Near-edge X-ray refraction fine structure microscopyMaryam Farmand, Richard Celestre, Peter Denes, A. L. David Kilcoyne, Stefano Marchesini, Howard Padmore,Tolek Tyliszczak, Tony Warwick, Xiaowen Shi, James Lee, Young-Sang Yu, Jordi Cabana, John Joseph,Harinarayan Krishnan, Talita Perciano, Filipe R. N. C. Maia, and David A. Shapiro

Citation: Appl. Phys. Lett. 110, 063101 (2017); doi: 10.1063/1.4975377View online: http://dx.doi.org/10.1063/1.4975377View Table of Contents: http://aip.scitation.org/toc/apl/110/6Published by the American Institute of Physics

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Near-edge X-ray refraction fine structure microscopy

Maryam Farmand,1 Richard Celestre,1 Peter Denes,1 A. L. David Kilcoyne,1

Stefano Marchesini,1 Howard Padmore,1 Tolek Tyliszczak,1 Tony Warwick,1 Xiaowen Shi,1,2

James Lee,1,2 Young-Sang Yu,1,3 Jordi Cabana,3 John Joseph,4 Harinarayan Krishnan,5

Talita Perciano,5 Filipe R. N. C. Maia,6 and David A. Shapiro1,a)

1Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA2Department of Physics, University of Oregon, Eugene, Oregon 97401, USA3Department of Chemistry, University of Illinois at Chicago, Chicago, Illinois 60607, USA4Engineering Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA5Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA6Laboratory of Molecular Biophysics, Uppsala University, SE-751 24 Uppsala, Sweden

(Received 8 November 2016; accepted 15 December 2016; published online 6 February 2017)

We demonstrate a method for obtaining increased spatial resolution and specificity in nanoscale

chemical composition maps through the use of full refractive reference spectra in soft x-ray spec-

tro-microscopy. Using soft x-ray ptychography, we measure both the absorption and refraction of

x-rays through pristine reference materials as a function of photon energy and use these reference

spectra as the basis for decomposing spatially resolved spectra from a heterogeneous sample,

thereby quantifying the composition at high resolution. While conventional instruments are lim-

ited to absorption contrast, our novel refraction based method takes advantage of the strongly

energy dependent scattering cross-section and can see nearly five-fold improved spatial resolution

on resonance. Published by AIP Publishing. [http://dx.doi.org/10.1063/1.4975377]

Soft x-ray spectro-microscopy is a powerful analytical

technique for quantitative chemical and morphological char-

acterization of materials, which can probe electronic states of

matter with high specificity and spatial resolution.1–8 It

also offers the added advantage of higher material penetration

and potentially less radiation damage than other spectro-

microscopy techniques such as electron energy loss spectros-

copy (EELS).9 In traditional scanning transmission x-ray

microscopy (STXM), the sample is raster scanned through a

focused x-ray beam and at each point the total transmitted

intensity is measured as a function of photon energy in

the vicinity of atomic resonances, which enables the extrac-

tion of spatially resolved near-edge x-ray absorption fine

structure (NEXAFS) spectra. Although the material contrast

may change dramatically with energy, following the energy

dependence of the materials’ refractive indices, the achieved

spatial resolution for STXM is essentially constant with the

x-ray spot size. Alternatively, x-ray ptychography can pro-

vide spatial resolution significantly finer than the spot size

through phase-retrieval based inversion of x-ray diffraction

data, which can be recorded to a numerical aperture far

larger than is technically feasible to manufacture in x-ray

optics.10–15 Since the energy dependence of the coherent scat-

tering cross-section is also dominated by the variation of a

material’s refractive index near an atomic resonance, the scat-

tered signal and hence the achieved spatial resolution as well

as the chemical contrast can be dramatically enhanced.

X-ray ptychography is conceptually similar to STXM,

except that a full diffraction pattern is measured at each

sample scan position and the x-ray wavefield exiting the

sample is subsequently reconstructed numerically by a

phase retrieval algorithm. When the scan positions overlap

sufficiently, there is a high data redundancy that makes phase

retrieval through iterative reconstruction possible and yields

the local complex transmission function, both absorption and

phase shift, of the sample as well as the complex illumina-

tion function.10 Rather than the optical point spread function,

ptychographic spatial resolution is instead limited primarily

by the angular extent of the measurable diffraction pattern.

This, in turn, depends upon the material refractive index,

n ¼ 1� dþ ib (with b related to absorption and d to disper-

sion) that is strongly energy dependent in the vicinity of

atomic resonances. Of course, additional experimental fac-

tors, such as relative sample and probe positioning accuracy,

can reduce the spatial resolution but they are straightforward

to establish at the nanometer scale.

For a broad class of materials, the increased sensitivity

to relative phase shift that ptychography brings can result

in higher fidelity chemical composition maps and hence

better quantification. Indeed, previous work has demon-

strated chemical contrast in ptychographic imaging via both

absorption and phase16 as well as measurements of the full

refractive index of heterogeneous materials as a function of

energy.13,15,17–19 These works, however, do not achieve

quantitative chemical analysis of materials, which requires

comparison with independently measured reference spectra

that are used as the basis for expansion of mixed spectra.20,21

Here, we present a novel method of chemical mapping from

ptychographic reference spectra, that is, measurements of dand b as a function of energy, which achieves higher spatial

resolution and higher chemical specificity than conventional

methods because of the availability of the full complex

refractive index. Such spectra are measured for multiple pris-

tine materials and used to map composition in a heteroge-

neous sample. We also quantify by numerical simulation

how the ptychographic spatial resolution depends on energya)dashapiro@lbl.gov

0003-6951/2017/110(6)/063101/5/$30.00 Published by AIP Publishing.110, 063101-1

APPLIED PHYSICS LETTERS 110, 063101 (2017)

near an atomic resonance. The achieved spatial resolution

presents a maximum at the energies that have the most nega-

tive phase shift relative to vacuum, or rather, the maximum

phase difference relative to non-resonant material.

We choose pristine and partly delithiated nanoparticles of

LiFePO4 as a model system because it is widely studied as the

cathode material in state-of-the art Li-ion batteries and it is

known to undergo a two phase separation upon discharge and

delithiation to FePO4.22–26 The two chemical phases can be

readily identified using soft x-rays by probing the Fe redox

state, which is reduced by the presence of Li and results in a

2p3=2 transition shifted lower by 2 eV. The delithiation mecha-

nism of LiFePO4 has been the subject of numerous theoretical

and experimental studies, and soft x-ray ptychography is par-

ticularly useful as a characterization tool for this material since

monitoring the separation of phases in single crystals requires

a spatial resolution below 10 nm and high chemical sensitiv-

ity.19,27 Reference spectra for pristine LiFePO4 and FePO4

were measured around the Fe L2 and L3 edges, with an energy

step of 0.25 eV, at the Advanced Light Source (ALS) x-ray

bending magnet beamline 5.3.2.1. Since measurement of the

complex spectra is tied to the ptychographic imaging process,

it requires measuring a three dimensional dataset by imaging

the pure material at multiple energies and then extracting an

average spectrum from a region of interest (ROI). The pristine

standard samples are in the form of agglomerates of nano-

plates with dimensions of 100� 80� 20 nm3. For brevity,

images of only the LiFePO4 sample are shown in Figure 1 at

two energies: (a) pre-edge at 700 eV and (b) on the absorption

resonance at 708 eV with resolutions of 14 and 9 nm, respec-

tively, using Fourier Ring Correlation (FRC) with a half-bit

threshold. Since the material scattering strength is nearly an

order of magnitude higher on resonance, the diffraction pattern

extends to larger angles and the image presents higher spatial

resolution with the plate thickness resolved. Figure 2 shows a

comparison of the calculated and measured refractive spectra

obtained from the full set of images. The calculated spectra

derive the real part of the refractive index from a Kramers-

Kronig inversion of independently measured bulk NEXAFS

spectra. All spectra were normalized by first subtracting the

pre-edge data to minimize thickness effects and then scaling

to unity optical density on the absorption resonance. As can

be seen, the experimental and calculated data do follow the

same general trend, but there is significant deviation in the

phase component, with both additional fine structure and

differences in relative peak heights being apparent. These dif-

ferences are likely due to a combination of the improved sensi-

tivity of ptychographic measurements, imperfect calculation

of the phase via Kramers-Kronig inversion over a finite energy

range, and subtle saturation effects in the spectra. Since calcu-

lated d values are only numerical estimations based on bobtained from experimental NEXAFS spectra, the experimen-

tal ptychographic spectra should be more accurate and detailed

features not accessible through calculation are now

FIG. 1. Experimental ptychographic

scattering contrast images of the pris-

tine LiFePO4 standard sample recorded

at the pre-edge energy of 700 eV (a)

and on the absorption resonance of

708 eV (b). The image recorded on the

absorption resonance shows higher res-

olution such that the individual par-

ticles with 20 nm thickness can be

resolved (inset). (c) FRC curves for the

images in (a) and (b). The data were

split in half columnwise for the resolu-

tion analysis.

063101-2 Farmand et al. Appl. Phys. Lett. 110, 063101 (2017)

observable. We define here the scattering contrast coefficient,

c2 ¼ ðd2 þ b2Þ=k2, which is related to the cross-section for

coherent scattering and allows us to account for the full refrac-

tive contrast with a single real number.28 We note the similar-

ity between this coherent scattering contrast function and the

contrast function defined for resonant soft x-ray scattering

(RSOXS).29 The scattering contrast spectra are shown in

Figure 2 and present two well-defined peaks, at 708 eV and

710 eV, thus providing for quantitative chemical specificity.

To experimentally examine chemical composition map-

ping with refractive reference spectra, an agglomerate of par-

tially discharged LixFePO4 (x� 0.5) was imaged. This

agglomerate consists again of nano-plates electrochemically

discharged to a 50% state of charge. Figures 3(a) and 3(b)

show two ptychographic images of the agglomerate at

708 eV and 710 eV, respectively. The red and blue arrows

point to regions rich in LiFePO4 and FePO4, respectively;

note that as expected regions rich in LiFePO4 exhibit high

(white) contrast at 708 eV and as the energy is increased to

710 eV, their contrast decreases sharply (the reverse is true

for regions rich in FePO4). Hence, using a ptychographic

stack of images, measured at multiple energies, the energy

dependent scattering contrast can be extracted. The individ-

ual complex valued images can be converted to a real num-

ber, W, which is proportional to the scattering contrast and

has the same functional form as the optical density (2pbt=k,

traditionally used for chemical mapping)

W ~xð Þ ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi�ln

jw ~xð Þjjw0j

!" #2

þ Im ln w ~xð Þ� �� �2

vuut ¼ 2pct ~xð Þ;

where wð~xÞ ¼ w0ei2ptðib�dÞ=k is the complex valued x-ray

wavefield exiting the sample, w0 is the average value of the

portion of the image unobstructed by the sample (i.e., the

incident wavefield propagated through a distance of vacuum

FIG. 2. Measured reference spectra for

LiFePO4 (red, Fe 2þ) and FePO4 (blue,

Fe 3þ). The ptychographic spectra

(solid lines) show the same general

trend as the conventional spectra

(dashed lines) but exhibit significant

differences in the phase component.

Conventional absorption spectra are

obtained by NEXAFS measurements

while the conventional phase spectra

are calculated via a Kramers-Kronig

inversion of the absorption spectra.

Bottom: scattering contrast spectra for

the two components relative to vacuum

(red and blue) and relative to each

other (black dashed). The two well

resolved peaks provide the chemical

specificity required for quantitative

chemical composition mapping.

FIG. 3. (a) and (b) Experimental scattering contrast images of partially dis-

charged cathode agglomerate (50% state of charge) at two energies with

peak contrast for the two components (708 for LiFePO4 and 710 for FePO4).

The arrows point to Lithium rich (red) and Lithium poor (blue) regions. (c)

Chemical composition map of the agglomerate obtained through mapping

the experimental total contrast spectra of the two components. (d) R-factor

map of the linear fitting shown in (c).

063101-3 Farmand et al. Appl. Phys. Lett. 110, 063101 (2017)

equal to the sample thickness, assumed flat), k is the x-ray

wavelength, and tð~xÞ is the unknown map of the material

thickness. Following the method of Lerotic, thickness effects

can be removed from the composition maps through a com-

bination of principal component analysis and singular value

decomposition.20,21 Figure 3(c) shows the chemical compo-

sition map obtained in this fashion. The R-factor distribution

indicates very good agreement between the measured data

and the fit to the reference spectra (supplementary material).

Since the exact solution for an arbitrary sample cannot

be known, the use of a simulated structure makes it straight-

forward to visualize and quantify the energy dependence of

resolution and contrast. To investigate the variation of reso-

lution with energy, a series of simulations were carried out,

with a three-component system resembling that of the

LiFePO4/FePO4/50% mixed state. Figure 4 shows the recon-

structed resolution as a function of energy along with a plot

of the energy dependent scattering contrast. All reconstruc-

tions contained the same number of incident photons. It is

interesting to note that the maximum image resolution occurs

at an energy slightly below the total contrast peak and the

resolution of the chemical map is similar while being nearly

a factor of five higher than the off-resonance resolution. The

peak falls at the energy of the most negative phase shift rela-

tive to vacuum, which yields the maximum phase contrast

relative to the non-resonant material and points to phase con-

trast being a primary driver in ptychographic image resolu-

tion. The spatial resolution of the off-resonant images could

be improved simply with increased x-ray exposure time (to

compensate for weaker scattering contrast) but this result

indicates that is not necessary as the resolution of the chemi-

cal map is driven largely by the energies where the optical

constants vary rapidly.

In conclusion, soft x-ray ptychography is a powerful

characterization technique that can offer both a higher spatial

resolution than traditional x-ray transmission microscopy

and also the capability to simultaneously map x-ray absorp-

tion and phase contrast of a material. The large phase shifts

and strong energy dependence near atomic resonances play

an important role not only in achieving high spatial resolu-

tion at single energies but also within the chemical composi-

tion map derived from multiple energies. This work

establishes refraction-based spectro-microscopy, which can

provide important insight into different materials characteri-

zation applications. For instance, in resonant soft x-ray scat-

tering (RSOXS) techniques, usually d is calculated through

the Kramer-Kronig inversion of b values obtained from

NEXAFS measurements.30 X-ray refraction microscopy can

readily provide experimental d and b values for any given

morphology with high spatial and energy resolution com-

pared to calculated values, hence acting as a powerful com-

plementary technique.

See supplementary material for a brief description of the

experimental system and data analysis protocol.

Soft X-ray ptychographic microscopy was carried out at

beamline 5.3.2.1 at the Advanced Light Source. The

Advanced Light Source is supported by the Director, Office

of Science, Office of Basic Energy Sciences, of the U.S.

Department of Energy under Contract No. DE-AC02-

05CH11231. This work was partially supported by the

Center for Applied Mathematics for Energy Research

Applications (CAMERA), which is a partnership between

Basic Energy Sciences (BES) and Advanced Scientific

Computing Research (ASRC) at the U.S. Department of

Energy. Partial support was also provided by the Northeast

Center for Chemical Energy Storage, an Energy Frontier

Research Center funded by the U.S. Department of Energy,

Office of Science, Office of Basic Energy Sciences under

Award Number DE-SC0012583.

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