X Ray Diffraction: why to use crystals It is impossible to register the diffusion of X ray from a single molecule: -X ray sources so powerful do not exist -Detectors for X ray photon so sensitive do not exist Therefore we use crystals: -Crystals contain a huge number of molecules -Crystals can be oriented within an X ray beam

X Ray Diffraction: why to use crystals Problems related to the use of crystals as molecule collector: - It is not easy to obtain and isolate single crystals

-Diffraction from a crystal means diffusion from a unit cell, that is a number of molecules (instead of a single molecule) -Crystal is periodic in nature, then diffusion becomes Diffraction. Diffraction is characterized by absence of diffusion mostly along all directions, and maxima of intensity along specific directions): absence of information on the phase differences between the various diffuse waves

X ray Diffraction from a crystal can be seen as reflection of X rays from lattice planes (h,k,l).

X ray Diffraction from a crystal occurs along discrete directions and the geometrical condition defining diffraction can be described by the Bragg Equation.

X Ray Diffraction The periodic nature of crystals is such that from any point r is possible to reach any other point in the crystal, identical for electron density and surrounding, just moving through integer multiply of the same unit cell vector

General overview of steps

Growing a Crystal

Collecting X-ray diffraction pattern

Solving of Phase Problem

Calculate Electron Density Map

Constructing a Structural Model

Refining the Structural Model

Diffractometer

Practical Aspects

How to obtain single crystals

Crystallization: It is basically an art more than a science, however there are several methods to obtain single crystals.

Solubility decreases decreasing T. Cooling down a saturate solution you can obtain single crystals.

Concentration increase: nucleation/crystallization/precipitation can be induced when concentration exceeds solubility.

Soxhlet apparatus evaporation

How to obtain single crystals

Anti-solvent: Solubility in a solvent can be reduced by introducing slowly another solvent in which your compound is not soluble.

Solvent diffusion

How to obtain single crystals

Dimension tra 0.1 – 0.5 mm

Shape - single crystal

- regular

How to mount single crystals

1mm

CRYSTAL SYSTEMand

UNIT CELL DIMENSIONS

FULL DATA SETCOLLECTION

BRAVAIS LATTICE

SPACE GROUP

CONSTRUCT ANELECTRON DENSITY

MAP

LOCATE ATOMPOSITIONS

STRUCTUREREFINEMENT

SELECT A SUITABLECRYSTAL

A

B

C

D

E

F

G

SOLVING A CRYSTAL STRUCTURE BY SINGLE CRYSTAL DIFFRACTION

Bragg's equation specifies that, if a crystal is rotated within a monochromatic X-ray beam, such that every conceivable orientation of the crystal relative to the beam is achieved, each set of planes will have the opportunity to satisfy the Bragg equation and will give rise to reflection.

Diffraction Photograph

Each spot contains information from all atoms! “Pattern of spots” (diffraction pattern) allows determination of crystal parameters (size of unit cell, symmetry within unit cell).

Structural information has to be derived (see below) from difference in spot intensities. ⇒ To obtain enough information, diffraction photographs are taken at various different angles of the crystal in the X-ray beam.

The first important point is to recognize the crystal inner symmetry. Two steps:

-Assigned crystal system

-Assigned space group

Unit Cell and symmetry determination

X-ray source

X-ray detector

Remember reciprocal lattice

The spots spacing define the unit cell (remember the relationship between d spacing and cell parameters)

1/a

1/b

2

2

2

2

2

2

2),,(

1cl

bk

ah

d lkh++=

2

2

2

22

2),,(

)(1cl

akh

d lkh

++

=

2

222

2),,(

)(1a

lkhd lkh

++=

For an orthogonal system (α = β = γ = 90°) the relationship between interplanar spacing (d) and the unit cell parameters is given by the expression:

This is the expression for an orthorhombic crystal. For the tetragonal system it reduces to

and, for the cubic system, it further reduces to

Calculations using X-ray reflections: Indexing

Calculations using X-ray reflections: Indexing

Initial estimates of the unit cell dimensions are made from the positions of the reflections and from the physical parameters of the experiment

Indexing is the process by which reflection indices, hkl, are assigned to the peaks in the diffraction data.

The unit cell parameters and the orientation of the crystal (with known instrument parameters such as crystal to detector distance, λ,..) tell us where the diffraction spots occur on the detector

Calculations using X-ray reflections: Indexing

Indexing involves several distinct processes: The 2D coordinates for each found spot can be mapped (using the Ewald sphere) to scattering vectors that correspond to 3D reciprocal lattice coordinates

D = crystal to detector Distance Xd e Yd = spot coordinates relative to the beam centre on the image s is in dimensionless reciprocal lattice units (r.l.u.) and the radius of the Ewald sphere is unity

),,(

1

lkhdreciprocal lattice measured as Å-1 and a sphere of radius 1/λ Å-1 .

),,( lkhdλ reciprocal lattice measured dimensionless

quantity (r.l.u.) and a sphere of radius 1 r.l.u..