximum value at 0.9 t / tm , which is plausible , 
 because the um of growth - dominated pcms 
 is considered to occur at a higher t / tm compared to nucleation - dominated pcms .
blue and red curves represent 
 the data for gst ( h2 ) and gst ( ch4 ) , respectively . 

the black dashed curve is the growth rate for gst films , while the black data points are from direct 
 measurements via transmission electron microscopy and atomic force microscopy . the directly 
 measured growth rate for nitrogen - doped gst films is also shown in 
 this figure ; see the blue stars in this 
 figure .
the light yellow shaded area denotes the actual measurement 
 regime accessed by ultrafast dsc .
although the nps ( ch4 ) possess a lower growth 
 rate at 
 lower temperature range ( below 520 k ) , it coincides with the one for 
 nps ( h2 ) when the temperature is beyond 590 k. the lower 
 growth rate for nps ( ch4 ) at low temperature is similar 
 to the retardation induced by carbon doping in gst films , as carbon ( a byproduct decomposed from methane 
 in plasmas ) is expected to be incorporated into the nps .
when the 
 temperature becomes higher , the fs crossover appears , and then the 
 fragile regime of viscosity is accessed . as a consequence , the viscosity 
 strongly drops to equivalent values generating final convergence of 
 the growth rates .
this trend is also indicated by the viscosity in figure 4 , where the difference 
 is less apparent , because figure 4 is normalized with respect to tg .
this makes the nps ( ch4 ) preferable for pc memory 
 application as lower growth rates at low temperatures associated with 
 a higher activation energy indicate a longer data retention time ; 
 meanwhile , the still comparable growth rates at higher temperature 
 enable sufficient rapid switching ( to the crystalline set state ) ; 
 see the more detailed discussion in section 5 of the si .
the growth rate undergoes an arrhenius - like behavior 
 at temperatures 
 just above tg , and non - arrhenius behavior 
 emerges with a further increase of temperature , demonstrating a temperature - dependent 
 activation energy ( eg , derived from the 
 gradient of this curve ) for crystal growth during crystallization . 
 with similar slopes to the independent data near tg , the eg is determined as 
 2.8 and 3.2 ev at for the nps 
 ( h2 ) and nps ( ch4 ) , as can be seen in figure s6 . for ge2sb2te5 films
it is well - established that the activation energy for 
 crystallization and for growth near tg is in the range 2.23.0 ev at . in comparison ,
the growth rate of gst films derived in ref ( 14 ) presents a considerably 
 higher activation energy , 5.0 ev at near tg , which appears unrealistic .
although a high 
 fragility of the gst thin film can lead to a high activation energy , 
 this fragility was obtained fully through modeling and fitting and 
 not based on any directly measured data , inferring that the high fragility 
 for the thin film could be erroneous .
however , it is still evident 
 that the growth rates for the nps 
 ( h2 ) observed in the present work exhibit a large gap ( 2 
 orders of magnitude ) with the directly measured data obtained for 
 gst films ( open black data points in figure 5 ) .
this discrepancy can have several 
 origins , e.g. : ( 1 ) the nps ( h2 ) crystallize at lower temperature 
 than films , leading to a faster growth rate at the same temperature . 

the nps ( ch4 ) represent an evidently lower growth rate 
 at the same temperature compared to nps ( h2 ) due to the 
 increase of tp .
similarly , 
 the nitrogen - doped gst films ( confined in memory cells ) even show 
 smaller growth rate than gst films , as 
 demonstrated by the blue stars in figure 5 .
( 2 ) the constant nuclei density hypothesis 
 that was adopted in jmak modeling is oversimplified and may result 
 in an erroneous fitting of the data in the kissinger plot and therefore 
 may cause a considerable shift to higher growth rates at the lower 
 temperatures
. however , several clearly more advanced models for nucleation 
 were also tested , and these models did not significantly reduce the 
 gap between the growth rates derived for the nps ( h2 ) ( blue 
 solid line in figure 5 ) and the directly measured data obtained for gst films ( black open 
 data points in figure 5 ) ; for more details see the si and in 
 particular figure s7 .
ultrafast differential 
 scanning calorimetry has been employed to 
 investigate the crystallization kinetics of ge2sb2te5 phase - change nanoparticles ( nps ) synthesized by gas - phase 
 condensation .
the nps show a relatively narrow size distribution around 
 an average diameter of 16 nm . varying the heating rate during 
 the dsc measurements with 3 orders of magnitude , it is observed that 
 ( 1 ) the crystallization rate complies with arrhenius behavior within 
 an ( unexpectedly ) large temperature range directly above tg ( for tg / t values from 0.85 to 1 ) and ( 2 ) a non - arrhenius 
 fragile behavior occurs at higher temperatures ( for tg / t values lower than 0.85 ) .
this unique 
 feature can be explained well ( only ) by utilizing a fragile - to - strong 
 crossover model for the viscosity , from which the overall viscosity 
 and growth rate of the nps have been derived .
this crossover is clearly 
 observed here for the ge2sb2te5 nps , 
 while it was not observed earlier for gst films .
this enables nps 
 to have both longer data retention times at low temperatures and high 
 switching speed at high temperatures , entailing the nps to be an advantageous 
 contender in phase - change materials based devices .
moreover , it is 
 demonstrated that ch4 incorporation during the np production 
 reduces the crystal growth rate by about 2 orders of magnitude at 
 lower temperatures and thus improves the data retention , whereas the 
 maximum growth rate remains unchanged .
effect makes ge2sb2te5 nps even more 
 suitable candidates for phase - change memory applications .
 although nanostructured 
 phase - change materials ( pcms ) are considered 
 as the building blocks of next - generation phase - change memory and 
 other emerging optoelectronic applications , the kinetics of the crystallization , 
 the central property in switching , remains ambiguous in the high - temperature 
 regime . 
 therefore , we present here an innovative exploration of the 
 crystallization kinetics of ge2sb2te5 ( gst ) nanoparticles ( nps ) exploiting differential scanning calorimetry 
 with ultrafast heating up to 40 000 k s1 . our results 
 demonstrate that the non - arrhenius thermal dependence of viscosity 
 at high temperature becomes an arrhenius - like behavior when the glass 
 transition is approached , indicating a fragile - to - strong ( fs ) crossover 
 in the as - deposited amorphous gst nps . 
 the overall crystal growth 
 rate of the gst nps is unraveled as well . 
 this unique feature of the 
 fs crossover is favorable for memory applications as it is correlated 
 to improved data retention . 
 furthermore , we show that methane incorporation 
 during np production enhances the stability of the amorphous np phase 
 ( and thereby data retention ) , while a comparable maximum crystal growth 
 rate is still observed . 
 these results offer deep insight into the 
 crystallization kinetics of nanostructured gst , paving the way for 
 designing nonvolatile memories with pcm dimensions smaller than 20 
 nm . 
Introduction
Experimental
Methods
Results and Discussion
Conclusions