lithium 
 ion batteries are the power source of choice for most mobile 
 electronic devices .
these systems generally work using the insertion 
 and removal of lithium ions into host materials , resulting in redox 
 and structural changes during the electrochemical cycling .
lifepo4 adopts the olivine structure type ( ( mg , fe)2sio4 , orthorhombic),with feo6 corner - linked octahedra in the bc plane and lio6 octahedra forming edge - sharing chains 
 on the b axis .
hence the li ions reside 
 within 1d channels , allowing their extraction and insertion during 
 charge and discharge via the reaction shown in figure 1 .
equation for charge and discharge of lifepo4 and structural 
 diagrams of the lifepo4 and fepo4 active materials 
 with iron atoms shown in orange , small gray phosphorus atoms , large 
 blue lithium atoms , and red oxygen atoms .
both structures adopt space 
 group pnma , with lattice parameters of a = 10.3290(3 )  , b = 6.0065(2 )  , and c = 4.6908(2 )  for lifepo4 and a = 9.8142(2 )  , b = 5.7893(2 )  , 
 and c = 4.7820(2 )  for fepo4 .
the discharge profile is characterized by a flat plateau 
 at 3.45 
 v vs li .
this flat potential discharge reaction is characteristic 
 of the coexistence of two phases , lifepo4 and fepo4 , each having a narrow compositional stability range in contrast 
 with nonstoichiometric electrode materials such as lixcoo2 that generally show sloping profiles .
the first in situ x - ray diffraction ( xrd ) study of lifepo4 was presented by andersson et al . using a  coffee bag
this cell can be placed directly 
 in the x - ray beam and diffraction is observed in transmission mode 
 through the coffee bag .
the study clearly showed the phase change 
 reaction and monitored the growth of the heterosite ( fepo4 ) phase as the triphylite ( lifepo4 ) phase diminishes during 
 charge , with the reverse occurring on discharge .
the intensities of 
 the peaks were found to be in good agreement with those anticipated 
 from the charge passed during cycling .
several other designs for in 
 situ diffraction studies have since been reported including a recent study that characterized a meta stable new phase 
 formation at high rates in large particle size lifepo4 . since some of the first commercial uses 
 of lifepo4 have 
 emerged for high power applications such as power tools , many different preparations of lifepo4 have been explored to improve the material s performance 
 in order to allow for practical use at high rates .
these have focused 
 on control of its particle size , doping on the li and fe site , and 
 various coating methodologies .
these strategies have been largely successful on the particle and 
 agglomerate levels , reducing solid state diffusion times , phase boundary 
 strain , and electronic resistance . given the above successes 
 in improving the discharge of single 
 particles and agglomerates such that intraparticle equilibration processes 
 are not rate limiting , attention has recently focused on the effects 
 of ion transport restrictions in composite electrodes containing dispersed 
 active material , an electron conducting additive , and electrolyte . 

in the case where electronic conductivity is not rate limiting , discharge 
 should begin at the electrode / separator interface where ion transport 
 restrictions are at a minimum . with nonstoichiometric electrode materials , 
 where the equilibrium potential decreases continuously with discharge
, 
 the progression of discharge from the front to the back of the electrode 
 can be described by ambipolar diffusion of lithium ions and electrons 
 according to the delevie description of a porous electrode . here
the active material is represented by a 
 series of capacitances distributed along the electrode thickness . 

these are connected to the bulk electrolyte through the infused electrolyte 
 within the pores , and to the current collector via the electron conducting 
 additive , so that parts of an electrode that are at different states 
 of charge are continuously equilibrated during discharge .
the interface 
 between charged and discharged material is diffuse , and further diffusion 
 occurs after the current has been switched off .
importantly , the driving 
 force for ambipolar diffusion is the increase in the potential with 
 the state of charge .
this is notably absent in the case of stoichiometric 
 materials such as fepo4/lifepo4 where the potential 
 is constant for most of the composition range , as shown by a long 
 plateau in the discharge curve .
ambipolar ( ion - electron ) diffusion 
 should not occur in these materials ; instead , the interface between 
 charged and discharged parts of the electrode should be linked directly 
 to the passage of charge and should stop moving once the current stops 
 despite the sharp change in the average concentration of lithium . 

we recently described this phenomenon as the sharp discharge front 
 ( sdf ) effect , and supported our hypothesis 
 with electrochemical discharge data that responded to changes of electrolyte 
 conductivity and salt diffusion as predicted , but previously had no 
 direct evidence for the distribution of discharged material within 
 the electrode .
the above example cites just one case among many 
 where a direct 
 observation of the profile of the extent of discharge with depth into 
 the electrode thickness could provide valuable insight into the discharge 
 process and verification of simulated discharge phase profiles . in 
 situ neutron depth
profiling can resolve variations in lithium concentration 
 through the thickness of an electrode via the energy profile of  
 particles formed as a result of neutron capture by li .
cross - sectional imaging by neutron absorption or tem can also 
 provide valuable information on variations through the electrode . 

the use of x - ray diffraction allows direct observation of the phase 
 distribution of the active materials during charge and discharge . 

this information is different from the lithium distribution , which 
 would include any lithium in the electrolyte , and can be collected 
 rapidly in situ providing the possibility of time resolution .
variation 
 of the incidence angle provides a depth sensitivity as absorption 
 of x - ray photons results in a limited path length so with low incident 
 angles the diffraction signal comes largely from close to the surface . 

the lifepo4/fepo4 system provides a model composite 
 electrode , which should provide a sharp and controllable discharge 
 front .
positive electrodes 
 for in situ cycling were formed by mixing appropriate 
 amounts of carbon - coated lifepo4 ( hydro - quebec ) and acetylene 
 black conducting additive ( shawinigan black ) , then mixing in a polytetrafluoroethylene 
 ( ptfe ) binder ( 6c  n , dupont ) .
the resulting mixture was calendared 
 to a controlled film thickness of 100 m and punched to produce 
 circular electrodes with a diameter of 8 mm .
the electrodes were dried 
 overnight at 120 c under vacuum , before being transferred to 
 an argon - filled glovebox .
two compositions of lifepo4 electrodes 
 were used for the testing : ( a ) 50% lifepo4 , 40% acetylene 
 black , and 10% ptfe by mass and ( b ) 25% lifepo4 , 60% acetylene 
 black , and 15% ptfe by mass .
currents 
 were calculated to achieve complete charge or discharge in a fixed 
 time period based on theoretical capacity , e.g. c/2 = complete charge 
 or discharge in 2 h and 2c = 0.5 h. scanning electron microscopy ( sem ) 
 used a jeol jsm-6500 fegsem with 15 kv accelerating voltage and secondary 
 electron imaging  powders or whole electrodes were mounted on 
 conducting carbon tape and imaged without any further coating .
initial 
 xrd patterns were collected with a bruker d2 phaser ( cu k x - rays ) 
 and rietveld refinement of the data used the gsas package . the 
 electrochemical cell used for the in situ work
is based on the commonly 
 used swagelok cell design and therefore consists largely of cheap , 
 commercially available parts .
this cell can be constructed readily 
 in any laboratory and does not require the use of specialized equipment 
 or the use of toxic beryllium metal windows .
the few bespoke parts 
 used in its assembly are easily fabricated with use of basic tools . 

furthermore , it is simple to assemble and clean after use , and the 
 positive current collector , which doubles as the x - ray window , is 
 disposable and easily replaced .
the cell consists of three main sections 
 as shown schematically in figure 2a and as 
 a photograph in figure 2b : ( 1 ) a 12 m 
 thick aluminum foil acts as the positive current collector .
this was 
 attached to a stainless steel washer with black silicone rubber adhesive 
 ( loctite type 5910this was found to be inert in the 
 environment of an operational cell ) .
the washer was similarly attached 
 to the swagelok nut used to seal the cell .
( 2 ) a 12.7 mm diameter 
 stainless steel piston was used as the negative current collector . 

this was placed under tension with a steel spring held in place with 
 a 12.7 mm diameter stainless steel rod , the bottom of which was machined 
 to fit into a standard goniometer head for mounting onto the beamline . 

( 3 ) ptfe sheaths , ferrules , and a nut sealing the bottom of the cell 
 were used to avoid short - circuits , including during handling of the 
 cell .
( a ) schematic and ( b ) image of the electrochemical cell used in 
 the in situ xrd studies .
the layered battery assemblies 
 consisted 
 of a composite positive electrode , two electrolyte - soaked 12.7 mm 
 diameter separators ( whatman gf / f grade glass fiber with eight drops 
 of 1.0 mol dm lipf6 in 1:1 ethylene 
 carbonate / dimethyl carbonate ( novolyte technologies ) ) and a lithium 
 metal negative electrode formed by compressing lithium ( 99.9% , aldrich ) 
 into a hemispherical mold and punching to a diameter of 11 mm .
the 
 shaped lithium negative electrode allowed an even pressure to be applied 
 across the diameter of the stack , countering the effect of deformation 
 of the aluminum window under pressure and allowing a similar electrochemical 
 performance to be achieved to that observed with the same electrode 
 material in a standard swagelok cell with flat electrodes . to study 
 the electrode composition as a function of depth and state of charge 
 the diffraction geometry shown schematically in figure 3 was used .
the sample was mounted on the hexapod stage at 
 beamline i07 of the diamond light source with use of an insulating 
 mount and visually centered in the xy plane such that the highest 
 point on the curved surface of the window was aligned with the center 
 of the diffractometer cirles .
the x - ray beam height was approximately 
 80 m and a scan in the vertical direction monitoring the direct 
 beam intensity was used to position the sample such that the beam 
 center was level with the top of the 100 m thick positive electrode . 

hence 40 m of the beam passed through the back of the sample 
 with 0 incidence angle and 60% of the electrode ( the part facing 
 the separator and negative electrode ) was not contributing to the 
 observed xrd pattern .
the sample was then tilted to increase the incidence 
 angle and the penetration depth into the electrode .
additional information 
 about sample mounting on the beamline is included in the supporting information .
schematic showing the 
 effect of changing the angle of incidence 
 on the penetration of the 80 m high x - ray beam into the positive 
 electrode at 0 ( left ) and 4 ( right ) angle of incidence . in situ xrd patterns
were collected 
 with 20 kev beam energy (  
 = 0.620  ) and an exposure time of 1 s using a pilatus 100k area 
 detector at a camera length of 497 mm such that a 7 
 range could be collected in a single frame with high resolution .
this 
 restricted the accessible 2 range but facilitated fast acquisition 
 times so that the phase change reaction could be observed at high 
 rates .
data were continuously collected with a series of different 
 incidence angles between 0 and 6 , although ultimately the analysis 
 focused on data collected at 0 and 4. collecting 1 s patterns 
 at 0 , 0.5 , 1 , 2 , 3 , 4 , and 6 incidence 
 angles resulted in a 20 s cycle of measurements ( patterns could be 
 recorded with acceptable quality in 0.1 s but the sample position 
 adjustment to effect the different angles of incidence was the rate 
 limiting step ) .
the peak width was between 0.05 and 0.06 
 at both incidence angles hence the variation in peak width with incident 
 angles was not found to be significant . with a battery performing 
 to theoretical capacity at our fastest rate of 20c under these conditions 
 9 patterns could be collected at each angle during the 3 min discharge . 

the peak heights of the most intense bragg reflections for lifepo4 at 15.7 and fepo4 at 16.3 were then 
 used to provide a measure of the electrode phase composition at each 
 angle of incidence .
this structural change was correlated to the state 
 of charge by using time stamps in both the electrochemical and xrd 
 data files .
the peak heights were extracted by using a matlab macro 
 with a baseline correction .
strictly peak area is proportional to 
 the phase fraction , but since peak widths of the lifepo4 and fepo4 phases were similar in any given pattern the 
 intensity was taken as a good indication of the relative phase contents .
commercially sourced 
 lifepo4 was used in this work to 
 take advantage of its optimized performance , achieving a capacity 
 of approximately 150 ma h g with a good cycle 
 life and rate capability .
powder xrd 
 studies showed it to contain single phase lifepo4 ( supporting information , figure s1 ) .
rietveld 
 refinement by using the standard triphylite model in space group pnma resulted in a good fit with a = 10.32227(12 ) 
  , b = 6.00341(6 )  , and c = 4.69092(7 )  , similar values to those described in the literature . to obtain a good fit it was necessary to employ 
 a preferred orientation parameter allowing for a small increase in 
 intensity along 010 ( march  dollase preferential 
 orientation ratio of 0.9105(12 ) along 010 ) .
the sem 
 ( figure s1 , supporting information ) showed 
 well - formed crystallites that are slightly elongated along one axis 
 and with an approximate size of 200 nm . since preferred orientation 

is only being observed along one axis it is likely that the large 
 flat face observable on some crystallites is becoming aligned with 
 the xrd sample surface during sample preparation and that this face 
 is the { 010 } plane of the crystallites .
figure 4 shows xrd patterns obtained during 
 the slow ( c/2 ) charge and discharge of a lifepo4 half cell . 

the electrochemical response is characteristic of the coexistence 
 of two phases with a flat plateau observed in the voltage capacity 
 profile during charge and discharge . in
the fully 
 discharged ( or as - constructed ) state the characteristic triphylite 
 lifepo4 phase can be clearly identified and as expected 
 after charging ( due to the near theoretical capacity extraction ) a 
 complete conversion to the heterosite fepo4 phase was observed . 
 in the partially charged or discharged condition we can clearly observe 
 a mixture of these two phases in the diffraction data with the phase 
 contributions to the pattern corresponding to the state of charge 
 ( specifically peaks at 16.2 and 13.7 corresponding to 
 lifepo4 and those at 15.7 and 13.6 pertaining 
 to fepo4 ) .
it can be observed that peak overlap is quite 
 limited due to the narrow xrd reflections and the significant differences 
 in lattice parameters between the lifepo4 and fepo4 phases .
charge and discharge curve for lifepo4 at a 
 rate of 
 c/2 with stacked diffraction patterns ( 4 incident angle ) showing 
 the linked structural changes between the lifepo4 and fepo4 phases .
a significant enhancement 
 in the 020 reflection relative to the 
 expected intensity distribution based on the literature powder patterns is observed in both lifepo4 and fepo4 , a larger elongation of the 020 reflections than observed 
 in the powder pattern of the starting material ( figure s1 , supporting information ) . here
the calendaring 
 process used to make the electrodes is likely to have induced this 
 orientational effect .
importantly the degree of 020 preferred orientation 
 was observed to be very similar in lifepo4 and fepo4 due to the topotactic transformation between them .
the discharge performance of 
 the batteries constructed for in situ testing using 25% and 50% active 
 material with rates between 2 and 20 c is summarized in figure 5b , d ( a constant charging rate of 2c was used for 
 all experiments irrespective of the discharge rate to ensure the condition 
 of the electrode at the start of discharge was as similar as possible ) . 
 at relatively slow rates of discharge
a characteristic flat discharge 
 plateau was observed around 3.45 v vs li in both cases . as the rate was increased the discharge changes 
 to a negative gradient linear profile as noted in our previous publication and explained by an ohmic potential drop in 
 the electrolyte within the composite electrode to the nearest delithiated 
 particle , increasing with the distance from the separator to the discharge 
 front .
discharges at rates greater than 5 c showed sharp end points 
 at capacities well short of those obtained at low rates , similar to 
 our previous work where an explanation 
 was given in terms of severe lithium salt polarization at high rates 
 due to a low lithium ion transference number . for electrodes containing 
 only 25% and 50% lifepo4 ( used in this work to ensure that 
 x - rays could pass from the front to the back of the electrode without 
 total absorption during the penetration path length ) the capacity 
 was well maintained up until rates of around 10c ( figure 5a , c ) , with a slight reduction in capacity easily 
 explained by premature termination of the discharge resulting from 
 an arbitrary choice of potential limit that did not account for the 
 discussed increase in ir drop . at rates greater than 10c we observed 
 that sharp end points are reached which are premature of that anticipated 
 entirely from ir drop and were hence consistent with the electrolyte 
 limitation discussed earlier .
the good retention of capacity at high 
 rates observed in these electrodes results from a reduced amount of 
 lifepo4 ; we chose relatively dilute amounts of active material 
 to ensure that x - rays could pass from the front to the back of the 
 electrode without total absorption during the penetration path length . 

if we assume that at the highest rates the electrodes are discharging 
 under the sdf model discussed in our previous work then we can calculate effective diffusion coefficients 
 of lithium ions in both electrodes using eq 1.1where 
 dod is the degree of discharge , f is c rate , [ lix]0 is the concentration of salt 
 ions in the electrode , t is the 
 transport number ( assumed to be 0.3 in this case ) , [ li ] is the concentration of li ions stored in the active 
 material within the electrode , d is the diffusion 
 coefficient , and l is the thickness of the electrode .
the effective diffusion coefficients for the salt in these structures 
 were found to be 1.7  10 and 2.2  
 10 m s for the 
 25% and 50% electrodes , respectively .
these values are significantly 
 larger than we reported for an electrode with 75% active material 
 in our previous work ( 10 ) and can be 
 explained by increased porosity and a lower tortuosity of the diffusion 
 paths .
electrochemical performance of 25% ( a , b ) and 50% lifepo4 ( c , d ) electrodes shown as electrode capacity retention as a function 
 of rate ( left ) and discharge capacity vs potential ( right ) . slow charging 
 rates and constant voltage top up periods were used to ensure full 
 charging of the battery .
based on the electrochemical performance an almost complete 
 discharge 
 of the cell at all rates is likely for the electrode containing 25% 
 active material and therefore relatively small concentration gradients 
 should be observed . for the 50% active material electrode
much larger 
 gradients are likely to be observed , especially at high rates . during the electrochemical measurements 
 presented in figure 5 ,
xrd patterns were collected 
 at a number of incidence angles to probe the structural changes as 
 a function of state of discharge rate .
our analysis focuses on data 
 collected at 0 and 4. grazing incidence xrd is widely used to 
 increase the effective sample thickness in the study of thin films . applying this technique to battery electrodes 

can provide an effective method to profile any differences in phase 
 behavior as a function of depth in the electrode by varying the proportion 
 of the signal that is scattered from the side on which the beam impinges . 

the absorption of x - ray photons is a significant consideration in 
 this geometry as with a 4 incidence angle the path length through 
 the electrode will be increased from the 100 m electrode thickness 
 to 1400 m .
based on calculated x - ray absorption characteristics 
 of the electrode components ( supporting information , table s1 ) only about 6% of photons are expected to reach the front 
 face of the electrode so the observed phase concentrations will be 
 significantly biased toward contributions from material close to the 
 current collector .
the battery could be assembled the other way up 
 to reverse this bias , but that geometry would also contain a compromise 
 in that the beam would have to pass through the negative electrode 
 and the separator , which would increase the contribution to the diffraction 
 patterns from these components .
importantly the absorption profiles 
 of the two electrode compositions discussed herein are similar ( table 
 s1 , supporting information ) and so direct 
 comparisons between their behavior can be made , while keeping in mind 
 the bias in the data toward the back of the electrodes .
the intensity 
 of the 020 reflection of fepo4 is approximately equal to 
 that of the 020 + 211 reflections of lifepo4 in an equimolar 
 mixture of these phases , hence the intensities of these reflections 
 were used as a semiquantitative measure of the content of the relevant 
 phase .
figure 6 shows the variation in the 
 phase fraction of fepo4 based on the intensity of the 020 
 reflection during discharge at various rates .
as expected the intensity 
 changes occur over shorter time periods as the discharge rate is increased . 
 with 25% active material in the electrode
the intensity profile at 
 all rates is similar using a 0 or 4 incidence angle .
it is striking , 
 however , that these profiles diverge with 50% active material and 
 that the observed intensity of the fepo4 020 reflection 
 is stronger with 4 incidence angle than it is with 0 incidence 
 angle at all rates above 4c .
this divergence shows that the back of 
 the electrode is undergoing less discharge at these rates than the 
 region being sampled closer to the front of the electrode .
the divergence 
 is largest at 8c and 10c , and is observed to decrease again at 20c . 

this indicates that the region of the electrode with the largest variation 
 in composition is moving further from the side of the electrode from 
 which the x - ray is impinging and hence closer to the electrolyte - soaked 
 separator .
the variation in fepo4 phase fraction expressed as the 
 fepo4 020 peak height ( relative to the combined heights 
 of the fepo4 020 and the lifepo4 020 + 211 ) 
 with time during cell discharge for electrodes prepared with 50% and 
 25% lifepo4 and linear fits to the data .
figure 7a , b shows the gradients 
 of the linear 
 fits to the data in figure 6 plotted versus 
 current density and c rate for both the 25% and 50% electrodes , respectively . 

this plot emphasizes the divergence in the observed intensity of the 
 fepo4 020 reflection of the 50% active material electrode 
 during fast discharge .
a particular strength of our approach of rapidly 
 collecting a series of incidence angles is that these data were collected 
 on a single electrode so are directly comparable .
the rate of change of 
 the intensity of the fepo4 020 
 reflection during discharge as a function of current density and c rate for ( a ) 25% and ( b ) 50% lifepo4-containing 
 electrodes .
points circled in red highlight those which indicate 
 significant concentration gradients within the electrode .
the variations in phase behavior that we have observed 
 during fast 
 discharge are consistent with the effects described earlier based 
 on observations from the electrochemical performance . in the electrode 
 containing 25% active material
the electrochemical data show only 
 a slight increase in the negative gradient of the discharge plateau 
 indicating that some small ionic diffusion gradients may exist in 
 the electrode resulting in some preferential discharge of material 
 near the bulk electrolyte as observed in figure 7a ( a notable deviation from this trend is seen at 20c which may be 
 due to a low number of data points increasing the bias from experimental 
 scatter ) . in the 50% electrode , little or no variation
was seen in 
 the gradients at the front and back of the electrode with rates of 
 4c or slower . however , at elevated rates there is a sharp deviation 
 in the rate of change between the front and back of the electrode 
 suggesting that a significantly different limitation is controlling 
 the electrode composition .
this effect is consistent with the salt 
 concentration polarization aspect of our previously reported sdf model , and originates from the insufficient concentration 
 of lithium ions in the electrolyte stored within the electrode ( see 
 table 1 ) . during the discharge of the battery 
 lithium ions
must be transported from the bulk electrolyte to the 
 active material by migration and diffusion . at slow rates
these mass 
 transfer processes are sufficient to allow complete discharge of the 
 battery , but at higher rates they are severely limiting .
calculated assuming that the 
 solid material is approximately 80% of the volume and that the free 
 space ( filled with electrolyte ) is 20% ( approximated from ref ( 48 ) ) .
densities were taken 
 as 3.6 , 2 , and 2.2 g cm for lifepo4 , carbon black , and ptfe , respectively .
it was also assumed that 
 changes in composition of the active material did not change the packing 
 of the solids and therefore the occupied volume .
the concentration 
 of the lipf6 in the electrolyte solution used was 1 m. in the flat discharge plateau 
 region of lifepo4 the 
 discharge reaction can be written as : the 
 fepo4 and lifepo4 phases coexist within 
 the electrode structure , so if one region of the electrode has an 
 insufficient supply of lithium ions then a slower discharge will occur 
 in one region and a faster rate of discharge in another . at high rates 
 of discharge lithium ions
this is followed by a mass transport process driven by diffusion from 
 the bulk electrolyte .
the lithium ions thus transported will react 
 with the first particles of electrode material encountered which will 
 be in the region of the electrode facing the separator .
hence this 
 region will fully discharge and the electrode region near the current 
 collector will be undercharged ( as observed at high rates in the 50% 
 active material electrode ) .
this is shown schematically in figure 8 ; when there is no limitation on the electrolyte 
 during discharge , an even concentration in the electrode can be seen 
 and when an electrolyte limitation is in effect , a preferential discharge 
 occurs at the electrode close to the bulk electrolyte and results 
 in an incomplete discharge .
schematic showing how the discharge proceeds 
 in an electrode where 
 there are no limitations on the discharge from the electrolyte and 
 also where there is a severe limitation as a result of insufficient 
 transport of li ions ( usually resulting from a high ratio 
 of lithium ion vacancies to lithium ions in solution and when the 
 electrode is discharged at high rates ) .
this schematic negates the 
 inclusion of any conductive additive or binder and assumes no electronic 
 limitations . during the in situ cycling experiments 
 described above , in which 
 the electrodes were cycled sequentially at rates of 2 , 4 , 6 , 8 , 10 , 
 and 20 c , a reduction in the crystallinity of the active electrode 
 was observed .
note that the peak widths of lifepo4 and 
 fepo4 were observed to be similar in any given pattern 
 throughout the study so this broadening does not affect the phase 
 faction calculations presented above .
however , xrd patterns recorded 
 at the start of discharge at each rate for the 25% electrode do show 
 a clear increase in peak width ( figure .
9a ) . 
 to check whether this breakdown could be caused by x - ray beam damage 
 we recorded patterns at the end of a 2c discharge while the battery 
 was under open circuit conditions for 40 min .
these results showed 
 no discernible degradation of the active material as a function of 
 time exposed to the beam , and since none of our measurements exceeded 
 5 h total collection time it seems unlikely that beam damage is a 
 significant factor .
we also investigated the behavior using ex situ 
 measurements of cells cycled with the same regime used during this 
 in situ test , and two cells cycled at 10c and 2c for the same number 
 of total cycles .
a significant broadening of the fepo4 reflections 
 was observed in the materials which were cycled at a range of different 
 rates ( figure 9b ) but very little extra broadening 
 was observed with either of the fixed cycling rates .
xrd patterns at the start 
 of charge during a sequence of cycles 
 at different rates ( 2c  20c ) , showing the increased peak width 
 ( a ) and the full width half - maximum value of the fepo4 020 
 reflection in patterns recorded ex situ with a fresh electrode , an 
 electrode cycled at a number of different rates ( as per the left - hand 
 image ) , an electrode cycled 10 times at 10c , and an electrode cycled 
 10 times at 2c ( b ) .
we also examined sem 
 images of the electrodes before ( figure 10a ) 
 and after ( figure 10b ) 
 cycling using the multi - rate 
 regime employed for the in situ measurements described above .
no obvious 
 breakdown in particle size can be seen in these images and we therefore 
 suggest that the line broadening is a result of increasing disorder 
 within the crystallites .
this disordering seems to be limited to cases 
 where multiple cycling rates have been applied .
sem images of electrodes 
 containing 25% lifepo4 before 
 ( a ) and after ( b ) cycling under the test regime employed in diamond . 

the results presented above have tracked the 
 formation of concentration gradients within electrodes under high 
 rates of discharge .
the limitations seen are consistent with effects 
 corresponding to an insufficient transport of li ions from the bulk 
 electrolyte through the electrode structure as predicted by sdf theory . 

this confirms that the rate performance of many modern materials used 
 in battery technologies is not a result of the intrinsic properties 
 of the material itself but rather the matrix in which it is stored . 
 in this study ,
this effect is observed in electrodes with relatively 
 dilute amounts of active material where the x - ray absorption is not 
 obscuring measurement .
however , these gradients should be much more 
 pronounced in electrodes with higher concentrations of active material 
 in the electrode ( such as those conventionally used in research laboratories 
 with 75% active material ) and thus the electrochemical rate 
 performance of these systems will be significantly hindered .
the effect 
 should also be far more pronounced in electrode materials which have 
 a much higher volumetric capacity , where the requirement of lithium 
 ions by the material stored in the electrode during discharge will 
 be much larger .
this means that to realize the full rate potential 
 of battery materials the following strategies should be considered : 
 ( 1 ) dilution of the active material ( which reduces the stored energy 
 density ) ; ( 2 ) reducing the electrode thickness ; ( 3 ) increasing the concentration of lithium ions 
 in the electrolyte : the electrolyte concentrations used herein are 
 typical for conventional liquid electrolytes but there are recent 
 reports of more concentrated electrolytes which retain high diffusion 
 rates , these would allow an increase 
 in the amount of lithium initially in the pores c.f .
values given 
 in table 1 ; and ( 4 ) increasing the diffusion 
 coefficient of lithium in the electrolyte .
a new method for the in situ study of battery materials that allows 
 for the visualization of concentration gradients formed in electrodes 
 during discharge is introduced . a significant difference in the performance 
 of the material dependent on whether it is near the bulk electrolyte 
 or current collector is observed . at higher rates of discharge ( > 10 
 c ) the electrode material near the current collector changes at a 
 much slower rate compared with the material close to the bulk electrolyte 
 in cells containing a high concentration of lithium ion vacancies . 

it is believed that this effect is the major limitation in the rate 
 performance of electrodes in conventionally prepared batteries . in parallel
we observed a significant breakdown in crystallinity 
 of the lifepo4 during the electrochemical measurements . 

it was shown that the breakdown is far more significant when the battery 
 is cycled at a range of different rates rather than for the same number 
 of cycles at either a high or low rate . ideally , to obtain the 
 maximum rate out of a battery material of 
 a given particle size and ionic and electronic conductivity we need 
 an electrolyte that can supply the ions at high rates . in some cases 

the particles of the electrode material may be significantly large 
 or the ionic or electronic conductivities sufficiently small such 
 that electrolyte is not limiting the discharge rate .
nevertheless , 
 modern synthesis techniques such as sol  gel and hydrothermal 
 routes mean that synthesis of materials on the nanometre scale is 
 routinely achieved which means that commonly the rate limiting step 
 in the discharge of the battery material even with intrinsically poor 
 electronic and ionic conductivities is the li ion transport through 
 the electrolyte .
 the phase changes that occur during 
 discharge of an electrode comprised 
 of lifepo4 , carbon , and ptfe binder have been studied in 
 lithium half cells by using x - ray diffraction measurements in reflection 
 geometry . 
 differences in the state of charge between the front and 
 the back of lifepo4 electrodes have been visualized . by 
 modifying the x - ray incident angle the depth of penetration of the 
 x 
 - ray beam into the electrode was altered , allowing for the examination 
 of any concentration gradients that were present within the electrode . 
 
 at high rates of discharge the electrode side facing the current collector 
 underwent limited lithium insertion while the electrode as a whole 
 underwent greater than 50% of discharge . 
 this behavior is consistent 
 with depletion at high rate of the lithium content of the electrolyte 
 contained in the electrode pores . increases in the diffraction peak 
 widths indicated a breakdown of crystallinity within the active material 
 during cycling even during the relatively short duration of these 
 experiments , which can also be linked to cycling at high rate . 