we adopt a simple cvd process , the salient stages of which are 
 outlined in figure 1 : ( 1 ) the preannealing stage , during which the samples are gradually 
 heated in h2 or nh3 , ( 2 ) the vacuum stage preceding 
 borazine exposure , ( 3 ) the borazine exposure period , and ( 4 ) the vacuum 
 cooling stage . figure 2 compares the morphology of the h - bn grown on as - received fe foils 
 ( 100 m ) at 900 c and 6  10 mbar borazine partial pressure following preannealing in 4 mbar 
 of either h2 or nh3 ( stage 1 ) as a function 
 of borazine exposure time ( stage 3 ) .
we observe a strong effect of 
 the preannealing gas on the growth . in particular , for the nh3 preannealing ,
an increase in growth time results in a gradual 
 closure of the monolayer h - bn film , without multilayer formation . 

conversely , the h2 preannealing does not lead to a continuous , 
 homogeneous h - bn film even for extended growth times , and primarily 
 results in thicker , few - layer h - bn domains .
the shaded areas correspond to the preannealing 
 stage in either h2 or nh3 ( 1 ) , the vacuum stage 
 prior to borazine exposure ( 2 ) , the borazine exposure period ( 3 ) , 
 and the vacuum cooling stage ( 4 ) .
sem images of h - bn domains grown at 900 c and 6  
 10 mbar borazine exposure on ( a , b , c ) h2-preannealed fe foil for 45 s , 90 s , and 480 s borazine exposure 
 time , respectively , and on ( d , e , f ) nh3-preannealed fe foil 
 for 45 s , 90 s , and 480 s borazine exposure time , respectively . the 
 preannealing pressure in both h2 and nh3 is 
 4 mbar for all of the above growths . the insets in ( a
, d ) correspond 
 to 14 s exposures and illustrate the longer incubation time preceding 
 nucleation of h - bn on the h2-preannealed sample .
the average domain size for the 
 h2-preannealed sample is < 1 m after 45 s borazine 
 exposure ( figure 2a ) . 
 for a 14 s borazine exposure following a h2 preannealing 
 ( figure 2a inset ) no 
 h - bn
was observed on the fe surface , indicative of an incubation period 
 preceding crystal nucleation of at least 14 s. we note that the h - bn 
 domain orientation , size , and density varies across the sample surface , 
 suggesting fe grain orientation - dependent growth kinetics , a feature 
 that is also observed for the nh3-preannealed foil ( see 
 supporting information figure s1 ) .
after 
 90 s , the domains grow to average lateral sizes of 3 m 
 ( figure 2b ) , and the 
 change in contrast from the edges to the center of the triangular 
 domains also indicates a notable thickness variation , with brighter 
 regions corresponding to multilayers and conversely dark gray regions 
 indicating monolayer h - bn . extended growth times ( 480 s , figure 2c ) lead to slightly 
 higher h - bn coverages ; however , growth appears to primarily proceed 
 through the formation of additional h - bn layers , rather than lateral 
 expansion of the existing layers .
additionally , we observe a bimodal 
 domain size distribution across the entire sample surface ( figure s2 ) , with large domains ( side length 15 
 m ) coexisting with domains about ten times smaller .
this observation 
 suggests that two distinct growth regimes appear to exist under these 
 growth conditions for the h2 preannealing . for the 
 nh3-preannealed fe foil , the most notable difference after 
 45 s borazine exposure is the formation of a lower density of triangular 
 domains with lateral dimensions of 20 m ( figure 2d ) , which are more than ten 
 times the size of the domains grown on the h2-preannealed 
 fe foil for the same exposure time .
we also note that the edges are 
 sawtoothed , a feature that we have observed previously for large h - bn 
 domains grown on fe / sio2/si substrates , and which can be ascribed to diffusion instabilities .
the incubation time for the nh3-preannealed 
 catalyst is shorter , highlighted by the appearance of triangular domains 
 after just 14 s of borazine exposure ( figure 2d inset ) .
the h - bn domains are largely merged 
 after 90 s exposure ( figure 2e ) , with only a few gaps left in the film . after 480 s of 
 borazine exposure ,
we achieve full coverage of the fe catalyst with 
 monolayer h - bn ( figure 2f ) .
the remaining variations in sem contrast over the surface of 
 the sample are due to channeling contrast from the polycrystalline 
 fe foil .
figure 3 summarizes the effect of three different cooling rates ( stage 4 
 in figure 1 ) on the 
 h - bn morphology after growth on the differently preannealed foils 
 ( h2 or nh3 , 4 mbar ) , followed by a fixed borazine 
 exposure ( 6  10 mbar ,  900 c , 
 5 min ) .
we note that the cooling rates refer to the initial cooling 
 period from 900 c down to 500 c , after 
 which the rate slows down and is comparable for all three cases .
figure 3a corresponds to 
 immediate quenching ( 300 c / min ) for a h2-preannealed 
 foil , with the heater turned off immediately after borazine exposure , 
 and shows a bimodal domain size distribution of few - layer h - bn . for 
 an intermediate cooling rate of 100 c / min ,
the h - bn domains 
 appear larger and more multilayered , and the density of the smaller 
 domains is considerably higher ( figure 3b ) , indicating that some portion of the h - bn is formed 
 on cooling .
for slow cooling rates of 50 c / min , the domains 
 are similar in size and thickness to the intermediate cooling rate ; 
 however , the shapes are no longer strictly triangular and the edges 
 become less sharp ( figure 3c inset ) .
the same cooling experiments were performed on the 
 nh3-preannealed foils ( figure 3d  f ) .
the h - bn domains remain as monolayers , 
 with no multilayers observed for any of the cooling rates used here . 

this illustrates that , contrary to the h2-preannealing 
 case , additional layer formation and nucleation do not occur on cooling , 
 both of which are effects that can be linked to precipitation of b 
 and n species from the catalyst bulk .
morphology of h - bn on h2-preannealed 
 fe foil after ( a ) fast cooling ( 300 c ) , ( b ) medium cooling ( 100 
 c / min ) , and ( c ) slow cooling ( 50 c / min ) .
inset : detail 
 of multilayered domains with irregular edges , indicating possible 
 dissolution of material back into the bulk during slow cooling .
morphology 
 of h - bn on nh3-preannealed fe foil after ( d ) fast cooling , 
 ( e ) medium cooling , and ( f ) slow cooling .
all growths were performed 
 at 900 c and 6  10 mbar borazine 
 exposure for 5 min . to further understand 
 this difference in behavior with preannealing atmosphere
, we performed 
 a growth where we first preannealed the sample in nh3 , 
 and then held it at the growth temperature in vacuum for 30 min after the nh3 preanneal but prior to borazine exposure ( i.e. , extended stage 2 in figure 1 ) .
figure s3 shows the postgrowth surface of this sample , which consists 
 of a h - bn domain size distribution tending to be more bimodal than 
 for the standard growth with the nh3 preannealing .
furthermore , 
 most of the domains are smaller and multilayered , and are reminiscent 
 of those grown on the h2-preanneled sample , despite the 
 lower nucleation density . the structure and crystallinity of 
 the h - bn formed by the optimized process using nh3 preanneling 
 was determined by transmission electron microscopy ( tem)/scanning 
 transmission electron microscopy ( stem ) .
figure 4a shows a scanning electron microscopy ( sem ) 
 image of a holey carbon / copper tem grid after transferring isolated 
 h - bn domains corresponding to figure 2d .
figure 4b shows a dark - field tem ( df - tem ) image of one such h - bn island , 
 confirming the single - crystalline nature of the domain .
the corresponding 
 selected area electron diffraction pattern ( upper right inset ) shows 
 one hexagonal set of diffraction spots also consistent with single - crystalline 
 h - bn .
the green circle indicates the diffraction spot used to produce 
 the df - tem image .
the lower right inset shows a defocused bright - field 
 ( bf ) tem image confirming that the domain is indeed isolated , and 
 a second differently oriented h - bn domain can be partially seen in 
 the lower left corner .
we further analyze the film by high angle annular 
 dark field ( haadf ) stem , which reveals atomic and element specific 
 contrast .
the high - resolution stem image 
 in figure 4c displays 
 the hexagonal lattice of h - bn and the intensity profile along the 
 marked yellow line exhibits a clear distinction of the b and n atoms 
 ( figure 4c inset ) , 
 where the extracted intensity ratio is consistent with monolayer h - bn .
further confirmation of the monolayer nature 
 of the h - bn was obtained by electron beam induced sputtering in supporting 
 information figure s4 , which exhibits direct , 
 step - free sputtering of the layer to vacuum consistent with single - layer 
 h - bn ( whereas multilayer h - bn is sputtered in a layer - by - layer fashion).figure 4d shows a 
 bright - field tem image of a suspended closed h - bn film , with the corresponding 
 diffraction pattern and film edge close - up ( top left and bottom right 
 insets , respectively ) , demonstrating the crystalline and monolayer 
 properties of the material .
an optical image of h - bn domains transferred 
 onto a sio2(300 nm)/si wafer , acquired with a green filter 
 to enhance the contrast with the substrate , is shown in figure 4e .
the raman spectrum from 
 the area indicated by the red dot ( figure 4f ) exhibits a peak at 1369 cm , in agreement with literature values for cvd h - bn .
( a ) sem image of h - bn domains from figure 2d transferred onto a holey carbon / copper 
 tem grid .
( b ) df - tem image of a triangular h - bn domain , confirming 
 its single - crystalline nature .
the upper right inset shows 
 the corresponding hexagonal diffraction pattern with the diffraction 
 spot , from which the df - tem image was acquired , indicated by the green 
 circle .
the lower right inset shows a defocused bf - tem image demonstrating 
 that the island is indeed isolated .
( c ) high - angle annular dark field 
 ( haadf ) stem image from the 
 center of a triangular domain showing atomic and element specific 
 contrast .
the image was processed following krivanek et al . to reduce 
 contributions from probe - tails .
the intensity 
 profile along the indicated yellow line ( inset ) exhibits an n / b intensity 
 ratio consistent with monolayer h - bn .
( d ) bright - field tem image of a suspended h - bn film from the sample 
 in figure 2f .
the top 
 left inset shows the diffraction pattern from this region and the 
 bottom right inset is an edge - analysis , confirming the monolayer nature 
 of the film .
( e ) optical image after transfer of the sample in figure 1e , showing coalescing 
 h - bn domains .
we note that the image was acquired using a green filter 
 to enhance the contrast .
( f ) raman spectrum acquired in the region 
 indicated by the red dot in panel ( e ) , displaying the characteristic 
 h - bn peak at 1369 cm and the si - related peak . in order to elucidate the growth mechanisms responsible for 
 the differing h - bn morphologies observed in figure 2 , we employ in situ xrd and in situ xps during growth .
figure 5 compares in situ xrd patterns acquired during h2- ( a ) and nh3-preannealed ( b ) h - bn growth .
the 
 as - loaded catalyst foils display reflections corresponding to body - centered - cubic 
 ( bcc ) -fe . for the h2 preannealing ( figure 5a )
, the foils transform to 
 face - centered - cubic ( fcc ) -fe upon heating and concurrently 
 grain growth occurs ( shown via a sharpening of the reflections ) .
we 
 note that in our experimental setup the large fe grain sizes ( 80 
 m estimated from sem ) result in the diffraction pattern originating 
 from only a few grains , and hence , the measured apparent texture directions 
 are not necessarily representative of the texture of the entire foil . 
 upon introduction of borazine following the h2 preannealing , 
 a strong reflection at 18
is observed , which is ascribed to 
 isothermal growth of few - layer h - bn , accompanied by multiple sharp 
 reflections at higher angles that can be attributed to the formation 
 of a small amount of fe - borides ( fe2b , and possibly feb ) . 

furthermore , the majority catalyst phase changes from -fe to 
 -fe ( with possibly small amounts of -fe remaining ) . 
 after cooling to room temperature ,
the catalyst state consists of 
 mostly -fe with some minor fe - borides and possibly some -fe . 

the observed fe - boride formation and the isothermal -fe  
 -fe transition are both indicative of b uptake into the fe 
 and are consistent with our recent work on h2-preannealed 
 h - bn growth on fe films . in situ xrd patterns 
 of fe foil catalyzed h - bn growth during the salient stages of the 
 cvd process , comparing the h2 preannealing ( a ) and the 
 nh3 preannealing ( b ) .
we note 
 that intensity is plotted here on a log scale to emphasize minority 
 phases .
the catalyst was annealed in 2.6 mbar of h2 ( a ) 
 and 4 mbar of nh3 ( b ) , and the growth was performed at 
 900 c ( estimated uncertainty in temperature 25 
 c ) in 6  10 mbar borazine 
 partial pressure for 10 min . in contrast
, the nh3 preannealing ( figure 5b ) leads to a very different 
 evolution : upon preannealing in nh3 the majority catalyst 
 phase changes from -fe to -fe ( as with h2 preannealing ) .
however , although the xrd pattern for nh3 preannealing can be fully assigned to -fe , we note that the 
 comparably broad peak at 30 could also correspond to 
 the highest intensity reflection of -fe3n ( not observed 
 for h2 preannealing ) , which requires n uptake into the 
 fe foil .
we corroborate such n uptake by control experiments on fe(250 
 nm)/sio2(300 nm)/si which are exposed to the same nh3 preannealing annealing conditions .
although trace levels 
 of diffused si have to be considered for these films , the lower degree of texture allows rietveld refinement 
 of lattice constants . upon nh3 exposure over a vacuum baseline
, 
 we find a lattice expansion corresponding to 0.6 atom % n uptake into the bulk of the -fe films ( figure s5 ) , confirming that n dissolves into 
 the fe under our nh3 preannealing conditions .
when borazine 
 is introduced , the preceding nh3 preannealing impacts on 
 the further catalyst evolution : in contrast to the h2-preannealed 
 foil , -fe remains the majority catalyst phase and neither fe - borides 
 are formed nor is a -fe  -fe transition observed 
 during borazine exposure .
additionally , we do not observe the emergence 
 of a few - layer h - bn related reflection at 18. this lack 
 of a signal corresponding to thick h - bn films is consistent with the 
 exclusive monolayer h - bn growth observed in our ex situ characterization 
 above ( we note that our xrd setup can not detect monolayer h - bn ; however , monolayer h - bn growth was confirmed 
 by ex situ sem for the nh3-preannealed sample grown during 
 in situ xrd ) . during cooling to room temperature , after borazine exposure , 
 a -fe  -fe transition occurs .
the additional emergence of fe4n reflections 
 upon cooling ( which were not observed in the h2 preannealing 
 data ) further corroborates n uptake into the catalyst during the nh3-preannealed h - bn cvd .
fe4n is only thermodynamically 
 stable below 680 c , which explains 
 why fe4n only nucleates upon cooling . in situ
xps 
 data summarized in figure 6 provides complementary , surface - sensitive information on 
 the h - bn nucleation and growth processes .
we note that the assignment 
 of all the xps peaks and their corresponding shifts is not trivial 
 for such a complex multicomponent system .
hence , we focus here on 
 the main signatures of h - bn cvd and the major differences arising 
 from the two preannealings .
figure 6a  d show the time - resolved evolution of the 
 xp b1s and n1s core level spectra 
 for a fe foil preannealed at 900 c in either h2 ( a , c ) or nh3 ( b , d ) and subsequently exposed to borazine . 
 the borazine exposure time
( measured from the time at which the desired 
 exposure pressure is reached ) for each scan prior to cooling is indicated 
 in the top left corner of each frame .
two main peak pairs are observed 
 for both preannealings and are related to the h - bn structure , where 
 the b atom is bonded to three n atoms in a planar hexagonal configuration . the b / n peak pair with higher binding energies 
 ( be )
both pairs can relate to monolayer h - bn and can arise due to differences 
 in coupling between the h - bn layer and the catalyst . in particular , 
 effects such as different grain orientations , intercalation , and rippling / restructuring 
 of the surface are known to change the interaction of the overlying 
 2d film with the substrate .
the increase 
 in the intensity of the lower be pair is then tentatively attributed 
 to few - layer h - bn : on the basis of our 
 previous work on cu - catalyzed h - bn cvd , we note that although the first h - bn layer in direct contact with 
 the catalyst does show such coupling effects , for few - layer h - bn this 
 interaction can be screened . hence , an increasing peak intensity of 
 the lower be pair here can be indicative of the presence of few - layer 
 h - bn .
for the h2-preannealed foil during the initial exposure 
 to borazine , the peaks of both the high and low be pairs appear concurrently , 
 with the low be pair dominating .
this is consistent with our sem images 
 showing the growth of multilayered islands for very short exposure 
 times . with continuing borazine exposure
, the relative peak intensity 
 of the lower be pair continues to rise , indicative of a thickening 
 of the h - bn domains , and then increases even further upon cooling . 

in contrast , for the nh3-preannealed foil , the high be pair is more intense in the early 
 stages of growth , relative to the h2 preannealing , indicating 
 isothermal growth of predominantly monolayer h - bn on fe .
the fact 
 that the low be pair dominates for the rest of the growth suggests 
 that few - layer h - bn evolves with extended exposure time , which is 
 indeed observed in the ex situ sem image of this sample taken after 
 growth and cooling ( figure s6b ) .
though 
 the xps growth results differ somewhat from those of our well - calibrated 
 reactor and the optimized growths in figure 2d  f , we attribute this to the different 
 conditions in the xps chamber , notably the much lower base pressure 
 [ 10 mbar ] and the lower permissible pressure 
 of nh3 [ 0.5 mbar ] .
effectively , the in situ xps 
 experiments resemble the cvd growth with an extended stage 2 , where 
 insufficient n - enrichment of the catalyst bulk causes the formation 
 of h - bn multilayers .
we note that the slightly different ratio of 
 the two be components between the b1s and the corresponding 
 n1s ( bottom two frames , figure 6 ) for the nh3 case can be attributed 
 to the fact that the n1s spectra were always acquired 
 after the b1s spectra , that is , with a typical time 
 lag of 1 min , the n1s spectra thus correspond to 
 a later stage of the growth .
the increase in the intensity of the 
 two peak pairs with extended borazine exposure ( as apparent from the 
 different intensity scalings of each frame ) confirms that , regardless 
 of the preannealing , h - bn formation occurs isothermally , which is 
 in agreement with our in situ xrd measurements and ex situ sem observations . 

we further note that for the h2 preannealing case , a minor 
 contribution from bulk precipitation upon cooling is also observed 
 ( figure 3a  c ) . 

conversely , for the nh3 preannealing case no signatures 
 of precipitation are observed , even for very slow cooling rates ( figure 3d  f ) .
time - resolved 
 in situ xps of the b1s core level for ( a ) h2- and ( b ) nh3-preannealed fe foil and the n1s core level for ( c ) h2- and ( d ) nh3-preannealed 
 fe foil during borazine exposure and initial cooling stage ( 900 
 c ,  1  10 mbar for nh3-preannealed sample and 1  10 mbar for h2-preannealed sample ,  10 min ) .
spectra 
 are collected in normal emission geometry at photon energies of 620 
 ev ( escape  13  ) .
figure 7a , b 
 show depth - resolved b1s core level spectra taken 
 after borazine exposure and cooling for h2- and nh3-preannealed foils , respectively . by changing the incident 
 x - ray energies , and hence the inelastic mean free path of the photoelectrons 
 ( escape ) , the information depth can be varied , giving 
 a more surface sensitive spectrum ( escape  
 10  ) for hv = 400 ev and a more bulk sensitive 
 ( escape  13  ) spectrum for hv = 640 ev . for the h2-preannealed foil ,
we 
 assign the component at 188 ev to b - related species ( dissolved 
 b or borides ) and note that this component does not have a corresponding pair 
 in the n1s spectrum , as would be expected .
comparison 
 of the relative intensities of this component shows that the b - related 
 species are stronger in the more bulk sensitive spectra ( figure 7a inset ) , which is 
 consistent with our xrd analysis , where we demonstrate that species 
 present at higher concentrations in the catalyst bulk can segregate 
 toward the surface during cooling , leading to the formation of additional 
 phases ( i.e. , borides for h2 preannealing and nitrides 
 for nh3 preannealing ) .
interestingly , the component at 
 188 ev is not detected for the nh3-preannealed 
 foil , neither in the surface sensitive scan nor in the more bulk sensitive 
 scan ( figure 7b ) .
this 
 is consistent with the b uptake being significantly reduced by the 
 presence of n dissolved in the fe bulk from the nh3 preannealing 
 step .
both preannealings lead to the appearance of a small peak at 
 200 ev , which has been attributed to the  * 
 plasmon shake up satellite corresponding to sp bonded 
 hexagonal boron nitride .
the sharper satellite peak 
 for the nh3-preannealed sample attests to the higher quality 
 of the h - bn grown ( figure 7b inset ) .
depth - resolved in situ xps b1s core level 
 lines measured at room temperature in vacuum for ( a ) h2- and ( b ) nh3-preannealed fe foil after borazine exposure 
 and cooling ( growth parameters : 900 c , 1  
 10 mbar for nh3-preannealed sample 
 and 1  10 mbar for h2-preannealed sample ,  10 min borazine exposure time ) .
the 
 spectra are collected at photon energies of 400 ev ( surface sensitive ; 
 escape  10  ) and 640 ev ( bulk sensitive ; 
 escape  13  ) .
we also find that the onset of h - bn growth is strongly dependent 
 on the borazine partial pressure , as summarized in figure s7 .
for a given constant temperature , upon introducing 
 1  10 mbar of borazine , the n1s and b1s scans for both types of preannealed 
 foils exhibit flat lines , indicating the absence of h - bn growth .
after 
 9 min at 1  10 mbar of borazine , 
 the n1s and b1s scans for the h2-preannealed sample remain flat .
small n1s and b1s peaks only start appearing for an increased 
 borazine partial pressure of 7  10 mbar . for the h2-preannealed sample ,
significant h - bn 
 growth is achieved by further increasing the borazine pressure to 
 1  10 mbar .
we note that the sample 
 was exposed to 7  10 mbar of borazine 
 for 15 min before increasing the pressure to 1  10 mbar , and then exposed to this pressure for a further 
 20 min .
in contrast , after 3 min of borazine exposure at 1 
  10 mbar of borazine , a notable peak appears 
 in both n1s and b1s scans for the 
 nh3-preannealed sample , which corresponds to h - bn nucleation . 
 upon continued exposure
( 6 min ) at this same pressure , the peaks increase 
 in intensity as the h - bn domains grow further . combined , our in situ 
 xrd and in situ xps characterizations suggest a strong influence of 
 nh3 preannealing not only on h - bn growth but also on the 
 underlying catalyst phase evolution and b / n uptake mechanisms .
our data reveals that the contribution of the fe bulk reservoir 
 is critical in determining the h - bn growth behavior .
although other 
 catalysts offer much lower b and n solubilities such that precipitation - driven 
 growth is minimized , our focus here on fe substrates is motivated 
 by our previous work , which shows fe to be an excellent catalyst for 
 high - quality h - bn growth .
in fact , we 
 are able to use the bulk solubility of b and n in fe 
 as a key advantage , and hence achieve better growth control using 
 a bulk prefilling method , as discussed below .
similarly , a finite 
 carbon solubility has previously been shown to substantially improve 
 graphene growth uniformity on polycrystalline ni and co substrates , 
 where the catalyst bulk acts as a mediating carbon sink that moderates 
 variations in growth across different catalyst grains .
figure 8 schematically 
 summarizes the processes taking place during the salient stages of 
 the cvd process on fe foils , comparing the effects of the h2 and nh3 preannealing on the catalyst chemistry and on 
 the growth of h - bn ( figure 8a , b ) , and interpreting them in the context of ternary phase 
 diagram considerations ( figure 9 ) .
the two suggested growth pathways are summarized in the 
 fe - rich corner of the fe 
n phase diagram at 950 c , and are marked by the red and blue arrows , denoting 
 the h2 and nh3 preannealing routes , respectively . 

the phase diagram is applicable to our experiments given that the 
 changes in the phase boundaries between the sections at 950 and 1050 
 c are minimal , and temperature 
 uncertainties of 50 c in commercial cvd reactors are not 
 untypical . in the framework of our discussion , we assume that the 
 b and n diffusivity does not vary significantly depending on their 
 relative proportions but is only dependent on temperature .
schematic illustrating 
 the near - surface region of the fe catalyst and the proposed mechanisms 
 involved in the growth of h - bn , comparing the ( a ) h2- and 
 ( b ) nh3-preannealed foils respectively during different 
 cvd stages .
the downward and upward arrows indicate species diffusing 
 into and out of the catalyst , respectively .
, , , and 
 represent the state of the catalyst during preannealing , short borazine 
 exposure , long borazine exposure , and vacuum cooling , respectively .
the red and blue arrows represent the reaction 
 pathway for the h2- and nh3-preannealed foils 
 respectively with the corresponding postgrowth sem images of the sample 
 surface .
cvd of a compound material , such as h - bn , requires simultaneous 
 feeding of b and n species into the growing stoichiometric crystal , 
 which presents a more complex scenario compared to graphene growth , 
 where only c atoms need to be incorporated into the graphitic lattice . 

first , we outline the b and n fluxes necessary for h - bn cvd , involving 
 precursor dissociation and the formation of h - bn domains . the impingement 
 of borazine molecules and their dissociation provides a flux of b 
 and n species at the catalyst surface . concurrently
, a flux of b and 
 n dissolving into the catalyst bulk will deplete the surface .
a net 
 flux is required for h - bn growth , which is equal to the difference 
 between the flux reaching the surface and that diffusing into the 
 catalyst . during the initial stages of borazine dosing these two fluxes 

will be matched and no h - bn nucleation occurs ( i.e. , incubation period ) . 
 however , the concentration of b and n at the surface will start to 
 increase gradually until a critical supersaturation at the fe surface 
 is reached , giving rise to the first h - bn nucleation events .
following 
 nucleation , growth of h - bn islands will proceed , fed by the net flux 
 resulting from the precursor dissociation at the surface and the diffusion 
 into the catalyst bulk .
we briefly outline the importance of the bulk 
 reservoir to cvd growth on catalysts with finite solubilities of the 
 precursor species . for h - bn cvd on catalysts 
 with significant b and n solubilities ( such as fe ) , the supply of 
 b and n to the catalyst surface to feed h - bn growth is mediated by 
 their diffusion into the catalyst bulk .
this allows uniform h - bn to 
 be formed over the catalyst by locally saturating the catalyst close 
 to the surface , while the bulk continues to provide a sink for b and 
 n species .
however , if the catalyst becomes saturated with these species 
 throughout its bulk during the growth process , then the bulk of the 
 catalyst no longer acts as a mediating sink and inhomogeneous few - layer 
 h - bn can readily form isothermally , as well as by the precipitation 
 of b and n to the surface upon cool - down .
how quickly the catalyst 
 becomes saturated throughout its thickness is ultimately dictated 
 by its permeability ( i.e. , the product of solubility and diffusivity ) . 

thus , low permeabilities , relative to the rate of b and n delivery 
 to the catalyst surface , favor a broad processing window for monolayer 
 h - bn formation , and hence , it is highly desirable to be able to control 
 this property .
preannealing up to 900 
 c ( figure 8a ) , 
 the fe surface undergoes a reduction reaction of fe oxides , formed from ambient air storage of the foils , 
 accompanied by the phase transformation -fe
 -fe , 
 as confirmed by the xrd data in figure 5a . on precursor exposure ,
uptake of both b and n from 
 the dissociation of borazine is confirmed by xrd , which shows the 
 formation of borides and an expansion of the fe lattice due to n dissolution 
 for similar growth conditions .
the catalyst 
 reservoir is therefore partially filled by the constituent species , 
 illustrated by the downward red and blue arrows in figure 8a , and results in a longer 
 incubation time for crystal growth because the critical supersaturation 
 required for nucleation will take longer to achieve .
n phase diagram , in which the 
 curve in the solvus for intermediate b : n ratios is crossed at relatively 
 high solubilies , and hence high permeabilities , of both species . at 
 such intermediate b : n ratios , it is not clear which of the species 
 it is whose supply is the limiting factor that controls the growth . 
 after 10 min of borazine exposure ,
the xrd data shows the appearance 
 of the few - layer h - bn reflection at 18 , demonstrating 
 that growth of additional h - bn layers occurs isothermally ( small triangular 
 domains in figure 8a ) .
this is further confirmed by in situ xps , which additionally 
 reveals the concurrent appearance of h - bn mono- and multilayers ( figure 6a , c ) . upon 
 borazine
removal and cooling ( figure 3b , c ) , we show that further nucleation of new domains 
 and thickening of existing domains occurs for relatively slow cooling 
 rates on h2-preannealed foils .
the fact that the h - bn domain 
 edges appear to be dissolving for a cooling rate of 50 c / min 
 ( figure 3c inset ) could 
 be explained by considering that while the catalyst surface is saturated 
 with b and n during growth , the catalyst is not saturated throughout 
 the bulk ( i.e. , the b and n concentration is not uniform across the 
 depth ) .
thus , the slow cooling rate is effectively equivalent to a 
 postanneal , which can result in the increased diffusion of b and n 
 into the catalyst bulk , decreasing the concentration of b and n near 
 the catalyst surface and leading to the partial dissolution of the 
 existing domains . for rapid quenching , a smaller contribution to growth 
 from bulk precipitation
we note that although we show clear 
 evidence of b and n uptake in the fe bulk , this does not necessarily 
 imply precipitation into h - bn upon cooling because the assembly of 
 an h - bn domain requires a stoichiometric arrangement of atoms in the 
 hexagonal lattice . for monoelemental systems such as c , growth of 
 a graphic lattice by precipitation on cooling
is simpler because only 
 one element needs to be incorporated at the growth front . for compound 
 materials like h - bn ,
however , our ex situ 
 sem indicates that precipitation - driven growth does in fact occur . 

this can be explained by noting that the high permeabilities of b 
 and n that saturate the catalyst surface ( evidenced by boride formation 
 and n - induced fe lattice expansion in xrd , as well as dissolved b / borides 
 in the fe subsurface observed by in situ xps ) can lead to inhomogeneous 
 isothermal multilayer growth , as well as further multilayer formation 
 upon cooling .
the compositional trajectory for the h2-preannealed 
 foil can thus be summarized by the red arrow in figure 9 , which  starting in the -fe 
 phase field  crosses the boundary -fe  -fe 
 + h - bn + fe2b during simultaneous feeding of n and b from 
 borazine dissociation . in terms of growth modes ,
the formation of 
 h - bn is predominantly isothermal , with a small contribution from bulk 
 precipitation on immediate cooling , which is relatively minor given 
 that the diffusivity of species rapidly decreases with temperature .
the chemical and structural changes in the fe catalyst for the 
 nh3-preannealed foil are markedly different . for the preannealed 
 sample ,
we measure a lattice expansion of the fe due to n uptake corresponding to 0.6 atom % n ( downward 
 blue arrows in figure 8b ) , and possibly due to the additional formation of -fe3n as a minority phase .
n phase 
 diagram does not predict the presence of -fe3n at 
 the temperatures and n content of our experiment ; therefore , the contribution 
 to the small reflection at 30 in figure 5b during preannealing is most likely due 
 to -fe .
the presence of n in fe has been shown to significantly 
 reduce the -fe  -fe transformation temperature , from 912 c for phase - pure fe to 875 c 
 for fe-0.6 atom %
n , which is therefore in line with our xrd phase 
 assignment . as a consequence of the n enrichment before borazine dosing , 
 the b : n ratio in the bulk of the foil is close to zero during dosing
due to the shape of the solvus , crossing it to form h - bn only requires 
 a small fraction of added b ( 0.002 at% b ) .
the fact that borides are not detected effectively means 
 that the solubility , and thus permeability , of b is greatly reduced 
 when the catalyst is saturated throughout with n. with lower b permeability , 
 the supersaturation required to form an h - bn nucleus therefore will 
 be reached for lower borazine partial pressures compared to the h2-preannealed foil or for shorter exposure times at the same 
 borazine exposure pressure .
the first case is clearly supported by 
 the in situ xps measurements . as shown in figure s7 , the borazine partial pressure required for h - bn growth 
 at 900 c depends on the preannealing performed and is 
 found to be 1  10 mbar for the h2-preannealed foil , upon which growth is immediately observed , 
 and 1  10 mbar for the nh3-preannealed foil where h - bn begins to form after 3 min of borazine 
 exposure .
we also confirm a shorter incubation time under the same 
 borazine exposure pressure for nh3-preannealed foils compared 
 to h2-preannealed foils through sem characterization ( figure 2a , d insets ) .
the 
 ex situ sem images show that as we start dosing borazine , the nucleation 
 of h - bn domains occurs much more rapidly on the nh3-preannealed 
 foil , with triangular - shaped islands already observed after 14 s exposure 
 ( figure 8b ) . for 
 longer exposure times the domains continue to grow laterally and neighboring 
 domains start to coalesce .
contrary to the h2 preannealing 
 case , we do not detect the isothermal -fe phase transformation 
 to -fe .
this , together with the lack of borides , both of which 
 are processes linked to b uptake , reinforces 
 the conclusion that the nh3-preannealing and the corresponding 
 n uptake into the catalyst limits b diffusion into the fe during subsequent 
 borazine exposure , that is , given that the b and n solubilities are 
 interdependent , the high n concentration in -fe makes the corresponding 
 b permeability very low .
additionally , the limited amount of b in 
 the bulk reduces the likelihood of multilayer formation on cooling , 
 as only n can escape from the sample surface .
we note that during 
 dosing at temperature , and in the absence of nh3 to replenish 
 the bulk with n , these species can diffuse back out to the surface 
 where they can leave as n2 ( upward blue arrows in figure 8b ) .
indeed , figure s3 provides evidence demonstrating that 
 the beneficial effect of the bulk n can be lost by long annealing 
 times in vacuum prior to borazine exposure .
hence , to achieve uniform 
 monolayer films , stage 2 ( figure 1 ) should be kept as short as possible .
the xrd 
 data in figure 5b illustrates 
 that during growth , and subsequently during simultaneous cooling and 
 borazine removal , we do not detect the appearance of the reflection 
 at 18 for the nh3 preannealing case , confirming 
 that the h - bn thickness does not increase significantly .
this is corroborated 
 by ex situ sem ( figure 2d  f ) , which shows that the h - bn remains as monolayers for 
 these growth conditions .
indeed , the sem images in figure 3d  f are further proof 
 that multilayers do not appear during cooling , even for slow cooling 
 rates , which typically allow sufficient time for species to segregate 
 at the surface , indicating a lack of b atoms that can be supplied 
 from the bulk .
the main difference compared with the h2-preannealing case is that b is now the limiting factor that governs 
 the growth , which thus becomes kinetically controlled . in this regime
, it therefore is possible to 
 exclusively grow monolayer h - bn on a n - prefilled catalyst , as long 
 as the extent of b diffusion into the catalyst bulk remains limited 
 ( figure 8b ) . on 
 the basis of our experimental evidence
, we propose that for the nh3-preannealed foil , the compositional pathway runs along the 
 fe 
n edge in the -fe phase field during annealing ( figure 9 , long blue arrow ) , 
 because no b is supplied at this stage and only n dissolves into the 
 fe . upon subsequent borazine dosing
, the trajectory crosses the boundary 
 into the -fe + h - bn + n2 phase field ( short blue 
 arrow ) based on the isothermal growth of h - bn monolayers observed 
 in combined sem , xrd , and xps .
our current work shows that the 
 general bulk - mediated growth model reported here is also applicable 
 to graphene cvd on fe foils using a c2h2 carbon 
 source .
analogously to the h - bn growth , we observe reduced incubation 
 times for nh3-preannealed foils ( i.e. , n - filled bulk reservoir ) 
 compared to vacuum - annealed foils ( unfilled bulk reservoir ) .
the data 
 will be presented in future work ; however , it demonstrates the robustness 
 and wide applicability of our model , which is anticipated to be relevant 
 for the fabrication of heterostructures .
indeed , the use of a catalyst 
 prefilling method for growth control has previously been used in other 
 material systems .
a notable example is the catalytic growth of si / ge 
 heterostructure nanowires ( nws ) with compositionally abrupt interfaces , 
 which requires the minimization of the solubility of si and ge in 
 the liquid au catalyst in order to reduce the catalyst bulk reservoir 
 effect .
in summary , a significant 
 level of improvement in the growth of h - bn is achieved through a bulk 
 reservoir filling effect in an as - received fe foil by predosing n , 
 one of the constituent species , in the form of nh3 during 
 preannealing . using in situ xrd and xps
, we demonstrate how n - induced 
 changes to the fe catalyst phase evolution and composition directly 
 impact the h - bn incubation time and the uptake of b and n species 
 during dosing .
these critical parameters then determine structural 
 h - bn features , such as number of layers , domain size , and nucleation 
 density .
when the catalyst bulk is enriched with n from the 
 high temperature and high pressure preannealing in nh3 , 
 the diffusion of b and n species in the fe subsurface during subsequent 
 borazine exposure is limited .
this effectively prevents significant 
 additional h - bn layer formation that typically occurs by precipitation 
 upon cooling , and which is indeed observed for h2-preannealed 
 fe foils ( i.e. , unfilled bulk reservoir ) .
bulk filling also leads 
 to shorter incubation times and lower borazine partial pressures required 
 to nucleate h - bn , which reduces the probability of multilayer formation 
 and a large domain size distribution .
preannealing the catalyst 
 with nh3 allows us to control the subsequent uptake of 
 precursor species during dosing .
importantly , given the interdependency 
 of the b and n solubilities , it allows us to lower the permeability 
 of b , which leads to uniform h - bn monolayer growth .
the catalyst bulk 
 prefilling method presented here therefore provides an elegant alternative 
 to using different catalysts or using catalyst alloying to control 
 the permeability of the growth species .
the general model that we 
 derive , based on complementary ex situ and in situ data , in combination 
 with phase diagram considerations , forms a coherent picture of the 
 key bulk contributions to growth control and , importantly , is applicable 
 to other catalytically grown 2d materials .
as - received fe foil ( 0.1 mm , alfa aesar , 99.99% purity ) is used 
 for all experiments . the h - bn domains and films are grown in a customized 
 aixtron bm3 cold - wall reactor ( base pressure 1  10 mbar ) .
cvd growth of h - bn is performed using a borazine ( hbnh)3 precursor at a temperature of 900 c and a total 
 pressure of 6  10 mbar .
the samples are 
 typically heated in 4 mbar of nh3 or h2 at 100 
 c / min up to 750 c and then at 50 c / min up to 900 
 c .
the estimated uncertainty in the temperature measurement 
 is 25 c . immediately after reaching 900 c 

borazine is dosed 
 into the chamber through a leak valve ( from a liquid reservoir ) and 
 after growth ( growth times varied from 14 s to 8 min ) the borazine 
 leak valve is closed and the heater is turned off .
samples are cooled 
 in vacuum . for raman spectroscopy , 
 optical microscopy , and df - tem / stem ,
we perform 
 the transfer by spin coating a support layer of poly(methyl methacrylate ) 
 ( pmma ) at 5000 rpm for 40 s onto the h - bn .
the sample is placed in 
 a naoh bath ( 1 m ) and during electrolysis h2 bubbles evolve 
 at the h - bn / fe interface , lifting the film from the substrate .
the 
 pmma / h - bn film is rinsed in deionized ( di ) water and scooped onto 
 a sio2(300 nm)/si wafer where it is left to dry .
the pmma 
 is removed by immersing the sample in acetone for 12 h , followed 
 by a rinse in ipa . for the ex situ 
 characterization of the h - bn on the catalyst , we use scanning electron 
 microscopy ( sem , zeiss sigmavp , 2 kv ) .
optical images are acquired 
 using a nikon eclipse me600l microscope and a green filter was introduced 
 for enhanced contrast .
raman spectroscopy is performed with a renishaw 
 raman invia microscope using a 50 objective lens and a 532 nm 
 laser excitation .
a philips cm200 was used for bright - field ( bf- ) 
 and dark - field transmission electron microscopy ( df - tem ) and selected 
 area electron diffraction ( saed ) at 80 kv .
a nion ultrastem 100 was 
 employed for scanning transmission electron microscopy ( stem ) , using 
 an electron acceleration voltage of 60 kv and a high angle annular 
 dark field ( haadf ) detector .
atomic - resolution stem data was processed 
 to reduce contributions from probe - tails ( an unprocessed stem image 
 is shown in figure s4 ) .
the intensity profile was extracted from the processed 
 image data by subtracting the remaining averaged intensity at intensity 
 minima between atoms from the profile followed by normalizing the 
 intensity at b sites to 1 .
as grown h - bn films were transferred from 
 the catalyst for s(tem ) via the bubbling method onto holey carbon 
 tem grids with regular hole arrays . in situ x - ray diffraction 
 ( xrd ) was measured at the european synchrotron research facility ( beamline 
 bm20/robl ) using a x - ray wavelength of 1.078  in a previously 
 described setup .
measurements were acquired in 
 symmetric theta-2theta geometry ( information depth in m range ) 
 with the fe foils clamped on one side by alumina spacers .
the intensity 
 step at 16 in all measurements is due to the arrangement 
 of detector and x - ray entrance / exit slits into the reaction chamber . 

we note that reflection positions shift between room temperature and 
 cvd temperature scans due to thermal expansion . for phase identification 

the inorganic crystal structure database ( icsd ) ( -fe , 53451 ; 
 -fe , 44862 ; fe2b , 391330 ; feb , 391331 ; -fe3n , 80930 ; -fe4n , 79980 ; h - bn , 167799 ) 
 and the international center for diffraction data ( icdd ) database 
 ( fe2b , 361332 ; feb , 320463 ) were used .
rietveld refinement 
 of data was done using xpert plus software . quoted in situ 
 xrd temperatures ( 900 c )
may be underestimated by up 
 to 25 c , thus explaining the observed -fe  -fe 
 transition for the h2 pretreatment ( figure 5a ) , which would be thermodynamically only 
 expected for > 912 c for pure fe . in situ high - pressure xps measurements during preannealing , 
 growth , and cooling
were performed at the isiss end station of the 
 fhi - mpg at the bessy ii synchrotron .
we employ a high - pressure setup 
 that consists of a cell ( base pressure  10 mbar ) that is attached to a set of differentially pumped electrostatic 
 lenses and a differentially pumped analyzer ( phoibos 150 , specs gmbh ) . 

all the spectra are acquired in normal emission geometry , using a 
 spot size of 80 m  150 m and with a spectral resolution 
 of 0.3 ev . to perform depth - resolution experiments ,
the photon 
 energy ( ephoton ) is varied in order to 
 change the kinetic energy of the emitted photoelectrons , thus changing 
 the inelastic mean free paths , escape .
 highly controlled fe - catalyzed growth 
 of monolayer hexagonal boron nitride ( h - bn ) films is demonstrated 
 by the dissolution of nitrogen into the catalyst bulk via nh3 exposure prior to the actual growth step . 
 this  pre - filling  
 of the catalyst bulk reservoir allows us to control and limit the 
 uptake of b and n species during borazine exposure and thereby to 
 control the incubation time and h - bn growth kinetics while also limiting 
 the contribution of uncontrolled precipitation - driven h - bn growth 
 during cooling . using in situ x - ray diffraction and in situ x - ray 
 photoelectron spectroscopy combined with systematic growth calibrations , 
 we develop an understanding and framework for engineering the catalyst 
 bulk reservoir to optimize the growth process , which is also relevant 
 to other 2d materials and their heterostructures . 