Alexander Björling, DLSR7 conference

hi everyone

uh my name is alex i am one of the

beamline scientists

at the nanomax instrument of max4

and i will be talking today about how we

use

the coherent flux that we have available

at the beam line

thanks to the fourth generation storage

ring

so let me spend just a few minutes

introducing the beamline

to you so nanomax is

one of the first beamlines actually to

come online at max4

we've been in user operation since 2017.

it's the only long beam line that we

have at the lab it's 100 meters

source to sample it's a hard

x-ray uh beamline which means we operate

between 6 and 30 kv

usually between them sort of 8 and 15.

and the instrument is designed to

provide

focused and coherent beams of high

quality

with emphasis on coherent flux

we have two end stations at nanomax one

which is in operation now

the diffraction end station located all

the way downstream here

and a second imaging end station which

is

being built now and which will hopefully

come online next year

here's an overview of the diffraction

and station

um it builds on fixed

kb mirrors for focusing and the whole

setup sits on a diffractometer or on a

goniometer

here on this big granite slab

the end station is designed to have a

relatively open and flexible

sample environment so that users can

come with their own

holders or reactors or cells as

illustrated here

and we have a variety of detectors

available so we have

inline detectors in this vacuum tube and

on this

on this detector table here we have a

brag detector mounted on this robot arm

and there's also fluorescence emission

detector sitting closer to the sample

our beam is relatively well described by

now we have a

flux of a fully coherent beam um

which is at least two times 10 to the 10

photon per second 10kb and we've

established that

diffraction limited focusing work so we

have

an energy dependent spot size which is

usually around

100 nanometers of normal operating

energies

i'm not going to say much more about the

beam line now

but if you would like any details

on the setup or ask any questions about

possible experiments

please check out our website or contact

me or any of my colleagues at nanomax

okay so coming to how we utilize the the

coherent plugs that we have access to

um i'd like to divide this question up

into

four different levels ranging from the

sort of trivial and practical

things to more exotic consequences of

having high quality flux so first of all

we do need

a great beam to provide a nano focus in

the first place regardless of whether we

then use the clearance of that beam

for the experiment um it turns out that

it's very

convenient to work with a coherent beam

in terms of characterizing it

and aligning the optics

we can of course make incremental

progress on the current state of the art

so we can do things like coherent

imaging for example

faster or better than what was possible

before

and then i think that we all hope that

there will be qualitative leaps so that

things that were not

possible at all before suddenly are

and i am not the person to say what

those new

types of experiments will be but uh

towards the end of this talk i'll

present a recent pro

a recent project of my own where we look

at

nanoparticles in in new ways

okay so starting with the practical

benefits of of having a coherent beam

as i said we do need a beam to provide a

nano focus

at all so we work with different

diffraction

limited focusing um here's a sketch

of one of our kb mirrors from the side

now the intensity profile that this

focus beam will have

in the focal plane will be proportional

to this squared sync function here

and you can see in the argument that we

have the the numerical aperture which is

the

the width of the mirror uh divided by

the

focal length of the mirror and of course

the beam

has to be coherent across this whole

aperture

um to see this we can imagine dividing

the beam in two

each half of the beam illuminates half

of the mirror

and if we then imagine that these two

sub beams are mutually incoherent of

course

to get the the new focus we would add

these two incoherently so we do an

intensity sum

of two beams each now with half the

numerical aperture

and you can just see that that means

that the sync function will be

half as fast and it will just have

um twice the width okay so

it doesn't matter if we're doing a

coherent imaging experiment

we still need the coherence to produce

the diffraction limited focus

it's also as i mentioned very convenient

to work with a coherent

beam and one of the

ways we we do this is that we use

coherent imaging in the form of

typography

to do our kb mirror alignment

so tychography is a coherent imaging

technique

where we scan a sample through the beam

and by phase retrieval we we get the

complex transmission function of the

sample and we also get the full complex

wavefront of the of the probe

right so we have the beam and phase and

amplitude in a particular plane

and we can propagate that numerically

along the optical axis and then simply

look at the beam

from the sides look at the intensity

distribution from the top and from the

side

and see where the focal are so in this

instance

the two mirrors they don't agree on a

focal plane

which is why the beam looks sort of fun

we have an astigmatic

focus now with our kb mirrors we can

simply adjust the pitch angles of the

mirrors to make them

focus in the same plane we repeat

typography repeat this numerical

exercise

and we now see that we have a stigmatic

focus

where both mirrors look at the same

plane

and we have a nice intensity

distribution

in focus now it's the same here it

doesn't matter if we're actually doing a

coherent

imaging experiment with this beam it's

still very good to have access to the

intensity profile

in the sample plane even if you're doing

for example

scanning fluorescence imaging

so moving beyond the practical and

convenient aspects of having a coherent

beam

let's look at how we can make

incremental progress on the state of the

art of the field

and here i'm going to use coherent

imaging nanotomography

as an example so just for comparison

um i've written down the

what i believe anecdotally is that is

the typical

operating fluxes at two leading

current imaging beam lines in the world

namely po6 et petra

and the sea stacks at the swiss light

source so they typically work in the mid

10th to the 7th whereas as i mentioned

at nanomax we we have what we consider

to be a fully green beam that's 2 times

10 to the 10. so it's a tremendous

step up and flux

now of course these facilities are

upgrading and i haven't even included

the esrf

ebs bmis which are currently in

operation

um but i mean it shows you that we're

looking at a huge

increase in coherent drugs

so what can we do with this in the case

of nanotomography

so there's a trade-off in nanotomography

between resolution

the volume of the sample that you can

look at and the time that this takes

and i've written this down as a sort of

rough scaling relation here

where you can see that the coherent flux

scales inversely with the

time taken for the experiment

and it's also linear scaling between

current flux and

sample volume so that's simple

but if we look at how the resolution

scales

the size of a resolution element in 3d

um actually scales polynomially with

coherent flux and this exponent

is typically like 1 over 5 so it's

pretty expensive

and that means that it's it's not

trivial to achieve

arbitrary resolution just by cranking up

coherent flux right

it is a little bit complicated in

reality of course you do

something between you maybe maybe you

look at

a slightly bigger sample and you do it

slightly quicker

and you get a slightly better resolution

right but i wanted to show this just to

hammer in this point that resolution is

actually really really expensive in

terms of flex

and then of course in reality you

typically have

practical limits in terms of scan speed

overhead

the computing power that you need to

keep up

with a fast experiment the

ability of your sample to tolerate the

intense beam and so on

but of course you can certainly improve

on nanotomography by having

a high appearance so we've been working

towards this

slowly at nanomax this is an example

from my colleague mike

kant who has imaged here

a metallic porous nickel sample

in three dimensions this is done with a

preliminary detector

setup that we've moved on from now so

it's

slightly dated but it shows you where

we're trying to go

so in this experiment mike was able to

use

very short exposures right thanks to the

high chain flux that we have

and what came out was a quantitative

quantitatively correct electron density

in three dimensions

and the resolution limits were well well

behaved so

that means that we understand where the

2d resolution comes from and where the

3d resolution comes from

now this experiment also uncovered

experimental bottlenecks so we had an

inefficient

way of scanning the sample detector

readout was expensive at this point

and we barely kept up with the phase

retrieval of the compute cluster

so we've been working on these practical

aspects quite a lot actually since this

came out

um and i hope that we will be able to

provide a new

benchmark um soon

okay so turning towards experiments that

that were not possible before

i'm going to use a recent project of my

own as an example of this

and it comes from inoperando brag cdi

imaging of

catalysts so the idea here is that you

use

bragg cdi which is a 3d strain imaging

technique

and you image the strain of a single

nanoparticle

as it performs a catalytic function

ideally that would involve absorption on

the surface

that would in turn produce strain in the

underlying lattice

which you could then detect and get

these types of

strain maps or indirect reactivity maps

of single

nanoparticles this was pioneered at the

aps

bmi 34 idc and it's also been done

at the p10 beamline and petra 3.

the problem so far is that there's a

massive gap between the types of

particles that you can study

with brexit the eye and the types of

particles that

are actually relevant for example in

fuel cell

catalysis so particles imaged are on the

hundreds of nanometers

length scale and particles in real

fuel cell catalysts are on the order of

two

five ten managers um

that's okay in principle right because

brag cdi doesn't have an inherent

resolution limit but since the signal

drops quickly with particle size

you can really see how flux or coherent

flux will be important here

looking at the maths it unfortunately

turns out

that the total

counts in a single detector frame

is proportional to the particle diameter

to the fourth

power so it's pretty steep scaling that

we're looking at here

it basically means that if we were to go

from 300 nanometers to 30 nanometers we

would have to pay

a factor of 10 000 in signal

so it's a good idea that we we have a

lot of new current products available

a practical problem here is that um

also work uh pioneered at at bmi 34 idc

the aps

showed uh that under intense

illumination nanopartic nanoparticles

actually

rotate and that can be because of

radiation pressure because of

temperature

but they do they do rotate so in this in

an ideal experiment you would actually

um move by a small rocking rotation you

would move your bracket through the

detector plane in a controlled and

smooth way

but what happens in reality is that the

particle just swings around here

and because this experiment has a high

angular sensitivity

um it's just a completely uncontrolled

experiment

we saw this at nanomax so we looked at

60 nanometer gold particles and we saw

them

going through these uncontrolled

spontaneous rocking curves

we saw this in many instances it just

happened all the time so the beam is

really pushing the particle around

and of course as we make particles

smaller and we make beams more intense

this is going to become more and more of

a problem

so the idea here is

that we'd like to take these movies and

just actually piece them together

and to form coherent diffraction volumes

out of them

so this is the same type of sketch again

instead of moving this diffraction

volume through the detector plane

there are now unknown trajectories in

two angles which

which this bag peak follows

and the question is can we piece this

together to form a coherent diffraction

volume

i won't go into the details here but we

solved this problem in analogy

with a different problem encountered in

free electron lasers

and cdi so this is worked by dwayne lowe

and more recently thomas

where they use maximum likelihood

mechanization to

assemble coherent diffraction volumes

so we did this we got this out in

december in

mprl and

again without going into the details

what we do is that we start with these

movies of particles moving on controller

b

we use the maximum likelihood uh method

that this paper describes to put

together these current diffraction

volumes

then by the way we get the angular

trajectories out so we can actually

reconstruct how the particle was

moving which i think is fantastic and

then sorry

we can use normal phase retrieval

software

in this case pinex from the href

to to retrieve our particles so in this

case we

very clearly retrieve this envelope of

the particle which was a truncated

octahedron which you can see here

and looking at the strain which is what

we're really interested in

several particles gave very similar

strain distributions

on this scale you have a positive strain

around the waist

and two negative poles top and bottom so

this is

very consistent and uh the resolution

is estimated to to somewhere around

10 nanometers so the next step here is

of course to move to

smaller particles get as much green flux

as we can

on these smaller things uh then put this

in an electrochemical

reactor in a cell and do the whole thing

in operando so hopefully we'll be back

with more results on that

okay my time is up um thanks to the

whole uh

nanomax team to everyone involved in the

spontaneous rocking curve work the

organizers of this

of this event for allowing me to talk

get in contact with me have a look at

our website

and get back to me with any questions

that you have

and i'll join you for the questions

session

thank you very much