where it all begins: powder...
TRANSCRIPT
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)
Wednesday, April 14, 2010
Where it All Begins:
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
Where it All Begins:
Powder Diffraction
Wednesday, April 14, 2010
Where it All Begins:
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)
Wednesday, April 14, 2010
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.
Wednesday, April 14, 2010
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)
Wednesday, April 14, 2010
Pair distribution Function (PDF)
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
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)
Wednesday, April 14, 2010
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
!
Create a structural model that allows direct analysis of real space.
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)
Wednesday, April 14, 2010
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.
Pair distribution Function (PDF)
Wednesday, April 14, 2010
Not a Completely New Idea...B. E. Warren, N. S. Gingrich.
Physical Review 46, 368 (1934)
Wednesday, April 14, 2010
Not a Completely New Idea...B. E. Warren, N. S. Gingrich.
Physical Review 46, 368 (1934)
Wednesday, April 14, 2010
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
Wednesday, April 14, 2010
Resurgence...
With increasing availability of computer resources and high energy experimental sources, the PDF began to be applied to crystalline materials
Wednesday, April 14, 2010
Resurgence...
Wednesday, April 14, 2010
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.
Wednesday, April 14, 2010
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.
Wednesday, April 14, 2010
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.
Correlations
between Carbon
Atoms in C60
Correlations between
C60 smeared due to
rotation of molecules
Wednesday, April 14, 2010
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
Wednesday, April 14, 2010
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.
Wednesday, April 14, 2010
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
Wednesday, April 14, 2010
Why Large Qmax?
G(r) = 4!r"0(g(r) #1) =
2
!Q S Q( ) #1$% &'
0
Q max
( sin Qr( )dQ
“Termination
Ripples”
Wednesday, April 14, 2010
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/
Wednesday, April 14, 2010
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).
Wednesday, April 14, 2010
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)
Wednesday, April 14, 2010