X Ray Diffraction © D Hoult 2009.

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Presentation transcript:

X Ray Diffraction © D Hoult 2009

Some x ray are

Some x ray are

Some x ray are reflected or

Some x ray are reflected or diffracted or

Some x ray are reflected or diffracted or scattered by the first layer of atoms

Other parts of the incident beam are diffracted by the next layer of atoms (and lower layers)

path difference =

path difference = 2 d sin q

path difference = 2 d sin q If this path difference is equal to

path difference = 2 d sin q If this path difference is equal to nl then the two sets of waves will interfere constructively

When x rays are diffracted (reflected, scattered) by the atoms in a crystal we will find maxima at angles given by

When x rays are diffracted (reflected, scattered) by the atoms in a crystal we will find maxima at angles given by n l = 2 d sin q

When x rays are diffracted (reflected, scattered) by the atoms in a crystal we will find maxima at angles given by n l = 2 d sin q This is known as the Bragg equation

What is the distance between these nuclei ?

Mass of 1 mol of Na Cl =

Mass of 1 mol of Na Cl = 58.5 g Density of Na Cl =

Mass of 1 mol of Na Cl = 58.5 g Density of Na Cl = 2.2 g cm-3

Mass of 1 mol of Na Cl = 58.5 g Density of Na Cl = 2.2 g cm-3 Volume of 1 mol of Na Cl =

Mass of 1 mol of Na Cl = 58.5 g Density of Na Cl = 2.2 g cm-3 Volume of 1 mol of Na Cl = 2.66 × 10-5 m3

Mass of 1 mol of Na Cl = 58.5 g Density of Na Cl = 2.2 g cm-3 Volume of 1 mol of Na Cl = 2.66 × 10-5 m3 This volume contains

Mass of 1 mol of Na Cl = 58.5 g Density of Na Cl = 2.2 g cm-3 Volume of 1 mol of Na Cl = 2.66 × 10-5 m3 This volume contains 6.02 × 1023 Na Cl pairs

Mass of 1 mol of Na Cl = 58.5 g Density of Na Cl = 2.2 g cm-3 Volume of 1 mol of Na Cl = 2.66 × 10-5 m3 This volume contains 6.02 × 1023 Na Cl pairs Volume associated with each pair is

Mass of 1 mol of Na Cl = 58.5 g Density of Na Cl = 2.2 g cm-3 Volume of 1 mol of Na Cl = 2.66 × 10-5 m3 This volume contains 6.02 × 1023 Na Cl pairs Volume associated with each pair is 4.42 × 10-29 m3

Volume associated with each ion is 2.21 × 10-29 m3

Therefore the length of the side of one of these cubes is

Therefore the length of the side of one of these cubes is the cube root of this volume

d = 2.8 × 10-10 m

So the separation between layers of ions in the crystal is also d = 2 So the separation between layers of ions in the crystal is also d = 2.8 × 10-10 m

Separation between layers of ions = 2.8 × 10-10 m

Separation between layers of ions = 2.8 × 10-10 m Calculate the first two angles at which diffraction maxima would be observed using x-rays of wavelength

Separation between layers of ions = 2.8 × 10-10 m Calculate the first two angles at which diffraction maxima would be observed using x-rays of wavelength l = 1.5 × 10-10 m

Separation between layers of ions = 2.8 × 10-10 m Calculate the first two angles at which diffraction maxima would be observed using x-rays of wavelength l = 1.5 × 10-10 m

Separation between layers of ions = 2.8 × 10-10 m Calculate the first two angles at which diffraction maxima would be observed using x-rays of wavelength l = 1.5 × 10-10 m about 15° and

Separation between layers of ions = 2.8 × 10-10 m Calculate the first two angles at which diffraction maxima would be observed using x-rays of wavelength l = 1.5 × 10-10 m about 15° and about 32°

Typical results of an x ray diffraction measurement