where it all begins: powder...

$: Where it All Begins: Powder Diffractionsces.phys.utk.edu/~dagotto/condensed/HW2_2010/Niedziela_LAS... · That’s Great, But... • Many materials have local disorder which gives$
Local Atomic Structure

Analysis Using The Atomic

Pair Distribution Function

Jennifer Niedziela, April 15, 2010, [email protected]

Condensed Matter II, Spring, 2010, Lecturer: Elbio Dagotto

Wednesday, April 14, 2010

Where it All Begins:

Powder Diffraction

Bragg Diffraction - Proc. Cambridge Phil. Soc. (1913)



Powder DiffractionPowder Diffraction makes it possible

to determine the average structure

of materials by generating a map of

reciprocal space from the

interference scattering

B AO

C

y x

z

Can build a model of the

structure for refinement

Structure

Fit

Difference between

Model and Fit

Impurity!

Diffraction

Data


Powder Diffraction



Powder Diffraction

• Diffraction is the first stop in most

materials characterization.

• Important tool in the condensed matter

physicists toolbox.

• Rietveld refinement an industry

standard. (Rietveld, J. Appl. Cryst. 2, 65, (1969)


That’s Great, But...

• Many materials have local disorder

which gives rise to important

properties, which can’t be easily seen in

crystalline diffraction.

• Limited usefulness for amorphous

materials.

• Completely breaks down at nanoscale.


Pair distribution Function (PDF)

G(r) = 4!r"0(g(r) #1) =

2

!Q S Q( ) #1$% &'

0

Q max

( sin Qr( )dQ

d! c Q( )d"

=b

2

N# Q( )

2

=1

Nb$bµe

iQ(R$ %Rµ )

$ ,µ

&Diffraction

experiment measures coherent SCS:

! Q,t( ) =1

bb"e

iQR" t( )

"

#Sample Scattering Amplitude:

b =1

Nb!

!

"

Q = k!

i" k f

!

Total Scattering Function: S Q( ) =

I Q( )

b2

I Q( ) =d! c Q( )

d"+ b

2

# b2

T. Egami and S. J. L. Billinge, Underneath the

Bragg Peaks, Pergammon (2003)



G(r) = 4!r"0(g(r) #1) =

2

!Q S Q( ) #1$% &'

0

Q max

( sin Qr( )dQ

PDF gives the probability of finding two atoms a distance r apart within a solid, and retains all information about diffuse scattering.

d! c Q( )d"

=b

2

N# Q( )

2

=1

Nb$bµe

iQ(R$ %Rµ )

$ ,µ

&Diffraction


! Q,t( ) =1

bb"e

iQR" t( )

"


b =1

Nb!

!

"

Q = k!

i" k f

!


I Q( )

b2

I Q( ) =d! c Q( )

d"+ b

2

# b2





G(r) = 4!r"0(g(r) #1) =

2

!Q S Q( ) #1$% &'

0

Q max

( sin Qr( )dQ

d! c Q( )d"

=b

2

N# Q( )

2

=1

Nb$bµe

iQ(R$ %Rµ )

$ ,µ

&Diffraction


! Q,t( ) =1

bb"e

iQR" t( )

"


b =1

Nb!

!

"

Q = k!

i" k f

!

Create a structural model that allows direct analysis of real space.


I Q( )

b2

I Q( ) =d! c Q( )

d"+ b

2

# b2




Create a structural model that allows direct analysis of real space.

IronBody Centered Cubica=b=c=2.87 Angstroms

2.485\A

2.87\A4.05\A

Height of PDF peaks correspond to the probability of encountering an atom at a distance from another atom.



Not a Completely New Idea...B. E. Warren, N. S. Gingrich.

Physical Review 46, 368 (1934)


Not a Completely New Idea...B. E. Warren, N. S. Gingrich.

Physical Review 46, 368 (1934)


Not a Completely New Idea...

B. E. Warren, N. S. Gingrich. Physical Review 46, 368 (1934)

Beevers-Lipson stripsfor performing calculations

King’s College Archives


Resurgence...

With increasing availability of computer resources and high energy experimental sources, the PDF began to be applied to crystalline materials


Resurgence...


Fullerenes

• C60 carbon allotrope.

• Materials with a complex

structure.

• Form into fcc-like lattice.

• Different information regarding

the intra-and inter-particle

distances evident.

• PDF data used as basis for new

methods of calculating

nanomaterial structures.


Fullerenes



structure.




distances evident.





Fullerenes



structure.




distances evident.




Correlations

between Carbon

Atoms in C60

Correlations between

C60 smeared due to

rotation of molecules


Iron Selenide Superconductors

•Crystallographically, Fe,Se share same atomic site.

•PDF analysis shows that the Fe, Se atoms have distinct atomic

positions in the structure, which does not appear in the

average crystallographic data.

•Important implications for the local magnetism in the materials,

since the iron spin state is strongly impacted by the distance

from the pnictide atom according to theory calculations.

M. C. Lehman, 0909.0480v1


Experimental Concerns

• PDF data can be collected with X-rays or neutrons.

• Neutron data are easier to interpret, and can obtain a wider range in momentum transfer for higher quality data. Need a lot of sample, and require long counting times for sufficient statistics due to signal limitations of neutron scattering.

• X-rays are easier to find and require much less sample and much shorter counting times, but the structure factor drops off steeply, preventing large q-range studies.


Experiments

High Intensity Powder Diffractometer (HIPD)Used 153 degree bank for Rietveld and PDFQ max = 60 Å-1

S(Q) damped to zero at 35 Å-1

Data collected ~3 hrs/pointOptimally doped Co

Neutron Powder Diffractometer (NPDF)Used 90 degree bank for RietveldUsed all banks for PDFQ max = 50 Å-1

S(Q) damped to zero at 35 Å-1

Data collected ~ 3.5 hrs/pointOverdoped Co, All P doped measurements


Why Large Qmax?

G(r) = 4!r"0(g(r) #1) =

2

!Q S Q( ) #1$% &'

0

Q max

( sin Qr( )dQ

“Termination

Ripples”


Software and Tools

Groups working full time to produce and support software for PDF analysis.

Part of DANSE package sponsored by NSF.

PDFGetN, PDFGetX2 for producing PDF from raw scattering data.

PDFGui for analysis of PDF data.

TotalScattering.org: http://nirt.pa.msu.edu/


For more Information

Underneath the Bragg Peaks. T. Egami and S.

J. L. Billinge, Pergammon Press (2003)

Local Structure from Diffraction. S. J. L. Billinge

and M. F. Thorpe. Fundamental Materials

Research (1998).

Zeitschrift fur Krystallographie 219, 122 (2004).


References[1] W. L. Bragg, Proc. Cambrige Phil. Soc. 17 (1913).

[2] S. J. L. Billinge and M. F. Thorpe, Local Structure from Di!raction (Fundamental Materials Research, 1998).

[3] T. Egami and S. J. L. Billinge, Underneath the Bragg Peaks (Pergammon Press, 2003).

[4] H. M. Rietveld, J. Appl. Cryst. 2, 65 (1969), URL http://www.ccp14.ac.uk/ccp/ web-mirrors/hugorietveld/xtal/paper2/

paper2.html.

[5] B. Warren and N. Gingrich, Physical Review 46, 368 (1934).

[6] S. J. L. Billinge, Zeitschrift fur Kristallographie 219, 117 (2004).

[7] W. Dmowksi, B. Toby, T. Egami, M. Subramanian, J. Gopalakrishnan, and A. Sleight, Phys.Rev. Lett. 61, 2608

(1988).

[8] H. W. Kroto, J. R. Heath, S. C. O!Brien, R. F. Curl, and R. E. Smalley, Nature 318, 162 (1985).

[9] P. Juh´as, D. M. Cherba, P. M. Duxbury, W. F. Punch, and S. J. L. Billinge, Nature 440, 655 (2006).

[10] T. Yildirim, Phys. Rev. Lett. 102, 037003 (2009).

[11] C.-H. Lee, A. Iyo, H. Eisaki, H. Kito, M. T. Fernandez-Diaz, T. Ito, K. Kihou, H. Matsuhata, M. Braden, and K.

Yamada, J. Phys. Soc. Jpn. 77, 083704 (2008).

[12] M. C. Lehman, D. Louca, K. Horigane, A. Llobet, R. Arita, N. Katayama, S. Konbu, K. Nakamura, P. Tong, T.-Y.

Koo, et al., arXiv cond-mat.supr-con (2009), 0909.0480v1, URL http://arxiv.org/abs/0909.0480v1.

[13] T. Pro!en, T. Egami, S. Billinge, A. Cheetham, D. Louca, and J. Parise, Applied Physics A: Materials Science &

Processing 74, s163 (2002).

[14] B. H. Toby and S. J. L. Billinge, Acta Crystallogr A Found Crystallogr 60, 315 (2004).

[15] P. Peterson, M. Gutmann, T. Pro!en, and S. J. L. Billinge, J. Appl. Cryst. 33, 1192 (2000).

[16] X. Qiu, J. Thompson, and S. J. L. Billinge, J. Appl. Cryst. 37, 678 (2004).

[17] C. Farrow, P. Juhas, J. Liu, D. Bryndin, E. S. Bozin, J. Bloch, T. Pro!en, and S. Billinge, J. Phys.: Condens. Matter

19, 335219 (2007).

[18] T. Egami, Zeitschrift fur Kristallographie 219, 122 (2004).

[19] Beevers-Lipson Strips. King!s College, London. http://www.kcl.ac.uk/about/history/archives/dna/individuals/

dna0305pic02.html (2010)


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