supported nanoparticles are used on a 
 tremendously large scale 
 for catalytic reactions . due to the inherent inhomogeneity of these
, 
 often industrial , materials , the basic understanding of their exact 
 atomic structure and relation to their functionality can become very 
 complex .
one route to overcome this problem is by design of so - called 
 bottom - up experiments in which well - defined nanoparticles are subjected 
 to controlled environments .
such studies can be performed by depositing 
 nanoparticles in ultrahigh vacuum on perfect single crystal substrates , 
 after which their structure is characterized under different thermodynamic 
 conditions and gas environments . in this 
 way , for example , oxidation  reduction - induced reversible shape 
 changes in nanoparticles have been discovered .
solid oxide fuel cells ( sofcs ) are devices used for energy conversion 
 and are considered as an important future green technology .
their 
 function is largely dependent on catalytic processes taking place 
 at their interfaces .
two important chemical reactions between the 
 surrounding gas atmosphere and the solid play a decisive role . at 
 the cathode , oxygen is dissociated , and the ions enter the electrolyte . 

fuel is being oxidized at the anode side , for which the required oxygen 
 reaches the interface through the solid electrolyte . both the cathode 
 and the anode consist of complex materials having a large surface 
 area , such as polycrystalline oxides ( cathode ) or nickel nanoparticles 
 ( anode ) .
usually , ni is grown on the electrolyte 
 by wet - chemical methods . here
we 
 investigate ni nanoparticles ( nps ) deposited on a polished 
 yttria - stabilized zirconia ( ysz ) substrate as sofc model anode by 
 surface sensitive x - ray diffraction methods .
ysz with 9.5 mol % y2o3 content is a widely used sofc electrolyte material 
 because of its high oxygen ion conductivity .
nickel films grown on 
 mgo(100 ) have been found to show several preferential orientations , 
 forming a complex epitaxial system and of which the core is stable 
 toward high temperature oxidation .
this 
 raises the question how smaller particles in the size regime from 
 310 nm , as typically encountered on the anodes of sofcs behave 
 when in contact with a solid electrolyte .
their sintering behavior 
 in different atmospheres is particularly important for catalytic activity 
 and long - term stability .
here we show the results 
 of such a study , whereby the ni nps are first annealed and finally 
 oxidized .
we find that ni nanoparticles grow with two very distinct 
 orientations on ysz(111 ) , in contrast to mgo(100 ) .
the nio formed 
 during oxidation grows epitaxially with repect to the ni nanoparticles . 
 from the measured particle heights and widths ,
the energy of adhesion , 
 which is an important quantity with respect to the nanoparticles 
 sintering stability , is determined .
the 
 experiments presented in the following were performed at the 
 mpi beamline of the ngstrm - quelle 
 karlsruhe ( anka ) using an x - ray energy of 10 kev .
x - ray data consist 
 of x - ray reflectivity , extensive reciprocal space mapping , and crystal 
 truncation rod ( ctr ) data . in addition , ex situ atomic force microscopy 
 ( afm ) measurements were performed in air once the synchrotron experiments 
 had finished .
polished single crystals of 9.5 mol % yttria - doped zirconia 
 with   orientation were used as substrate having a surface diameter 
 of 10 mm .
prior to the ni deposition , the substrates were annealed at 673 k 
 in 10 pa o2 for 120 min , a procedure 
 which was found to result in smooth and well - defined surface structures .
the ni nps were grown with a substrate temperature 
 of 623 k at a growth rate of 0.2 nm / min resulting in a nominal 3 nm 
 of deposited material .
here , we present results from two such growth 
 runs with different samples , named sample i and sample ii hereafter . 
 for sample i
, only the as - prepared nps were structurally characterized , 
 and after the in situ synchrotron experiment , the sample was investigated 
 by atomic force microscopy ( afm ) in air . in a second experiment on 
 sample ii
, the ni nps were further treated , and extensive x - ray characterization 
 was carried out .
the as - prepared ni nps were first annealed at 973 
 k for 75 min , then exposed to 10 pa of methane 
 at 573 k for 30 min and finally oxidized at 10 pa of o2 at 573 k for 35 min . after each of these steps , 

extensive x - ray data were taken , which allow us to determine changes 
 in the orientation , size , and composition of the nps .
because the 
 methane exposure did not result in any notable structural changes , 
 these data are not included in the present report .
in addition , at 
 each of the sample preparation steps , the ysz surface structure was 
 investigated by measuring several ctrs with a nonzero in - plane momentum 
 transfer .
these data do not indicate any considerable changes after 
 ni evaporation and after the oxygen treatment . because these ctrs 
 probe the 3d atomic structure of the ysz(111 ) surface , which is partly 
 covered by the nps
, we conclude that each of these processing steps 
 does not result in any significant atomic relaxations of the substrate .
afm images 
 were taken ex situ after the first growth run of nickel 
 nanoparticles on ysz(111 ) without further treatments ( sample i ) .
particles are clearly observed , and typical heights 
 of 3 nm can be derived . just after growth , with the sample still in 
 the uhv chamber , x - ray reflectivity ( xrr ) measurements
were taken 
 ( see figure 2 together 
 with the xrr curves from sample ii described more extensively in this 
 paper ) .
the curves of the as - prepared states in both experiments are 
 very similar .
analysis of the xrr data is performed by fitting the 
 electron density profile along the surface normal .
here we use a so - called 
 slab model , based on the fully dynamical parratt formalism . by comparison of the value obtained for the 
 ni nps to that of a closed bulk ni layer , their coverage can be estimated . 
 at the same time , the average height of the ni nps can be obtained 
 from the xrr measurement .
this information is contained mostly in 
 the period of the oscillations of the reflectivity .
the result from sample i gives an average height of 3.6 nm , in 
 good agreement with afm performed on the same sample when considering 
 that due to tip convolution effects those values will be systematically 
 lower .
in contrast to the height determination procedure described 
 in the section nanoparticle shape and adhesion 
 energy , xrr gives a value averaged over all np orientations .
( left ) 
 afm phase contrast image of the ysz(111 ) surface after nickel 
 evaporation ( sample i ) .
( middle ) height profile from the topographic 
 data along the line as indicated ( left ) .
x - ray reflectivity vs the momentum transfer along the surface normal qz(= 4 sin( ) / , 
 with  half the scattering angle and  the wavelength ) 
 measured after nickel evaporation . shown
are the measurements ( symbols ) 
 and fits ( solid lines ) for sample i as - prepared ( gray ) and sample 
 ii as - prepared ( black ) , annealed ( blue ) and oxidized ( red ) nps , whereby 
 the curves are scaled for clarity .
the oscillations are a clear indication 
 for the presence of the nps . from fitting an electron density profile 
 to the data , the thickness and coverage of the nps are determined 
 and these results are listed in table 1 . due to coexistence of ni and nio , 
 it is not possible to reliably determine a coverage and merely the 
 total apparent thickness is determined .
once the crystalline ni nps 
 were grown , the positions of their bragg peaks with respect to those 
 of the underlying substrate were used to determine their orientation . 
 in the following ,
several notations will be used interchangeably , 
 depending on the particular frame that is referred to . due to conventions 
 in surface diffraction
, use is made of the ysz(111 ) surface unit cell 
 to construct the reciprocal basis vectors of the substrate frame . 

the direct space axes of this nonprimitive hexagonal cell are a = b = 0.361 nm and c = 0.921 nm .
the cell parameters of the conventional cubic lattices 
 of both materials are ani = 0.354 nm and aysz = 0.541 nm . in the remainder of this article , 
 subscripts of ( h , k , l ) coordinates
are used to indicate with respect to which basis they 
 are defined : ysz for the ysz(111 ) surface unit cell and ni - bul for 
 the conventional fcc ni lattice and ni-111 for the ni(111 ) hexagonal 
 surface unit cell .
table 2 lists different ( h , k , l ) values in the different frames . by mapping out reciprocal 
 space in selected areas ,
we have found two preferred np orientations 
 and at least one other not yet reported for the epitaxial growth of 
 ni nps .
the first major one corresponds to the ni ( 111)-direction 
 parallel to the substrate surface normal .
the in - plane directions 
 of the ni lattice were found to align with the substrate surface unit 
 cell directions .
this orientational relationship ( or ) is described 
 by yszni111 and [ 110]ysz[110]ni111 and will be 
 denoted or1 in the remainder of this paper .
the ( 1,0,l)ni111 bragg peaks are found in a plane 
 ( h,0,l ) at h= 1.44 
 ( see figure 3 ) , indicating 
 that the ni is completely relaxed and adopts its bulk lattice parameter 
 because this value corresponds exactly to the ratio between the bulk 
 lattice parameters aysz / ani . two peaks , which belong to -oriented particles 
 as described above , at h = 1.44 but at different l - values are seen , corresponding to the ni - bul ( 11 1 ) 
 and ni - bul ( 002 ) reflections .
these ni peaks indicate that the ni 
 atoms follow an abc - type stacking along the substrate surface normal . 

if there were only one unique stacking sequence of the ni atoms , only 
 one of these peaks would be visible , because the 3-fold symmetry axis 
 of the fcc ni along its body diagonal would be preserved .
instead , 
 the observation of both peaks indicates that the ni atoms have two 
 different stackings , which results in an apparent 6-fold symmetry 
 axis around the stacking direction , which was also evident from scanning 
 the sample around the surface normal whereby diffraction peaks separated 
 by 60 appeared ( not shown ) .
this diffraction feature indicates 
 that the ni nps possess an internal twin structure , that different 
 nps possess different stacking sequences starting from the substrate , 
 or a combination of both of these . from the peak widths along the l direction
, it is concluded that internal twinning does 
 not occur frequently because this effect would lead to additional 
 broadening and would result in lower apparent np heights , as explained 
 in more detail in the section nanoparticle shape and adhesion energy .
the substrate 
 bragg peak at ( 1,0,2 ) and the corresponding ctr along the l - direction . the ( 1 , 0 , 1)ni111 and ( 1 , 0 , 2)ni111 bragg peaks from ( 111)-orientated 
 ni nps .
at ( 1.25 , 0 , 2.53 ) a peak belonging to ( 100)-oriented 
 ni nps and at ( 1.66 , 0 , 1.86 ) a peak orignating from internal 
 twinning as described in the text .
the peak at ( 1.02,0,3.28 ) , 
 which is labeled as ( 0 , 0 , 3)ni  tilt , originates 
 from the tilted nps as described in the text .
table 2 gives an overview of the ( h , k , l ) coordinates 
 expressed in different frames .
the hk projection 
 ( inset ) shows the substrate ( black ) and ni ( blue ) reciprocal lattice 
 vectors .
another strong ni - bul ( 111 ) peak is observed at 
 ( 1,0,3.28 ) , 
 which originates from np which are 41.33 tilted with respect 
 to the ( 111)-oriented particles .
this or2 is described by yszni111r41.33 
 and [ 120]ysz[120]ni111 , where r indicates a rotation .
the full 3d information 
 is confirmed by the observation of a ( 2,2,0)ni  bul reflection , belonging to or2 and which is rotated by 34.4 
 from the substrate surface plane .
the angular position of this reflection 
 is obtained by rotating the ( 0,2 , 2)ni  bul of or1 , which makes an angle of 30 with the plane of the rsm 
 shown in figure 3 , 
 around the [ 120]ysz direction by 41.33. the 
 atomic - scale arrangement , schematically depicted as a side view along 
 the rotation axis , is shown in figure 4 .
the orientation can be understood from a so - called 
 coherent tilt strain - relieving mechanism , which is rather common in 
 thin film heteroepitaxy . for fcc metals , this epitaxial 
 relationship originates from the diffusion of dislocations along ( 111 ) 
 slip planes .
the resulting edge dislocations 
 line up laterally at the hetero interface , thereby reducing the strain 
 and tilting the metal lattice .
the energetics of this mechanism competes 
 with other types of strain relaxation and can be kinetically hindered by dislocation movement .
therefore , 
 depending on the growth technique in combination with temperature , 
 which determines the supersaturation and surface diffusion , different 
 orientations are expected .
nanoparticles as investigated here , would 
 actually form the very early growth stage of textured polycrystalline 
 thin films .
the np nickel lattice is tilted such that the projection 
 of ( 111 ) planes fits much better to the substrate atomic distance 
 of 0.314 nm along this direction and therefore accommodates strain .
the particular arrangement originates from an interfacial strain 
 driven slip mechanism , which is common in fcc metals . by the diffusion 
 of dislocations along the ( 111 ) slip planes toward the interface , 

the projected d - spacings have a better match with 
 the substrate thereby relieving strain . as a consequence ,
figure 3 also shows 
 much weaker peaks at ( 1.25,0,2.53 ) and ( 1.66,0,1.86 ) , 
 which are ascribed to ( 100)-oriented nps and from internal twinning 
 around the ni 111-direction pointing toward a side facet , respectively . 

because these orientations represent only a fraction of all the nps , 
 as judged from the much weaker diffracted bragg intensities , these 
 are left out of further consideration .
the or1 found here has 
 been reported before for a variety of different 
 growth methods of ni on ysz(111 ) , like pulsed laser deposition and mbe . because 
 this or results from a simple cube - on - cube stacking and most likely 
 is energetically favorable
, it has also been found for the ni - ysz(100 ) 
 interface grown by directional solidification
. these studies also report on other ors , but not on the or2 found 
 by our x - ray diffraction study .
interestingly , from the geometrical 
 analysis of coincident lattice points , sasaki et al . find that the best match would be formed by yszni  bulk and yszni  bulk , an or that has experimentally never been verified , 
 also not in this study .
this point illustrates that ni - ysz lattice - matching 
 alone is not enough to describe the different ors and that other energy 
 terms such as chemical bonding and dislocation formation and their 
 kinetic interplay during growth play a potentially more important 
 role .
moreover , it has been shown previously that the ysz(111 ) possesses 
 a surface morphology with 2d monolayer high islands , which is expected to play a role in the np binding .
the average 
 size of the nps can be determined from the widths of their corresponding 
 bragg peaks , under the assumption that the line broadening can be 
 mostly attributed to their finite size and that nonuniform strain 
 plays a minor role .
the experimentally observed diffraction peaks 
 are further broadened by the instrument resolution , which in the case 
 here is anisotropic due to the synchrotron radiation characteristics 
 in combination with the beamline focusing optics . from the single - crystal 
 substrate
bragg peaks the in- and out - of - plane instrument resolution 
 is determined . because our sample coordinate system is chosen such 
 that the hk - plane lies horizontal and the l - direction is vertical , the instrument resolution can be 
 described by ( h , k,l ) = ( 0.025,0.060 ) , expressed 
 in dimensionless reciprocal lattice units .
all the experimentally 
 determined diffraction peaks were well described by gaussians , so 
 that the peak breadths are corrected for the instrumental resolution 
 by  = exp2res2 . the average height of the nps 
 is given by the following reciprocal relationship:1where c = 0.890 nm is the 
 direct lattice parameter of the ysz(111 ) surface unit cell and l the peak width ( fwhm ) along the l - direction corrected 
 for the instrument resolution .
a similar expression holds for the 
 determination of the average widths ( w ) , for which 
 the peak profile along the h - direction must be considered together 
 with the fact that the h - direction makes an angle of 30 with 
 the real space atomic layers within the hexagonal surface unit cell . 

the np heights and widths have been determined after each of the treatments , 
 and the resulting values are presented in table 3 .
the errors that are listed are calculated 
 from the spread in values obtained from several bragg peaks at different 
 positions in reciprocal space . in a next step
, the average 
 sizes are used together with wulff s 
 construction to deduce the nps 
 equilibrium shape when in contact with a foreign substrate .
the underlying 
 principle is that the nps are faceted and that those facets with the 
 lowest surface energy will have the largest surface area .
this aspect 
 is now combined with the geometrical constraint that the nickel nps 
 are supported by the ysz substrate .
it is important to note that the 
 description of the nps shape used in the following is valid 
 for isolated particles ( i.e. , in the absence of particle 
particle 
 interaction ) . from the afm measurement , shown in figure 1 , it can be concluded that 
 coalescence may have set in for certain particles / areas but probably 
 not for all .
a more detailed analysis is hampered by the inherent 
 lateral resolution of the used afm .
nevertheless , the sample used 
 for this study is probably not far off a model system with completely 
 isolated nps . for fcc metals like
ni , the wulff shape ( i.e. , without 
 support ) is given by a polyhedron with predominantly ( 111)-oriented 
 hexagonal facets together with smaller square ( 100 ) facets .
this basic 
 shape is taken as a starting point to construct the shape when in 
 contact with a substrate . using the dimensions and orientation with 
 respect to the substrate
, the wulff shape has to be cut at particular 
 positions . for the ( 111)-oriented particles , 
 the wulff shape is shown in the upper part of figure 5a ) .
the width of 8 nm and height of 5 nm , 
 as determined previously , require a truncation of the wulff - shape , 
 as shown in the lower part of figure 5a ) .
the resulting shape of the ( 111)-oriented nps is 
 then given by a large ( 111)-oriented top facet , six ( 111)-oriented 
 side facets and three ( 100)-oriented side facets .
the shape of the 
 tilted nps is determined by rotating the wulff - shape by 41.3 
 in order to comply with the experimentally determined orientation
. 
 then this tilted particle is truncated at the experimentally determined 
 height , see figure 5b ) .
( a ) wulff shape for the unsupported ( 111)-oriented np ( top ) and when 
 supported by the ysz substrate ( bottom ) .
the different treatments did not significantly 
 change the nps shapes , although the heights and widths did 
 change , as described in the text and seen in table 3 .
the energy of adhesion for relatively round supported nps 
 ( i.e. , 
 which are not very flat and at least half as high as the wulff - constructed 
 free particle ) is given by2with h the height of the 
 np and h * the height of the  buried  
 part .
it seems a reasonable approximation to relate the experimentally 
 determined heights and widths to the geometric lengths of eq 2 as w = h + h*. taking a value of 111 = 1.89 jm , this gives wadh = 1.4 jm for the ( 111)-oriented 
 ni nps after annealing .
( note : these surface - energy values were checked 
 and recalculated with density functional theory ( dft ) using the latest 
 perdew  burke 
enzerhof ( pbe ) potential , which does not 
 suffer too much from overbinding . )
because the error bar on the widths 
 is relatively large , the criterion for using eq 2 might not hold anymore and they could actually 
 be much flatter , in which case the following relation holds:3 this relation gives , together with 100 = 
 2.2 
 j / m ( see parenthetical note 
 above ) , wadh = 2.1 j / m .
the 
 adhesion energy value obtained from eq 2 is somehwat smaller than typical values obtained for 
 other materials systems , such as ptrh - al2o3 and pd  al2o3 .
the value obtained using eq 3 is much closer to those values and is in 
 very good agreement with the value obtained for much larger ( w = 200 nm , h = 150 nm ) ni particles . for the tilted nps , a higher h / w ratio is observed , pointing to a reduced adhesion 
 energy .
the occurrence of two distinct np growth directions can be 
 related to a difference in interfacial binding which either could 
 originate from a lateral chemical inhomogeneity of the ysz substrate 
 or a kinetically trapped state . also a size dependence can not be ruled 
 out which is difficult to investigate due to the inherent size distribution 
 of the nps after growth via thermal deposition . at a temperature of 573 k , the 
 nps were exposed to molecular oxygen at a pressure of 10 pa for approximately 35 min , after which the oxygen was pumped off 
 again .
figure 6 shows 
 a reciprocal space map after oxidation from the same plane as that 
 shown in figure 3
. 
 clearly observable are two new bragg peaks along the l - direction at h = 1.24 , which originate 
 from nio . from the position of these two peaks with respect to the 
 nearby bragg peaks of the ni -oriented nps
the average heights 
 and widths of the -oriented and tilted nps after oxidation are 
 listed in table 3 . 
 additionally , the temporal evolution during oxidation of some structural 
 parameters were followed as well , see figure 7 .
the integrated bragg peak intensity , which 
 is proportional to the amount of pure metal , is seen in the decay 
 below half of its initial value , which means that about 65% of the 
 ni contained by the -oriented nps transforms into nio . at the 
 same time , the average height of the -oriented nps changes only 
 by approximately 0.2 nm , which is equal to the estimated error , see table 3 .
nevertheless , the 
 data do indicate a trend , whereby the average height of the pure metal 
 ( core ) is reduced .
the particular bragg reflection that was followed 
 during oxidation gives an average height somewhat smaller than the 
 value obtained from other bragg reflections and therefore is not identical 
 to the values listed in table 3 .
the position of the bragg peak along l can 
 be used to determine changes in the uniform strain of the nps 
 ni ( 111)-planes along the substrate surface normal . by comparing its 
 shift from its initial value , which relates to d0 , the relative strain state d / d0 is calculated .
it is seen in figure 7 that as oxidation proceeds , 
 the lattice expands along the surface normal and levels off after 
 an approximately 0.5% increase , a value very close to that found during 
 thin ni film oxidation .
we argue that 
 this can be attributed to oxygen incorporation into the ni lattice . 
 from the trend in the intensity curve
, it is concluded that the oxidation 
 process had not yet finished , although the lattice did not expand 
 anymore , which indicates that the oxygen dissolution has reached a 
 final state .
l plane after oxidation at 573 k and 10 pa of 
 molecular oxygen for 35 min .
kinetics of the 111-oriented ni np evolution during oxidation . 
 shown are the average height ( top ) , relative 111 bragg peak intensity 
 ( middle ) and relative strain d / d0 ( bottom ) as a function of oxidation time . in order to rationalize the obtained results , we 
 postulate the 
 following oxidation mechanism .
one important ingredient is that small 
 nps oxidize relatively faster than large ones ; their so - called burn - up 
 time is even lower than expected from the oxidation rate of planar 
 surfaces , because the geometry of the electric field around these 
 often more - rounded particles is predicted to accelerate the oxidation 
 process .
larger nps will first form an oxide skin 
 around them , and eventually , they also burn up completely , but with 
 a much lower rate .
schematically , an intermediate state of this scenario 
 is depicted in figure 8a , which represents the situation after the oxidation step presented 
 here . given a certain particle size distribution , the resulting bragg 
 peak shape
figure 8 shows the results for such a calculation , using a hypothetical 
 gaussian width distribution , around an average of 8 nm and a standard 
 deviation of ann = 3 nm .
gaussian - shaped diffraction 
 peaks corresponding to each of the np size represented in the distribution 
 are used in the calculation .
a cutoff value around 5.5 nm is used , 
 below which the nickel nps are completely oxidized . from the resulting 
 ni and nio
therefore , the width of a nio np , which has 
 formed from a metal ni particle , is larger by a factor of 1.19 , which 
 reflects the ratio of their lattice parameters .
metal ni . in this particular 
 numerical example , the average ni np width before oxidation is 8 nm , 
 whereas after oxidation , both ni and nio widths are 9 nm .
although 
 this numerical simulation certainly does not include all the details 
 of the oxidation process , it does show how the average np sizes can 
 in principle be affected by a preferential oxidation of small particles 
 and how this can lead to average np widths that are larger after oxidation . 

the simulation presented here does not differentiate between partially 
 and completely oxidized particles , although the experimental results 
 point toward such a situation .
this is mostly seen in the large anisotropy 
 between the oxidation of the nps top 111 facet and the average widths . 

both xrr and high - angle bragg peaks indicate that upon oxidation , 
 the average height of the metal ni nps is slightly reduced , at most 
 by 0.2 nm .
it has been observed that during the oxidation of a ni(111 ) 
 single - crystal surface under identical conditions as used in this 
 work , a nio skin of approximately 2 nm forms after approximately 14 
 h. therefore , it seems reasonable to 
 assume that for the oxidation time investigated here , at most , only 
 one single outermost layer of ni atoms , which constitute the top facets , 
 form an ultrathin nickel oxide .
the oxidation process at the other 
 facets , like 100 , seems to proceed much faster and even leads to complete 
 oxidation of nickel nps .
( a ) small nps oxidize comparatively faster and burn up 
 completely , whereas at the same time , an oxide skin has formed on 
 larger nps and the core is still metallic .
the evolution of the diffraction 
 peaks is simulated using np width distributions during this partial 
 oxidation process .
( b ) np width distributions before and after oxidation : 
 initial metallic ni nps ( black line ) with an average of 8 nm and a 
 spread of  = 3 nm .
after oxidation , the width distribution 
 of the metallic core of the partially oxidized particles has become 
 asymmetric and peaks at around 9 nm ( filled white ) .
the width distribution 
 of the oxidized metallic ni ( red ) is shifted due to the lattice expansion 
 and is used to calculate the expected nio bragg peaks , see text for 
 more explanation .
( c ) bragg peaks calculated as weighted averages 
 using the gaussian width distributions . shown
are the initial ni peak 
 ( black ) , the final ni peak ( red ) , and the newly formed nio peak ( filled 
 red ) . from the diffraction lines , average widths of 8 , 9 , and 9
nm 
 for the initial ni , final ni , and nio particles are found , respectively .
the oxidation behavior of the 
 nps belonging to or2 has not been 
 followed in situ , but the overall changes in height and width , as 
 listed in table 3 , 
 are very similar to those of or1 .
the intensity loss on the metal 
 ni bragg peaks is about 50% , very similar to that of the peaks belonging 
 to or1 .
we therefore conclude that the fact that the particles belonging 
 to or1 have different facets exposed to the gas phase leads to minor 
 changes in oxidation behavior and the stability of the particles is 
 not much different .
nickel nps 
 were grown in uhv by pvd using an electron beam evaporator 
 with a nominal average height of approximately 4 nm at substrate temperatures 
 of 623 k. x - ray diffraction revealed that two distinct np orientations 
 form ; there is no random orientational growth which would give rise 
 to powderlike diffraction patterns .
the np orientations are or1 : ni 
 ( 111 ) planes parallel to the surface whereby the in - plane directions 
 are also aligned ( niysz and ni[1 10]ysz[1 
 10 ] ) and or2 : ni 111 planes tilted by 41.33 from the 
 substrate normal in the plane spanned by ysz and ysz[1 10 ] . 

the average heights and widths of the nps were determined from the 
 x - ray diffraction line breadths .
the relatively well - defined height 
 is furthermore extracted from x - ray reflectivity and afm in a separate 
 growth run , which all give systematically comparable values .
the average heights and width of nps in both ors increase by approximately 
 25% , indicating that the particles exhibited already equilibrium shape 
 at the growth temperature . from the height - to - width ( h - to - w ) ratio , together with the ni ( 111 ) and ( 100 ) 
 surface energies , the adhesion energy is determined .
depending on 
 the np shape being more round or flat , two different relations hold . 
 because the nps average aspect ratio h / w is close to , either of the relationships might give 
 representative values .
this is even more likely when taking into acount 
 the appreciable size distribution , which is more broad in w than in h. the more rounded nps will 
 then have an adhesion energy of 1.4 j / m and the flatter 
 ones 2.2 j / m .
this adhesion energy calculation does not hold for the tilted nps 
 forming or2 because of their asymmetric shape . when exposing 
 the nps to methane at a pressure of 10 pa and 
 a temperature of 573 k for 30 min , no changes are observed . 

a possible adsorption of the hydrocarbons on the nps is thus concluded not to affect the structure of the nps .
the most distinct changes are caused by an oxygen treatment at 
 10 pa and 573 k for 35 min .
the intensity of the 
 or1 bragg reflections , which is a measure for the total amount of 
 metal , decreases to less than half its initial value .
after the oxidation 
 step , nio bragg reflections are detected , and from their positions 
 in reciprocal space , it is deduced that nio has grown epitaxially , 
 in a cube - on - cube fashion , on the nps from or1 or in contact with 
 the ysz ( 111 ) surface . at the same time , the average height has changed 
 by 0.2  0.3 nm and the average width + 1  3 nm . 

the average size of the nio is approximately equal to that of the 
 remaining pure metal particles .
these results can be rationalized 
 by considering a preferential oxidation mechanism in combination with 
 an anisotropic size distribution , whereby the spread in h is much narrower than that in w. it has been predicted 
 that small , more rounded , nps will oxidize at an enhanced rate compared 
 to larger ones . on the basis of these 
 and our experimental results
, we postulate that ni nps smaller than 
 approximately 5.5 nm have burnt up completely and that larger ones 
 have a nio skin formed around them .
a simulation , using a hypothetical 
 gaussian width distribution , shows that indeed this scenario can explain 
 the experimentally observed average widths before and after oxidation . 

this description does not include all the details of the oxidation 
 process , such as exact oxidation rate and nio thickness on the different 
 facets , and even assumes that part of the larger nps does not oxidize 
 at all , which is not very realistic .
nevertheless , it shows numerically 
 the effect one important aspect of the mechanism , namely , size - dependence , 
 can have on the final average size .
the size - dependent oxidation behavior 
 might also be related to the kink seen after approximately 3 min in 
 the time - dependent intensity reduction of the 111 bragg peak of figure 7 .
the average 
 size of the nio particles and/or skin is of the same 
 order of magnitude as the remaining pure ni metal ( cores ) because 
 of two effects : ( 1 ) due to the lattice expansion after oxidation ( i.e. , 
 nio has larger lattice constants than ni ) , a completely oxidized np 
 will be larger than the original one .
this effect shifts the average 
 oxidized np size to higher values , thereby compensating for the fact 
 that the smaller metal particles have prefentially oxidized .
( 2 ) the 
 oxide skin on the top facet is formed by a completely structurally 
 correlated nio lattice .
therefore , the in - plane nio size will be comparable 
 to the underying metal particle . from ni(111 ) single - crystal oxidation 
 studies , it was found that an approximately 2 nm oxide forms after 
 14 h at conditions similar to the ones here . extrapolating to the oxidation time
used here , it would be expected 
 to have oxidized only a monolayer from the 111 facets , which is about 
 0.2 nm thin .
this value corresponds very well to the reduction in 
 the average height of the ( 111)-oriented nps upon oxidation and would 
 imply that the oxidation proceeds mostly along the ( 100 ) facets .
the results obtained here can be discussed in relation to real 
 sofcs , in particular with respect to the so - called redox cycling ( i.e. , 
 the oxidation  reduction process of ni ) . during sofc operation ,
the anode is continuously supplied 
 with fuel , the amount of which is burnt depends on the availability 
 of oxygen .
instabilities around the ideal ratio of fuel and oxygen 
 levels can lead to the formation of nio , which is known to lower the 
 sofc performance and lifetime by stress development , lowering of the 
 metal triple phase boundary density , and mechanical failure .
our results may add another cause to sofc anode 
 failure , namely , that during the time when there exists a surplus 
 of oxygen , probably the smallest ni nps will completely oxidize and , 
 depending on the reducing properties of the fuel , might not revert 
 to pure metal anymore .
after many cycles of such a process , the sofc 
 might gradually loose its efficiency because the smallest particles 
 are most likely to be the most reactive and therefore relatively more 
 important for the functionality
. moreover , such a preferential oxidation 
 process , whereby the particle size distribution shifts toward larger 
 values , might result in the sofc operation to drift away from complete 
 reaction leaving unburnt fuel and increasing oxygen levels thereby 
 oxidizing ever more ni .
x - ray diffraction revealed 
 two distinct orientations of ni nanoparticles 
 grown in uhv by mbe : -oriented particles and ones with their 
  planes tilted by 41.33 from the surface normal . a combination 
 of diffraction line width analysis , x - ray reflectivity , and afm delivered 
 information on the average np height and width .
these sizes were used 
 to determine the energy of adhesion to be in the range of 1.42.2 
 jm , whereby particles that have a more round shape 
 are more weakly bound than those that have a flatter geometry .
annealing 
 the nps in uhv to 923 k led to the observation of sintering : most 
 significantly , their average height increased and the data also indicate 
 an increase in average width . this sinterering process does not lead 
 to a significant shape change from just after growth .
exposure to 
 methane at 10 pa at a temperature of 573 k did 
 not show any structural changes . however , oxidation at 10 pa of o2 at the same temperature led to the formation 
 of expitaxial nio on the -oriented particles .
an oxidation mechanism 
 is postulated , which is based on a preferentially faster burn up rate 
 for small particles and the formation of an oxide skin around larger 
 ones .
such a preferential oxidation mechanism which shifts the np 
 size distribution toward higher values might be one factor responsible 
 for the long - term degradation of sofcs .
 nickel 
 nanoparticles supported by the yttria - stabilized zirconia 
 ( 111 ) surface show several preferential epitaxial relationships , as 
 revealed by in situ x - ray diffraction . 
 the two main nanoparticle orientations 
 are found to have their [ 111 ] direction parallel to the substrate 
 surface normal and 41.3 degrees tilted from this direction . 
 
 the former orientation is described by a cube - on - cube stacking at 
 the oxide  
 metal interface and the latter by a so - called coherent 
 tilt strain - relieving mechanism , which is hitherto unreported for 
 nanoparticles in literature . 
 a modified wulff construction used for 
 the 111-oriented particles results in a value of the adhesion energy 
 ranging from 1.4 to 2.2 jm2 , whereby the lower end corresponds 
 to more rounded particles and the upper to relatively flat geometries . 
 upon oxidation at 103 pa of molecular oxygen and 
 673 k , a nio shell forms epitaxially on the [ 111]-oriented particles . 
 
 only a monolayer of metallic nickel of the top ( 111 ) facets oxidizes , 
 whereas the side facets seem to react more severely . 
 an apparent size 
 increase of the remaining metallic ni core is discussed in relation 
 to a size - dependent oxidation mechanism , whereby smaller nanoparticles 
 react at a faster rate . 
 we argue that such a preferential oxidation 
 mechanism , which inactivates the smallest and most reactive metal 
 nanoparticles , might play a role for the long - term degradation of 
 solid oxide fuel cells . 