Bulk Structural Analysis

Apurva Mehta

J. Stubbs

J. Lezama Pacheco

M. Michel

Outline

Peak Shape & Width:

crystallite size

Strain gradient

Peak Positions:

Phase identification

Lattice symmetry

Lattice strain

Peak Intensity:

Structure solution

Crystallite orientation

Apurva

Joanne

Juan

Marc

Misra

Joanna

Outline

Peak Shape & Width:

crystallite size

Strain gradient

Peak Positions:

Phase identification

Lattice symmetry

Lattice strain

Peak Intensity:

Structure solution

Crystallite orientation

Q1

Q0

QD

Scattering from a Single crystal

4

Ewald’s Sphere

Q1

Diffraction for Polycrystals

5

Ewald

Sphere

Reciprocal

Sphere

s

s

Deformation of Reciprocal Sphere

Strain Ellipsoid

χ

Q0

s s

Q

Coordinate Transformation

Q

c

χ

Q

Experimental Setup – 11-3 SSRL

X-ray Beam

Detector

Sample

DIC Camera

Sample

Dogbone

Force Transducer

3 mm

Strain Determination

110 200 211

c c

Q (nm-1) Q (nm-1)Q (nm-1)

c

110 Em = 167 GPa

0.3

400

300

200

100

0

Str

ess

(MP

a)

0-.10 .05 .05 .10 .15 .20 .25

% Strain

00

Pois

son’s

Rat

io

Stress (MPa) 400

eyyezz

shear

1

200 211Em = 211 GPa Em = 218 GPa

Elastic Strain Tensors for Iron

eyy

ezz

Outline

Peak Shape & Width:

crystallite size

Strain gradient

Peak Positions:

Phase identification

Lattice symmetry

Lattice strain

Peak Intensity:

Structure solution

Crystallite orientation

Strain Gradient : example

Outline

Peak Shape & Width:

crystallite size

Strain gradient

Peak Positions:

Phase identification

Lattice symmetry

Lattice strain

Peak Intensity:

Structure solution

Crystallite orientation

Structure Solution

Single Crystal

Protein Structure

Sample with heavy Z problems Due to

Absorption/extinction effects

Mostly used in Resonance mode

Site specific valence

Orbital ordering.

Powder

Due to small crystallite size kinematic equations valid

Many materials can not be readily prepared in single-crystal form: their structures obtained via synchrotron powder diffraction

Peak overlap a problem – high resolution setup helps

Much lower intensity – loss on super lattice peaks from small symmetry breaks. (Fourier difference helps)

Diffraction from Polycrystals

Long range order ----> diffraction pattern periodic

crystal rotates ----> diffraction pattern rotates

From 4 crystallites

From Powder

Powder Pattern

Loss of angular information

Not a problem as peak

position = fn(a, b & a )

Peak Overlap :: A problem

But can be useful for precise lattice parameter measurements

J. Lezama will explore

this further

Diffraction Physics

FT FT

S e2pi (risin(2q)/l)

A(DK) = fi

S ei (ri Q)

A(DK) = fi

A(Q) = Fhkl = Fourier Transform ( ri )

ei (r Qi)

A(r) = FhklSA(Q )/Fhkl is a complex number

We measure A(Q ) * A(Q )

amplitude but not the phase of

A(Q ) is known

Phase Problem

Amplitude unknown Phase Unknown

-200 0 200 400 600 800 1000 1200 1400 1600

-1.0

-0.5

0.0

0.5

1.0

-200 0 200 400 600 800 1000 1200 1400 1600

-1.0

-0.5

0.0

0.5

1.0

0 200 400 600 800

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

1+1

1+ 0.5

0 200 400 600 800

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0 + 45

0 + 0

Solution to Phase Problem

Phase/Structure must be guessed

And then refined.

How to guess?

Heavy atom substitution, SAD or MAD

Structure with one stronge scatterer – e.g. U in Phosphates matrix - Stubbs

Similarity to homologous compounds, e.g. NaCl KCl

Patterson function or pair distribution analysis.

M. Michel

Inverse Modeling Method 1

Reitveld Method Data

ModelRefined Structure

40 60 80 100 120 140 160

0

1000

2000

3000

4000

5000

6000

7000

Inte

nsity

q

Profile

shape

Background

Inverse Modeling Method 2

Fourier Method Data

ModelRefined Structure

40 60 80 100 120 140 160

0

1000

2000

3000

4000

5000

6000

7000

Inte

nsity

q

Profile

shape

Background

subtract

phases

Integrated

Intensities

Fhkl

Fhkl

Inverse Modeling Methods

Rietveld Method

More precise

Yields Statistically reliable uncertainties

Fourier Method

Picture of the real space

Shows “missing” atoms, broken symmetry, positional disorder

Should iterate between Rietveld and Fourier.

Be skeptical about the Fourier picture if Rietveld refinement does not significantly improve the fit with the “new” model.