25-08-2017, 09:32 PM

Diffraction Basics

[attachment=57881]

The qualitative basics:

Coherent scattering around atomic scattering centers occurs when x-rays interact with material

In materials with a crystalline structure, x-rays scattered in certain directions will be “in-phase” or amplified

Measurement of the geometry of diffracted x-rays can be used to discern the crystal structure and unit cell dimensions of the target material

The intensities of the amplified x-rays can be used to work out the arrangement of atoms in the unit cell

The Bragg Law “bottom line”:

A diffraction direction defined by the intersection of the hth order cone about the a axis, the kth order cone about the b axis and the lth order cone about the c axis is geometrically equivalent to a reflection of the incident beam from the (hkl) plane referred to these axes.

The Reciprocal Lattice

How do we predict when diffraction will occur in a given crystalline material?

How do we orient the X-ray source and detector?

How do we orient the crystal to produce diffraction?

How do we represent diffraction geometrically in a way that is simple and understandable?

The first part of the problem

Consider the diffraction from the (200) planes of a (cubic) LiF crystal that has an identifiable (100) cleavage face.

To use the Bragg equation to determine the orientation required for diffraction, one must determine the value of d200.

Using a reference source (like the ICDD database or other tables of x-ray data) for LiF, a = 4.0270 Å, thus d200 will be ½ of a or 2.0135 Å.

From Bragg’s law, the diffraction angle for Cu K1 ( = 1.54060) will be 44.986 2. Thus the (100) face should be placed to make an angle of 11.03 with the incident x-ray beam and detector.

If we had no more complicated orientation problems, then we would have no need for the reciprocal space concept.

Try doing this for the (246) planes and the complications become immediately evident.

The Powder Diffraction Pattern

Powders (a.k.a. polycrystalline aggregates) are billions of tiny crystallites in all possible orientations

When placed in an x-ray beam, all possible interatomic planes will be seen

By systematically changing the experimental angle, we will produce all possible diffraction peaks from the powder

[attachment=57881]

The qualitative basics:

Coherent scattering around atomic scattering centers occurs when x-rays interact with material

In materials with a crystalline structure, x-rays scattered in certain directions will be “in-phase” or amplified

Measurement of the geometry of diffracted x-rays can be used to discern the crystal structure and unit cell dimensions of the target material

The intensities of the amplified x-rays can be used to work out the arrangement of atoms in the unit cell

The Bragg Law “bottom line”:

A diffraction direction defined by the intersection of the hth order cone about the a axis, the kth order cone about the b axis and the lth order cone about the c axis is geometrically equivalent to a reflection of the incident beam from the (hkl) plane referred to these axes.

The Reciprocal Lattice

How do we predict when diffraction will occur in a given crystalline material?

How do we orient the X-ray source and detector?

How do we orient the crystal to produce diffraction?

How do we represent diffraction geometrically in a way that is simple and understandable?

The first part of the problem

Consider the diffraction from the (200) planes of a (cubic) LiF crystal that has an identifiable (100) cleavage face.

To use the Bragg equation to determine the orientation required for diffraction, one must determine the value of d200.

Using a reference source (like the ICDD database or other tables of x-ray data) for LiF, a = 4.0270 Å, thus d200 will be ½ of a or 2.0135 Å.

From Bragg’s law, the diffraction angle for Cu K1 ( = 1.54060) will be 44.986 2. Thus the (100) face should be placed to make an angle of 11.03 with the incident x-ray beam and detector.

If we had no more complicated orientation problems, then we would have no need for the reciprocal space concept.

Try doing this for the (246) planes and the complications become immediately evident.

The Powder Diffraction Pattern

Powders (a.k.a. polycrystalline aggregates) are billions of tiny crystallites in all possible orientations

When placed in an x-ray beam, all possible interatomic planes will be seen

By systematically changing the experimental angle, we will produce all possible diffraction peaks from the powder