like co@fe3o4 , which recently underwent extensive study to 
 elucidate both the 
 oxidative stability of the core and the phase of the shell , fept@fe3o4 core 
shell 
 nanoparticles can be used as building blocks to form nanocomposites 
 with enhanced magnetic properties with the potential for novel applications . 
 these include magnetic data storage , catalysis , and targeted drug 
 delivery . in terms of nanomagnetics specifically , our hope 
 is that the presence of an inert oxide shell may function to inhibit 
 agglomeration of the cores upon annealing ; this is a necessary step 
 in creating an ordered l10 fept bimetallic structure with 
 a higher magnetic coercivity .
the determination of the core composition 
 is important for tailoring their synthesis in order to ultimately 
 achieve the desired 50:50 fept alloy composition . a solution 
 of core 
shell particles was drop - cast onto a 3 mm holey carbon 
 copper grid .
edx data were acquired using an fei osiris tem equipped 
 with a high brightness schottky x - feg gun and a super - x edx system 
 comprising four silicon drift detectors , each approximately 30 mm in area and arranged symmetrically around an optic axis to 
 achieve a collection solid angle of 0.9 sr .
edx data were 
 collected in the form of spectrum images , in which a focused electron 
 probe was scanned in a raster across a region of interest in the scanning 
 tem ( stem ) . at each point in the scan ,
structural information was 
 obtained from the electron scattering incident on a high angle annular 
 dark field ( haadf ) detector , and simultaneously , an edx spectrum was 
 obtained by collecting x - rays emitted from the local volume probed 
 by the electron beam .
the resulting edx spectrum image was a three - dimensional 
 data set whose ( x , y ) axes correspond 
 to the position of the probe and whose z axis corresponds 
 to the energy of the detected x - ray .
spectrum images were acquired 
 with a probe current of approximately 0.7 na , an acceleration voltage 
 of 200 kv , a spatial sampling of between 0.5 and 1 nm / pixel and 50100 
 ms / pixel dwell times .
x - ray intensities were obtained 
 by fitting a model of the edx spectra to the experimental data using 
 weighted least - squares and atomic fractions were quantified from intensities 
 using the cliff  lorimer quantification .
the edx model and the 
 quantification were implemented in hyperspy and will be available 
 in future releases of the software .
figure 1a displays a haadf stem image obtained 
 during the acquisition of a spectrum image enclosing a cluster of 
 13 co@fe3o4 nanoparticles .
although the particle 
 morphologies are seen to vary slightly from one particle to another , 
 the majority of particles have a round core approximately 20 nm in 
 diameter surrounded by a thin shell approximately 5 nm in thickness . 
 the edx elemental maps for cobalt , iron , and oxygen ( figure 1b  d ) , obtained by integration of the element s 
 background - subtracted k - line x - ray peak , show that individual particles 
 are comprised of a cobalt core surrounded by a shell composed of iron 
 and oxygen , as expected .
the largest particle in the lower left region 
 of the map appears to have more iron in the core compared to the smaller 
 particles .
these conventional edx element maps show the location of 
 the various elements , but the composition of the particle core , for 
 example , can not be determined by elemental mapping due to the presence 
 of the shell above and below the core in projection .
elemental maps of ( b ) cobalt , 
 ( c ) iron , and ( d ) oxygen display the location of the various elements 
 with respect to the particle morphology ( scale bar = 50 nm , greyscale 
 = x - ray counts ) .
the edx spectrum image 
 data of the co@fe3o4 nanoparticle cluster shown 
 in figure 1a was 
 subsequently processed using bss methods in hyperspy .
first , the 
 spectral dimension in the data set was binned by four from 5 ev / channel 
 to 20 ev / channel in order to increase the number of counts per channel . 
 next ,
we note that the binning 
 step is necessary in order to optimize the accuracy of the variance 
 stabilization channel .
the first three principal 
 components , pc#0 , pc#1 , and pc#2 , exhibited significantly greater 
 variance than the remaining components ( figure 2a ) , which suggests that there are only three phases present in the 
 sample .
that being the case , those three pca components should be 
 a linear combination of the spectra and distribution maps of those 
 phases , but the mixing matrix is unknown .
next , we compute numerically 
 the first derivative of the pca spectral components in order to diminish 
 the correlation caused by the edx background , and we use fastica to estimate the mixing matrix and compute the 
 independent components ( ics ) ic#0 , ic#1 , and ic#2 ( figure 2b ) and their distribution maps ( figure 2c  e ) from the pca results . component independence 
 is a much more stringent property than uncorrelatedness imposed by 
 pca .
if we disregard the small copper peaks contained 
 in all the independent components , likely originating from the copper 
 support mesh , we see that ic#0 contains cobalt x - ray peaks , ic#1 iron 
 and oxygen peaks , and ic#2 a carbon peak .
the three ics appear to 
 belong to the three phases present in the originally scanned area : 
 the core , shell , and supporting film .
this hypothesis is explored 
 further in the next section . at this point , however , it is important 
 to note that , unlike in the conventional edx mapping shown in figure 1 , no elements were selected prior to performing 
 ica , and thus , the analysis is free of external bias , except for the 
 choice of the number of components .
result of bss by pca and ica of an edx 
 si of a co@fe3o4 core 
( b ) corresponding independent 
 component spectra contain the expected x - ray lines for the elements 
 present .
independent component maps ( c  e ) show that ( c ) ic#0 
 is concentrated in the nanoparticle cores , ( d ) ic#1 in the shells , 
 and ( e ) ic#2 everywhere on the carbon supporting film ( scale = 50 
 nm , greyscale = normalized weighting ) .
we now move on to the analysis of a second cluster of particles 
 comprised of a bimetallic iron / platinum core surrounded by an iron 
 oxide shell .
a crystalline core surrounded by a polycrystalline oxide 
 shell is observed in the representative high - resolution stem haadf 
 image shown in figure 3 .
the 
 particle morphologies were found to have 
 a mean core diameter of approximately 3.3 nm and mean shell thickness 
 of approximately 1.7 nm ( figure 4a ) . also visible 
 were pure iron oxide particles ( in the lower right - hand corner of 
 figure 4a ) .
ica of a cluster of bimetallic platinum / iron 
 nanoparticle seeds 
 coated by fe3o4 shells .
( b ) 
 scree plot of the first 50 principal components showing the first 
 three components lying above the noise .
( c  e ) element maps 
 of ( c ) platinum , ( d ) iron , and ( e ) oxygen . ( f  h ) .
the ic maps 
 ( f ) ic#0 , ( g ) ic#1 , and ( h ) ic#2 and ( i ) the corresponding ic spectra . from the selected element maps 
 ( figure 4c 
e ) , it is clear that , with 
 the exception of the two particles 
 in the lower right - hand corner , the particles are comprised of a platinum 
 rich core surrounded by an iron oxide shell .
however , it is not clear 
 from the maps alone whether iron is present in the core . by conventional 
 elemental
mapping , one can not tell whether the particles contain a 
 pure platinum core surrounded by an iron oxide shell or whether iron 
 is alloyed with platinum to form a bimetallic core .
we now address 
 these questions by performing bss on the same edx 
 spectrum image using the same procedure detailed before .
once again , 
 by inspecting the scree plot ( figure 4b ) , we 
 find that the sample consists of three phases .
the spatial distribution 
 of ic#0 is concentrated in the particle cores , ic#1 in a shell around 
 the cores , and ic#2 is approximately uniformly distributed over the 
 map ( figure 4f  h ) . if we again disregard 
 the spurious copper peak , ic#0 contains iron and platinum x - ray peaks , 
 ic#1 iron and oxygen peaks , and ic#2 a single carbon peak ( figure 4i ) . from this analysis
it appears that the ica components 
 represent the different phases present in the edx spectrum image ; 
 ic#0 , ic#1 , and ic#2 genuinely represent the bimetallic fept cores , 
 iron oxide shells and the carbon support , respectively . in order 
 to verify the accuracy of the ica results , we evaluated 
 whether ic#0 represented the true composition of the core by analyzing 
 bare fept seed particle clusters obtained from the same chemical synthesis 
 but extracted prior to the shell addition step .
being made from the 
 same synthesis , the composition of the bimetallic seed particles are 
 expected to match to the composition of the bimetallic cores in the 
 core  shell particles analyzed in figure 4 .
a total of 12 edx sis were acquired in order to capture and 
 analyze 
 multiple fept bimetallic seed clusters .
the segmentation of one of 
 the edx sis is shown in figure 5a , b . to accurately extract the intensity of the fe k and pt l 
 peaks , a model composed of one gaussian per x - ray line and
a background 
 based on kramers and small expressions as developed elsewhere was used , as shown in green in figure 5c .
the only free parameters of the model were the 
 area of the gaussian and the height of the background , which was negligible . 

the mean reduced  over the fit of all particles 
 was 1.01 , indicating that the discrepancies between the model and 
 the data are in accordance with the poisson noise variance . the intensities 
 of fe k and pt l peaks in the fitted model were quantified 
 using the cliff  lorimer method .
the obtained compositions are 
 plotted for each particle in figure 5d along 
 with the fitting error estimated from poisson statistics .
the raw 
 data were decomposed using pca on all fept seed data and the first 
 three components were retained for noise reduction .
the 103 individual 
 fept bimetallic seeds analyzed were found to have a mean composition 
 of 82.0 at .
% pt , which lies well within one standard deviation of 
 the average bimetallic seed composition .
the data points in figure 5d are displayed in order of ascending particle size . 

as such , the calculated compositions on the right - hand side tend to 
 have a smaller error bar on account of the signal  noise ratio 
 being higher for larger particles .
the compositions of the larger 
 seed particles are also closer to the mean composition and to the 
 composition of ic#0 , confirming the homogeneity of the composition 
 and the validity of the bss analysis .
summary of the composition of 103 bare 
 fept bimetallic nanoparticles 
 extracted from a synthesis prior to the shell addition step .
( b ) segmentation of the edx spectrum 
 image prior to quantification of each particle .
( c ) fitting of the 
 edx spectrum from a single seed ( circled in ( b ) ) to a model spectrum 
 to determine the fe k and pt l peak intensities .
( d ) 
 particle seed compositions obtained by quantifying the fitted intensities 
 from 103 different particles ( error bars = 1 standard deviation ) .
a comparison 
 of raw edx spectra extracted 
 from fept bimetallic seed particles and from pure fe3o4 particles with ic#0 and ic#1 , respectively , is provided in 
 figure 6 . in both cases ,
the ics were scaled 
 by a constant to obtain a best fit to the raw spectra . despite the 
 strong overall agreement in each case ,
the carbon peak difference in both cases is 
 caused by the separation of carbon into a different component ( ic#2 ) . 

the difference in the shell cu peaks are not due to a compositional 
 difference as the cu signal is spurious in origin .
the iron oxide 
 particle spectrum also contains small silicon and sulfur peaks which 
 likely originate from residue on the carbon film .
the difference in 
 the pt m core peak may be due to the attenuation of pt m 
 x - rays in the shell of the core  shell nanoparticles and in 
 nearby particles along the trajectory to the detector .
the strong 
 overall similarity between the raw and ic spectra provide direct evidence 
 showing that the spectral components extracted by ica from the core  shell 
 spectrum image data are strongly representative of the buried core , 
 surrounding shell , and carbon support compositions .
comparison between raw 
 edx spectra extracted from a fept bimetallic 
 seed particle ( top ) and from an iron oxide particle ( bottom ) with 
 ic#0 and ic#1 , respectively . the fept seed and fe3o4 x
when analyzing beam - sensitive materials , the main 
 limitation to 
 the accuracy of the bss analysis method that we propose is the intensity 
 of the edx signal achievable without inducing significant sample damage . 
 in our case , despite the use of a high efficiency edx system ,
the 
 number of collected x - rays is low . in order to avoid the artifacts 
 that arise
when using the variance - stabilizing transformation out 
 of its domain of application , we have binned the data by four in the spectral dimension from 5 ev / channel to 
 20 ev / channel .
given that the resolution of our edx detector is approximately 
 130 ev at mn k and that there were no overlapping x - ray lines , 
 in our case , the increase in the number of counts per channel ( and 
 hence in the accuracy of the analysis ) comes without significant resolution 
 loss and , therefore , should not have any adverse effect in the analysis .
a blind source separation method based 
 on pca and ica has been applied to the analysis of edx spectrum images 
 of core 
the analysis has accurately 
 determined the number of phases in the analyzed volume ( core , shell , 
 and supporting film ) as well as their spectra and distribution maps . 

we have confirmed the accuracy of the analysis by comparing the calculated 
 spectra from the platinum  iron core and the iron oxide shell 
 to those obtained from these structures in isolation , and the excellent 
 agreement suggests that bss , therefore , can be used to accurately 
 analyze edx data .
the use of ica on edx spectrum image data promises 
 to be a powerful technique for extracting buried compositions at the 
 nanoscale in a variety of materials , and further testing on the method s 
 applicability to different systems is now being initiated .
 the chemical composition of core  shell 
 nanoparticle clusters 
 have been determined through principal component analysis ( pca ) and 
 independent component analysis ( ica ) of an energy - dispersive x - ray 
 ( edx ) spectrum image ( si ) acquired in a scanning transmission electron 
 microscope ( stem ) . 
 the method blindly decomposes the si into three 
 components , which are found to accurately represent the isolated and 
 unmixed x - ray signals originating from the supporting carbon film , 
 the shell , and the bimetallic core . 
 the composition of the latter 
 is verified by and is in excellent agreement with the separate quantification 
 of bare bimetallic seed nanoparticles . 
Materials and Methods
Results
Discussion
Conclusions