Studies of atomic scale diffusion by X-ray photon correlationspectroscopy

M. Stana∗1, M. Ross1 and B. Sepiol1

1Universität Wien, Fakultät für Physik, Boltzmanngasse 5, 1090 Wien, Austria∗markus.stana@univie.ac.at

1 Theoretical background

Solving the rate equation for discrete atomicjumps on a Bravais lattice yields a correlationtime τ(�q):

τ(�q) = τ0SRO(�q)�

npn�

Δ�rnj

�1−exp�i�q ·Δ�rnj�� (1)

n ... number of neighboring shell

pn ... jump probability to certain position in nth shell

Δ�rnj ... relative jump vector to jth position in nth shell

�q ... scattering vector

SRO ... short-range order intensity in Laue units

For a coherent methodlike XPCS short-range or-der plays a role, hencethe SRO in Eq. (1).

Δ�rnj depends on lattice constant d and the sym-metry of lattice. �q depends on the parametersdescribed below. For a certain choice of such pa-rameters an inverse correlation time 1/τ(�q) canbe calculated (here bcc).

1/τ(�q) (∝ Hz)

Images on the right show different jump mech-anisms without SRO-correction (1/τinc) (top) andcorrected with SRO shown above (bottom).

12

12

12 jumps: 1 0 0 jumps: 1 1 0 jumps: 1 1 1 jumps:

2 Experiment

A CCD camera is used to collect a series ofimages from a detail of reciprocal space corre-sponding to a certain �q and for a certain T:

�q= �kout− �kin

Variable parameters in the experiment:

• scattering vector �q

scattering angle 2Θazimuthal angle φ| �kin|= | �kout|∝ Ephoton

• temperature T• sample orientation relative to k̂in• exposure time → frame rate

Different atomic configurations in real space yielddifferent intensities in the diffuse regime (here in(100) plane):

intensity

time

=1 2 3 4 5 6 7

CCD images for different t at particular �q are used tocalculate the Intensity Autocorrelation function:

g(2)(�q,Δt) =⟨(�q,t)(�q,t+Δt)⟩⟨(�q,t)⟩2 = 1+βexp

�−2

Δt

τ(�q)

�(2)

0.9

1

1.1

1.2

1.3

0 600 1200 1800 2400 3000

g(2

) (q,

Δt)

Time lag Δt (s)

3 Results for Fe55Al45

Projection of model for121212 - jumps. Models from

section 1 (SRO(�q) = 1)compared with φ-scan at2θ=20◦ for Fe55Al45 bi-nary intermetallic alloy[1]:

[1] Data measured at PETRA III at E = 7 keV, 2Θ =20◦ and T = 653 K

(preliminary results).

1

1.5

2

2.5

-90 -60 -30 0

1/τ

(10

-3 s

-1)

ϕ (°)

1/2 1/2 1/2 jumps1 0 0 jumps1 1 0 jumps1 1 1 jumps

Without SRO - correction 111 jumps appear to be thedominating process.

Arrhenius plot of aXPCS data in comparison to litera-ture values acquired by different techniques:

10−23

10−21

10−19

10−17

10−15

10−13

10−11

0.6 0.8 1.0 1.2 1.4 1.6

1100 900 800 700 600 500 450 400

D (

m2 s

−1)

1/T (10−3

K−1

)

T (°C)

Fe52Al48 measured with tracer diffusion technique (59Fe) [2]

Fe50.5Al49.5 measured with QMS [3]

Fe55Al45 measured with QMS [4]

Fe55Al45 measured with aXPCS [5]

D=D0 exp�

EakBT

�

[2] M. Eggersmann and H. Mehrer, Phil. Mag. A 80:5, 1219 (2000)[3] G. Vogl and B. Sepiol, Acta metall. mater. 42, 3175 (1994)[4] R. Feldwisch, B. Sepiol and G. Vogl, Acta metall. mater. 43, 2033 (1995)[5] preliminary data

As atomic-scale X-ray Photon Correlation Spec-troscopy (aXPCS) is a coherent method, it re-quires information about short-range order inthe system. Reliable SRO measurements aretherefore essential for data evaluation.aXPCS is a valuable tool to determine atomicdiffusion mechanisms. It is applicable over awide range of temperatures being only limitedby CCD-readout times and intensity towardsfast processes and by setup and system sta-bility towards slow processes. This allows forinvestigations at relatively low temperaturesthat were unaccessible to any other atomisticmethod so far. Furthermore there is no limita-tion to special isotopes.

We thank Y. Chushkin and the whole team of beamline ID10A atthe ESRF in Grenoble and M. Sprung and the team of beamlineP10 at PETRA III in Hamburg.

This research was funded bythe Austrian Science Fund(FWF) contract P-22402.