over the past few years , 
 semiconductor nanowires ( nws ) have become 
 a large research field due to their interesting electrical and optical 
 properties due to quantum effects , large surface to volume ratio , 
 and capability for bottom - up assembly .
nw - based memory devices , lasers , single - molecule sensors , and solar cells have been demonstrated 
 in recent years . additionally , one outstanding feature of the nw growth 
 is that the crystal structure can be different from the stable bulk 
 crystal structure , with possible striking effects on their optical 
 properties .
the stable bulk crystal structure for most 
 iii  v binary semiconductor materials is cubic zincblende ( zb ) , 
 while synthesis of the hexagonal wurtzite ( wz ) structure in bulk gaas 
 requires high pressure and temperature .
however , nws can adopt both zb and wz crystal structures , and previous 
 research has demonstrated the control of wz and zb crystal structure 
 in gaas nws grown by metal  organic chemical vapor deposition 
 ( mocvd ) .
v nws 
 is [ 111 ] with a stacking sequence of abcabc , 
 which could also be denoted as 3c using the ramsdell notation .
the equivalent growth direction in the hexagonal 
 case is [ 000.1 ] , with the stacking sequence ababab 
 for wz , or 2h in the ramsdell notation .
3c ( zb ) and 2h ( wz ) thus differ 
 only in the stacking sequence in the [ 111]/[000.1 ] 
 direction and exhibit a small difference in cohesive energies , with 
 3c being the highest , hence the stable phase in bulk
. however , with the large surface to volume ratio of nws , compared 
 to bulk , the relative contribution of lateral surface energies to 
 the total free energy of formed nws has to be considered and is a 
 key parameter in growth models attempting to explain formation of 
 polytypes in iii 
nws with a structure different 
 from their bulk counterpart should be treated as metastable , and the 
 growth is kinetically controlled . treating nws as metastable implies 
 that their phase could change to a more stable one upon perturbation . 

in addition , if it is the large surface to volume ratio that enables 
 growth of metastable nws , will the structure be maintained under large 
 radial overgrowth , where the surface to volume ratio decreases ?
phase transformation of grown gaas nws has been observed previously , 
 where 2h structure epitaxially buried in planar 3c overgrowth gradually 
 adopted the structure of the burying layer .
phase transformation has also been observed in ingaas nws , using 
 an electron beam to deliver a high energy dose to the structure , enough 
 to transform 2h to a mixed 3c/2h structure . in the case of epitaxial burying ,
one layer at a time of the metastable 
 2h is gradually surrounded with a layer of the stable 3c structure . 
 with a lateral mismatch of the top layer burying the nw ,
a linear 
 defect is created at the interface between the burying layer and nw , 
 which could be viewed as a shockley partial dislocation in the 3c 
 matrix .
once the dislocation has formed along at least two sides of 
 the nw , it could propagate into the nw without changing its length . 
 as the surrounding 3c layer has a higher cohesive energy , the total 
 energy associated with the linear defect
is decreased as the dislocation 
 propagates through the nw and changes its structure to 3c . by completely 
 burying the structure in a 3c matrix ,
the low energy surfaces of 2h 
 can not stabilize the structure any longer , and the structure is forced 
 into 3c . to further develop the model to apply to free - standing structures , 
 contributions from the surface energies
in addition , the dislocation line between a buried structure and its 
 surrounding matrix compared to the dislocation line formed between 
 free - standing structures has different geometries , which could have 
 a big impact on the propagation of the dislocation line . in 
 this work ,
we investigated what happens when adjacent wz nws 
 radially merge with each other , for different amounts of radial overgrowth 
 and merging .
the approach resembles the epitaxial lateral overgrowth 
 ( elo ) technique , which has been used since the 1960s to reduce threading 
 dislocation densities in growth of lattice - mismatched thin films .
elo is widely used to grow high quality gan films , but is not as common for non - nitride iii - vs . using a mocvd 
 system
, we first grew gaas 2h nws on 3c gaas substrate , and by radial 
 overgrowth in a second step increased the nw diameter . during radial 
 growth , the shell will adopt the same crystal structure as the core , 
 which has been observed in several nanowire core 
shell material 
 combinations . with increasing radial overgrowth time , more and 
 more of the initial 2h nws radially merge with each other .
for the 
 longest growth times , the initial gaas 2h nws have merged to form 
 a nearly continuous film .
the crystal structure of samples with different 
 amounts of radial overgrowth and merging was investigated .
we used 
 high resolution xrd and high resolution transmission electron microscopy 
 ( hrtem ) for structural investigations .
although one might expect to 
 find a 2h film after the radial overgrowth , our observations show 
 that this is not the case .
once individual nws merge together , the 
 crystal structure of the merged nws is transformed progressively from 
 the initial pure 2h structure to a mixed 2h/3c structure .
we use a 
 rather simple combinatorial approach to explain the main features 
 in the resulting crystal structure of radially merged nws .
comparing 
 energy contributions from differences in cohesive energy , surface 
 energies and dislocation line energy , only a small energy difference 
 for transforming 2h compared to 3c is found , which justifies the use 
 of a combinatorial model .
gaas 2h nws were grown on gaas ( 111)b substrates using mocvd and 
 70 nm size - selected au seed particles with a surface density of 1 
 m with 2h growth parameters as reported 
 previously .
a pregrowth annealing step 
 was performed in a 100 mbar mocvd reactor under hydrogen ( h2 ) and arsine ( ash3 ) for 10 min at 650 c to remove 
 the surface oxides and form catalyst droplets .
after annealing , 
 the temperature was reduced to the growth temperature of 550 c , 
 and tmga was introduced to initiate the growth .
the molar fractions 
 of tmga and ash3 flow were 1.46  10 and 5.5  10 , respectively ( v / iii ratio 
 of 4 ) , with a total gas flow of 6 slm .
after 2h nw growth , the samples 
 were cooled down under h2 only to prevent formation of 
 a 3c neck region .
after cooldown , the 
 samples were removed from the mocvd system in order to remove the 
 au - alloy seed particles by etching in a cyanide based etching solution 
 ( tfac from transene ) .
removing the au seed particles is essential 
 to limit axial elongation of the nws during subsequent radial overgrowth . 
 for this step
, the samples were reintroduced into the mocvd system 
 and annealed under a h2/ash3 environment at 
 650 c for 10 min to remove surface oxides formed as the nws 
 were exposed to air .
the temperature was then reduced to 630 c , 
 and tmga was introduced to initiate radial overgrowth .
the growth 
 time ranged from 5 to 240 min with molar fractions of tmga and ash3 of 1.5  10 and 2.2  10 , respectively ( v / iii ratio 150 ) .
( a ) growth of wz gaas nws , ( b ) removal of au particles , 
 ( c ) radial overgrowth of gaas nws , ( d ) merging of nws in order to 
 form the designed structure . for structural investigations of large ensembles of nws and 
 parasitic 
 substrate growth
, we performed high - resolution x - ray diffraction ( xrd ) 
 measurements on as - grown samples . two laboratory diffractometers with 
 cu anode and channel - cut
monochromators were used together with one - dimensional 
 detectors to record reciprocal space maps ( rsms ) .
the measurements 
 were performed in the scattering plane spanned by the [ 111 ] 
 and [ 112 ] directions of the substrate .
symmetric rsms 
 around the 3c gaas ( 333 ) reciprocal lattice point 
 and 2h gaas ( 000.6 ) as well as asymmetric rsms between 3c gaas 
 substrate ( 224 ) bragg peak and ( 331 ) 
 twinned gaas bragg peak were recorded , which also covers the 2h gaas 
 ( 101.5 ) .
the occurrence of the 3c ( 331 ) 
 from twinned nws in the same azimuth as the 3c substrate ( 224 ) 
 is due to the 180 rotation around [ 111 ] 
 caused by twin defects . to characterize the local crystal structure 
 and the quality at 
 the interface between merged nws , we used focused ion beam ( fib ) to 
 prepare cross sectional lamellae samples for transmission electron 
 microscopy ( tem ) .
using fib could potentially induce defects , but 
 our method is gentle enough to preserve high crystalline quality of 
 the prepared sample .
high resolution 
 tem ( hrtem ) , dark field tem ( dftem ) , scanning tem ( stem ) , and selected 
 area electron diffraction ( saed ) were used for analysis .
the grown nws have 
 an average length of 2 m and average diameter of 100 nm prior 
 to radial overgrowth , with 2h structure including low densities of 
 stacking defects in the range of < 1020 m , as revealed by hrtem ; see figure 2a  c . after the etching process
, most of the 
 au catalyst particles on the tops of the nws were removed , but the 
 nws were insignificantly affected by the etchant ( see detail in supporting 
 information , figure s1 ) .
( a  c ) tem and 
 hrtem images of a 2h structured nw before 
 overgrowth imaged in the 112.0 zone axis .
( d  i ) 
 sem images of nws with radial overgrowth for different times . with 
 30 tilting angle : ( d ) 5 min ; ( e ) 20 min ; ( f ) 60 min ; top view 
 sem images of nws radial overgrowth with different time : ( g ) 120 min ; 
 ( h ) 180 min ; ( i ) 240 min .
the insets shown in ( g ) and ( h ) are sem 
 images taken at a 30 tilting angle , scale bars are 2000 nm . figure 2d 
i 
 shows the nw overgrowth at different stages ranging from 5 to 240 
 min overgrowth time .
after the first 5 min , we observed mainly an 
 increase in the volume of the pyramidal base of the nws ; see figure 2d .
the 2h nws are 
 terminated by low energy { 101.0 } facets , which gives a low 
 possibility of nucleation directly at the side facets .
the pyramidal 
 base consists of higher index facets , which have a higher surface 
 energy due to the increased density of dangling bonds , resulting in 
 an increased rate of nucleation of new layers .
after 20 min ( see figure 2e ) , the base starts 
 to form { 101.0 } facets , and the morphology evolution of the 
 nws changes with radial overgrowth time of 60 min ( compare figure 2e , f ) . at the kink 
 site between the base and the nw side facets ,
the higher coordination 
 number is expected to have an even higher rate of nucleation .
nucleation 
 at the kink site followed by growth of layers along the nw [ 000.1 ] 
 direction could explain the homogeneous shell at 60 min with steps 
 at the top of the nw . as the growth time
is increased further , the 
 area between the nws becomes smaller , and the nws eventually merge . 

after 240 min of growth , most of the nws have merged with each other , 
 and a nearly continuous film is formed . in parallel with the radial 
 growth of the nws , we observe continuous growth on the substrate surface . 
 as the parasitic substrate growth proceeds ,
some of the lower parts 
 of the initial 2h nws are buried , which explains the apparently thinner 
 base in figure 2f compared 
 to 2d and 2e .
however , most parts of the nws are radially merged before 
 being buried in parasitic substrate growth , as seen in the insets 
 in figure 2g , h .
average 
 nw length and diameter and parasitic substrate growth thickness are 
 plotted in supporting information , figure s3 .
the nws never become fully buried in the parasitic substrate growth , 
 as the openings between the nws become too small to allow adatoms 
 to reach the bottom of the pits between them .
instead , growth on the 
 nw top facets increases with decreased openings between the nws . using high resolution xrd 
 to characterize the crystal structure of the samples ,
the measurements 
 collect diffraction data from several mm area of the sample , 
 and signals from the substrate and grown structures can not be separated 
 directly .
however , as the 2h structure only originates from the nws , 
 the nw signal can be distinguished from the substrate . as 3c occurs 
 in two different twin directions , two sets of 3c
diffraction peaks 
 occur ; one originates from the substrate and possible 3c formed during 
 the growth in the same twin direction , and the other set solely from 
 3c formed during the growth with the other twin direction .
figure 3 displays rsms from 
 the sample with 120 min radial overgrowth time . in the symmetric rsm , 
 the 3c gaas ( 333 ) peak at q[111 ] = 5.777  and 2h gaas ( 000.6 ) at q[111 ]
both the substrate and twinned 3c contribute to the signal of 
 the 3c ( 333 ) bragg peak and can not be distinguished . 
 between the 2h and 3c peaks , a weaker signal is visible at q[111 ] = 5.758  , which originates from gaas 4h .
x - ray diffraction reciprocal 
 space maps ( rsms ) of the sample with 
 120 min radial overgrowth time .
panel ( a ) shows a symmetric rsm around 
 the 3c ( 333 ) and 2h ( 000.6 ) bragg peaks , 
 ( b ) shows asymmetric rsm including zb substrate ( 224 ) , 
 ( 331 ) twin 3c , 2h ( 101.5 ) , and 
 4h ( 101.9 ) , ( 101.10 ) , and ( 101.11 ) 
 bragg reflections . in ( c ) and ( d ) , details of the twin 3c and 2h peaks 
 are shown . with roman numerals ,
the positions of possible detector 
 streak ( i , white line ) , broadening due to tilt distribution ( ii , red 
 line ) and finite nw radius ( iii , black line ) are marked .
linecuts 
 from the rsms are shown in ( e ) and ( f ) for the symmetric and asymmetric 
 case , respectively .
linecuts from rsms recorded in both ( 331 ) 
 and ( 224 ) azimuths are overlaid in ( e ) and ( f ) . in the asymmetric rsms in figure 3b ,
the peaks are attributed 
 to the 3c ( 224 ) bragg peak , which originates 
 from the substrate and grown 3c material with same twin orientation 
 as the substrate as the peak with highest intensity and the 3c ( 331 ) 
 bragg peak from 3c grown with opposite twin - orientation as the second 
 strongest peak . in between the two 3c peaks , the 2h ( 101.5 ) 
 is visible next to a weak 4h gaas ( 101.10 ) peak . 
 on either side of the 3c peaks ,
two more 4h peaks are visible , 4h 
 gaas ( 101.9 ) and 4h gaas ( 101.11 ) . 
 for asymmetric rsms for all six growth shell times
figure 3c , d shows details in the rsm 
 around the 2h ( 101.5 ) and 3c ( 331 ) 
 bragg peaks .
the position of possible detector streak is marked with 
 white ( i ) , broadening due to tilt distribution with red ( ii ) and broadening 
 due to finite radius of the nanowires as black ( iii ) . in figure 3e , f , line cuts from 
 the symmetric and asymmetric rsms for both ( 331 ) 
 and ( 224 ) are shown .
using the bragg peak 
 integrated intensity , we estimate the change 
 in scattering volume .
first , line cuts along [ 111 ] 
 are made in the asymmetric rsms ; see figure 4a . to each peak ,
a voigt shape curve was 
 fitted after removal of background signal , and the curves 
 integrated intensity was normalized with respect to the substrate 
 peak intensity .
as a consistency check , peaks from both azimuths on 
 each sample were used . using different azimuths , the difference in 
 structure factors for ( 224 ) and ( 331 ) 
 as well as the difference in illuminated area
the peak 
 intensities for the 2h , 4h ( 101.10 ) and twinned 
 3c peaks are plotted .
as seen , the 2h initially increases , and the 
 largest 2h volume was found for the sample with 60 min radial overgrowth 
 time . for the twinned 3c ,
the volume increases for the full radial 
 overgrowth series . for the 4h ( 101.10 )
peak intensity , 
 the scattering intensity follows a similar trend as for 2h , but with 
 the strongest scattering signal at 120 min radial overgrowth time .
( a ) linecuts 
 along q_[111 ] from asymmetric 
 rsm with substrate peak at ( 224 ) plotted with 
 offsets . the position for different bragg peaks
decreasing intensities for the 4h and 2h peaks are visible 
 for the longer radial overgrowth times .
( b ) integrated intensities 
 for the 2h ( red , square ) , 4h ( triangles , green ) , and the 3c ( blue , 
 circles ) peaks arising from the twinned zb .
the trend lines are guides for the eyes only . by preparing a cross sectional lamella sample by 
 fib ,
the crystal 
 structure along the nws and the parasitic substrate growth were investigated 
 after 120 min radial growth .
figure 5a , b shows merged sections in bright - field ( bf ) and 
 dark - field ( df ) tem images , respectively .
the dark field is taken 
 around ( 111 ) and ( 002 ) reflection for the two different 
 3c twin directions , and ( 000.1 ) for the 2h .
the top part includes 
 two free - standing nws , which have pure 2h crystal structure with no 
 visible stacking faults . beneath this section ,
the merged region includes 
 two crystal orientations with twin boundaries perpendicular to the 
 nw growth direction , and the barcode - like pattern of twin regions 
 span the majority of the formerly individual nanowires . the parasitic 
 substrate growth results in 3c crystal structure which is heavily 
 twinned including boundaries not perpendicular to the nw growth direction 
 ( diffraction pattern and additional tem image in supporting information , figure s5 ) .
the crystal structure of the merged 
 region is confirmed by the saed pattern shown in the inset of figure 5b .
the saed pattern 
 indicates two dominant 3c crystals twinned in the nw growth direction 
 only .
( a ) bftem images from an fib lamella with two partly merged nanowires . 

( b ) dftem image of the same region as in ( a ) highlighting the crystal 
 structure in different parts marked with different colors .
the free - standing 
 nanowires have 2h crystal structure with no visible stacking faults , 
 while the merged regions have 3c crystal structure .
the substrate 
 growth has 3c crystal structure which is heavily twinned including 
 boundaries not perpendicular to the growth direction .
the inset in 
 ( b ) shows saed from the merged region , which indicates two dominant 
 3c crystals twinned in the growth direction only .
figure 6 shows 
 the 
 tem image of a fib lamella with two merged nws after 120 min radial 
 overgrowth in which a large section of 4h was found .
the corresponding 
 saed patterns of the 2h and 4h phases are shown in figure 6b , c , respectively .
the independent 
 gaas nw segment before the merging exhibits a pure 2h crystal structure 
 with almost no stacking faults , which is clear from the saed pattern 
 in figure 6b .
the appearance 
 of a ( 000.1 ) reflection indicated by a small arrow in figure 6c and two times shorter 
 distance between ( 000.0 ) and ( 000.1 ) reflection compared to 
 saed pattern of 2h in figure 6b confirms the existence of 4h crystal structure . the hrtem 
 image shown in figure 6d and the fft shown in the inset
the length of the 4h segment is approximately 
 200 nm , which is consistent with the observation in xrd ( see below ) .
( b ) 
 saed from the region in the blue circle in ( a ) showing 2h structure , 
 and ( c ) saed from the region in the green circle in ( a ) showing the 
 4h crystal structure .
( d ) hrtem image from the region marked with 
 rectangular in ( a ) showing a band of 4h crystal structure merging 
 the two nanowires .
the inset in ( d ) shows a fft from the left nanowire , 
 which is a typical 4h diffractogram .
xrd performed on 
 nanostructures is affected by finite size effects , which in the case 
 of nws are usually dominated by their small diameter , causing a broadening 
 in the [ 112 ] direction .
nws also tend to not grow exactly 
 perpendicular to the substrate surface , but a small mosaicity due 
 to a random nw tilt distribution causes a broadening in the same direction 
 as the finite width in the symmetric rsms . with both finite size and 
 tilt contributing to the same broadening in symmetric rsms , it is 
 not possible to distinguish one from the other . since the effects 
 scale differently for different reflections as well as
show up in 
 slightly different directions in asymmetric rsms , a distinction of 
 the two effects is possible in the asymmetric rsms .
the finite size 
 contribution is always inversely proportional to the width of the 
 nws , while the broadening due to tilt distribution increases linearly 
 with q. in the asymmetric scans , the tilt distribution and finite 
 width broadens the peak in different directions , which is indicated 
 in figure 3c , d . for 
 the 120 min radial overgrowth time
shown in figure 3 , the broadening due to tilt distribution 
 is larger than that due to finite nw width .
the tilt distribution 
 found is on the order of 0.1 deg , which is on the same order of magnitude 
 as for other nw samples , such inas 2h and insb 2h on inas 3c and gap 

tilt distribution is a general 
 feature in nw samples and is a limiting factor when performing high 
 resolution xrd on such samples .
another finite size effect present 
 in the asymmetric rsms is the broadening of the diffraction peaks 
 in the [ 111 ] direction , caused by short segments 
 of the respective polytype in the nw growth direction .
the inverse 
 width of the diffraction peaks is proportional to the average segment 
 length and for the 4h peaks segment lengths of 100200 nm were 
 estimated .
worth noting is that no 4h was found in the reference nws 
 prior to radial overgrowth . for the 3c and 2h peaks ,
the widths are 
 limited by the instrumental resolution and length estimations are 
 therefore not possible . with a very high crystal quality as 
 seen in both the hrtem analysis 
 and xrd , we are able to accurately calculate the lattice parameters 
 of both gaas 2h and 4h using the asymmetric rsms . the accuracy of 
 the measurements is similar to the case of inp 2h , limited mainly by experimental setup and beam broadening 
 due to measurement geometries .
table 1 summarizes the calculated lattice parameters with 
 relative differences with respect to ideal tetrahedral structures , 
 using geometrically converted cubic 3c lattice parameters .
both the 2h and 4h unit cells are elongated 
 in the nw growth direction and contracted in the radial direction 
 compared to 3c .
from the sem images shown in figure 2 , a continuous increase 
 in 2h volume would be expected for the full radial overgrowth time 
 series , since the radii of the nws continuously increase with time . 

however , from the xrd data , a decrease in 2h is found for radial overgrowth 
 times longer than 60 min .
intuitively , one could argue that the decrease 
 in 2h is due to epitaxial burying in a 3c substrate layer , similar 
 to what has been observed in refs ( 18 and 19 ) , which would also be supported by the continuous increase in 3c 
 diffraction signal with increasing growth time .
however , comparing 
 the volume of not - yet - buried nws for 5 and 180 min radial overgrowth , 
 the volume is 2 orders of magnitude larger for the longer growth time , 
 yet the 2h diffraction signal is weaker .
hence , the burying of the 
 nws is not sufficient to explain the drastic decrease in the 2h signal . 

in addition , epitaxial burying of the 2h nws in a 3c matrix would 
 not explain the appearance of 4h segments , estimated to be 100200 
 nm long in the samples with the most 4h , as an epitaxial burying driven 
 phase transformation would force the structure to adopt the burying 
 matrix structure , in this case 3c .
interestingly , the largest increase 
 in 4h scattering intensity is found as the 2h scattering signal starts 
 to decrease .
the decreasing 2h signal coincides with the onset of 
 the radial merging of adjacent nws , as seen in the inset in figure 2g , h . as reported 
 by ng et al .
, a high energy electron 
 beam could potentially induce crystal phase transformation , which 
 could affect the results obtained by tem .
however , the agreement of 
 the xrd and tem results suggests that the crystal phase transformation 
 is independent of measurement technique .
in addition , reference nws 
 and the parts not yet merged showed only pure 2h structure under similar 
 tem analysis ; therefore , the possibility of electron beam induced 
 transformation is discarded . instead of explaining the phase 
 transformation by epitaxial burying
, 
 we propose that the transformation could be explained by a nw  nw 
 interaction . to understand the process of the merging better we come 
 back to the stacking sequences of the different crystallographic phases . 

the stacking along the hexagonal [ 000.1 ] direction of the 2h 
 crystal structure can be described as ababab , 
 while for 3c crystal structure it is described as abcabc 
 along the equivalent [ 111 ] direction .
each capital 
 letter denotes a pair of layers consisting of one group v and group 
 iii atom , a bilayer , at three distinct lateral positions . as the nws 
 grow in [ 111]/[000.1 ] , the position of 
 as in each new bilayer will determine whether the layer is in cubic 
 or hexagonal position .
the stacking sequences of 2h can also equivalently 
 be described as bcbcbc , acacac , 
 etc .
( nw 1 ) retains the stacking 
 order as ababab and the second 
 2h structured nw ( nw 2 ) retains the stacking order as bababa. 
 when the bottom bilayer of nw 1 reaches the periphery of nw 2 , the 
 as atoms in the bottom bilayer of nw 1 is not in lateral registry 
 with that of nw 2 . in principle now two scenarios compete with each 
 other . either this mismatch is kept at the cost of having a line defect 
 at the interface of the merging nws , or in order to release this mismatch , 
 the line defect may propagate through one of the nws to accommodate 
 the corresponding as plane .
for such a gliding process , three different 
 translation vectors ( the burger vectors , b ) are possible , 
 1/3[101.0 ] , 1/3[110.0 ] , and 1/3[011.0 ] ; see figure 7 .
this edge dislocation could be seen as a shockley 
 partial dislocation , and when propagating through the crystal changes 
 the configuration of the as from hexagonal to cubic position ( or vice 
 versa ) .
( a ) schematic of two miss - matched 2h nws viewed in the { 000.1}/{111 } 
 direction .
the mismatch causes a translation in the [ 110.0 ] 
 direction of the as atoms in nw 1 closest to the interface .
( b  d ) 
 schematics displaying propagation of a defect through one of the nanowires . changing a 2h gaas to 3c gaas 

would to a first approximation result 
 in a lower total energy for the crystal , as the cohesive energy is 
 24 mev / iii  v pair higher for 3c . changing from 2h { 101.0}-type facets to 3c { 112}-type 
 facets increases the surface energy due to the increase of dangling 
 bonds , with a net energy difference of 3.06 mev / nm .
in addition to the change in cohesive energy 
 and surface energies , the dislocation line itself has an energy per 
 unit length .
the dislocation line energy originates from the strain 
 field around it and the distorted bonds at the dislocation core .
detailed 
 calculations on defects in gaas 2h are lacking , but as an approximation 
 the dislocation line energy could be calculated as edis = gb , where g is the shear modulus and b is the magnitude of 
 the burgers vector . using the shear modulus of gaas 3c , as the shear modulus of 2h is unknown , the dislocation 
 line energy is estimated to be 10.74 ev / nm . the 2h nws are hexagonal 
 and have { 101.0 } type facets , which are perpendicular to the 
 burgers vector , and the nws all have facets parallel to each other . 
 for two nws merging along the full length of a side facet , as in figure 7 , the dislocation 
 line has initially the same length as the side facet of the nws .
for 
 the dislocation line to propagate into one of the two nws by only 
 changing the position of one as , it has to increase its length ; see figure 7b  d .
the minimum 
 increase in length would then be b / cos(30 ) , if the 
 propagation occurs at a nw facet . in total
similarly , if the dislocation propagates 
 into a 3c structure , the total energy increases by 2.88 ev for the 
 first as moved .
the difference between the two values is less than 
 thermal energy at the present growth temperature . with the dislocation 
 line energy as the dominant factor for the energies related to the 
 phase transformation , the initial structures of the two merging nws 
 are of minor importance  the probability of either one to transform 
 is roughly equal . comparing our phase transformation with the 
 case of epitaxial burying 
 described by patriarche et al .
, the 
 dislocation is of the same type , and both transformations are triggered 
 by the interaction between two crystals with as atoms at different 
 lateral positions .
however , in the case of epitaxial burying where 
 the burying matrix completely surrounds the nw , the nw has to adopt 
 the structure of the burying matrix or keep the dislocation at the 
 periphery of the nw . to let the dislocation propagate through the 
 nw makes the dislocation shorter , and eventually disappear , which 
 is the thermodynamically most favorable case , and the final structure 
 will be easy to predict  the one of the burying matrix . in our 
 case , with a nw 
nw interaction , the dislocation could propagate 
 into either crystal , and the final structure is much harder to predict . 

as the dislocation line energy depends on the shear modulus of the 
 crystal and the burgers vector , changing growth conditions would not 
 change the dynamics of the crystal phase transformation .
changing 
 the growth temperature could however change the propagation rate of 
 the dislocation , as the peierls energy barrier sets an activation 
 energy for the propagation .
hypothetically , by reducing growth temperature 
 enough , propagation of the defect could be kinetically hindered such 
 that it stays at the interface between the nws , which then would retain 
 their initial structure .
however , since growth temperature in this 
 study is high enough to ensure reasonable growth rates , we assume 
 that the defect propagation is not kinetically hindered . assuming 
 equal probability for the dislocation to propagate in either nw , a 
 combinatorial approach gives the probabilities of different structures . assuming that a dislocation can propagate with the same probability 
 into either nw as two nws merge , each merging bilayer gives rise to 
 two equally likely outcomes .
for merging of two nws with 10 bilayers 
 each there will be 2 possible outcomes .
if we involve 
 a third 10 bilayer nw in the merging process , there will be ( 2 ) outcomes . to estimate the amount of 3c , 2h , 
 and 4h in each outcome ,
we define a 3c segment to be of at least six 
 bilayers ( two unit cells ) , 2h as six bilayers ( three unit cells ) and 
 4h as eight bilayers ( two unit cells ) .
if the 10 bilayer long segment 
 does not include any of the above segments , it is considered to be 
 a mixed structure . using a simple matlab script , we simulate the merging 
 of two , three , and four 2h nws with each 10 bilayers ( where the 10 
 bilayer limit is chosen to limit computation time ) . a schematic view 
 on the merging process
the simulations shows that the merging 
 of just two nws gives a mixed fraction of around 80%that is , 
 most of the possible outcomes have only segments consisting of less 
 than six bilayers of any considered polytype .
2h is still the most 
 common polytype , with 1516% , depending on the initial stacking 
 sequences of the nws and how many nws merge .
both 3c and 4h show up 
 with lower amounts ( 36% and 0.30.5% , respectively ; 
 see supporting information , figure s7 ) . 

this result fits well with our experimental observation : the most 
 likely structure for radially merged 2h nws is a mixture between 2h 
 and 3c .
the increase in twinned 3c seen in the xrd measurements comes 
 not only from the nws , but also from the parasitic substrate growth , 
 and the 36% of 3c found in the nws in our combinatorial model 
 is not the major contribution to the signal .
for a structure with 
 very short segments of 2h and 3c sandwiched , streaking between the 
 xrd peaks is expected , and this is also what we observe in our rsms ; 
 see figure 3b and supporting 
 information figure s4
. using this simple 
 combinatorial approach , we are able to describe the main features 
 of the merging process . the 
 lattice parameter 
 for 2h gaas has been reported previously , both using xrd and electron diffraction on nws and on 2h in gaas powder obtained at high pressure . however , the 2h lattice parameters in the former 
 report were measured from nws with a mixed crystal structure , consisting 
 of 2h segments sandwiched between 3c , and most likely strained by 
 the 3c segments . for our structures ,
the very few sfs in the pure 
 2h before any merging process are not likely to influence the overall 
 2h structure , and the 2h crystal is fully relaxed . using the sample 
 with 60 min radial overgrowth , we measured the 2h and 4h unit cell 
 parameters on the sample with the largest volume of pure 2h .
the results 
 are summarized in table 1 . with a larger lattice plane spacing along the c - axis in 2h as compared to the 3c counterpart and a smaller in - plane 
 distance , the c / a ratio is measured 
 to be 1.649 , which is 0.98% higher than the ideal 1.633 for hexagonal 
 close - packed structures with perfect tetrahedral coordination . the 
 value found is in good agreement to theoretical values of 1.6461.651 .
similarly , we found a c / a ratio of 3.282 for 4h , which is 0.49% 
 higher than ideal .
the measured gaas 4h lattice parameters reported 
 here are to the authors best knowledge the first experimental 
 report on gaas 4h lattice parameters .
the higher c / a ratio compared to the ideal is typical for metastable 
 hexagonal structures and gives bonding slightly distorted from an ideal 
 tetrahedron .
for 4h , the deviation from the ideal close - packing is 
 smaller than for 2h , suggesting 4h to be the more stable structure , 
 but still with 3c as the most stable one .
hence , the cohesive energy 
 for 2h should be lower than for 3c , with 4h in between the two .
the 
 difference in cohesive energy gives a higher nucleation barrier for 
 2h compared to 4h or 3c in gaas , which should result in a higher probability 
 of 4h than 2h during growth .
however , the surface energies of the 
 nucleus and its surroundings play a crucial role in determining the 
 structure formed during nw growth .
v nws is the assumption that the surface energies of 
 2h are considerably lower than those of 3c , which overcomes the difference 
 in cohesive energy .
assuming surface 
 energies of 2h to be considerably lower than those of 4h as well explains 
 why observations of 4h grown in nws are very few , and mostly only 
 occur in a transition region between 2h and 3c .
in this work , we studied the crystal structure 
 of radially overgrown 
 gaas wurtzite ( 2h ) nws , especially the resulting crystal structure 
 as nws progressively grow into each other and merge .
we characterized 
 the grown structure by high resolution xrd and tem with diffraction 
 analysis .
we observed that the free - standing gaas nws retain the pure 
 2h structure until they merge with each other , at which point the 
 merged segments transform progressively from pure 2h structure to 
 a mixture between zinc blende ( 3c ) structure with twins and 2h .
we 
 also found sections with the 4h crystal structure in the merged nws 
 and determined lattice parameters of both 2h and 4h gaas .
the phase 
 transformation continues as long as the merging process proceeds , 
 driven by a dislocation formed between adjacent nws due to lateral 
 mismatch of as in the ( 111)/(000.1 ) plane . 
 using a combinatorial approach
, we estimated the probability of the 
 resulting structure after radial merging of 2h nws , which shows that 
 a heavily mixed structure is the most probably outcome , in agreement 
 with our xrd and tem measurements .
 iii  v nanowires ( nws ) grown 
 with metal  organic chemical 
 vapor deposition commonly show a polytypic crystal structure , allowing 
 growth of structures not found in the bulk counterpart . in this paper 
 
 we studied the radial overgrowth of pure wurtzite ( wz ) gaas nanowires 
 and characterized the samples with high resolution x - ray diffraction 
 ( xrd ) to reveal the crystal structure of the grown material . 
 in particular , 
 we investigated what happens when adjacent wz nws radially merge with 
 each other by analyzing the evolution of xrd peaks for different amounts 
 of radial overgrowth and merging . by preparing cross - sectional lamella 
 samples we also analyzed the local crystal structure of partly merged 
 nws by transmission electron microscopy . 
 once individual nws start 
 to merge , the crystal structure of the merged segments is transformed 
 progressively from initial pure wz to a mixed wz / zb structure . 
 the 
 merging process is then modeled using a simple combinatorial approach , 
 which predicts that merging of two or more wz nws will result in a 
 mixed crystal structure containing wz , zb , and 4h . 
 the existence large 
 and relaxed segments of 4h structure within the merged nws was confirmed 
 by xrd , allowing us to accurately determine the lattice parameters 
 of gaas 4h . 
 we compare the measured wz and 4h unit cells with an ideal 
 tetrahedron and find that both the polytypes are elongated in the c - axis and compressed in the a - axis compared 
 to the geometrically converted cubic zb unit cell . 
Introduction
Experimental Details
Results
Discussion
Conclusion