Crystal Structure By Means Of X Ray Diffraction Engineering Essay

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X-Ray Crystallography is an analytical method in which x-ray diffraction patterns are used to determine the three-dimensional arrangement of atoms in a crystal. Many crystal used for x-ray crystallography are less than 1 millimeter in diameter.

X-ray crystallography is a method of determining the arrangement of atoms within a crystal, in which a beam of X-rays strikes a crystal and diffracts into many specific directions

X-rays are electromagnetic radiation with wavelengths between about 0.02 Šand 100 Š(1Š= 10-10 meters).  They are part of the electromagnetic spectrum that includes wavelengths of electromagnetic radiation called visible light which our eyes are sensitive to (different wavelengths of visible light appear to us as different colors).  Because X-rays have wavelengths similar to the size of atoms, they are useful to explore within crystals.

The energy of X-rays, like all electromagnetic radiation, is inversely proportional to their wavelength as given by the Einstein equation:

E = hn = hc/l

where E = energy

h = Planck's constant, 6.62517 x 10-27 erg.sec

n = frequency

c = velocity of light = 2.99793 x 1010  cm/sec

l = wavelength

Thus, since X-rays have a smaller wavelength than visible light, they have higher energy.  With their higher energy, X-rays can penetrate matter more easily than can visible light.  Their ability to penetrate matter depends on the density of the matter, and thus X-rays provide a powerful tool in medicine for mapping internal structures of the human body (bones have higher density than tissue, and thus are harder for X-rays to penetrate, fractures in bones have a different density than the bone, thus fractures can be seen in X-ray pictures).

X-rays are produced in a device called an X-ray tube.  Such a tube is illustrated here.  It consists of an evacuated chamber with a tungsten filament at one end of the tube, called the cathode, and a metal target at the other end, called an anode.  Electrical current is run through the tungsten filament, causing it to glow and emit electrons.  A large voltage difference (measured in kilovolts) is placed between the cathode and the anode, causing the electrons to move at high velocity from the filament to the anode target.  Upon striking the atoms in the target, the electrons dislodge inner shell electrons resulting in outer shell electrons having to jump to a lower energy shell to replace the dislodged electrons.  These electronic transitions results in the generation of  X-rays.  The X-rays then move through a window in the X-ray tube and can be used to provide information on the internal arrangement of atoms in crystals or the structure of internal body parts.

Continuous and Characteristic X-ray Spectra

When the target material of the X-ray tube is bombarded with electrons accelerated from the cathode filament, two types of X-ray spectra are produced.  The first is called the continuous spectra

The continuous spectra consists of a range of wavelengths of X-rays with minimum wavelength and intensity (measured in counts per second) dependent on the target material and the voltage across the X-ray tube.  The minimum wavelength decreases and the intensity increases as voltage increases.

The second type of spectra, called the characteristic spectra, is produced at high voltage as a result of specific electronic transitions that take place within individual atoms of the target material.

This is easiest to see using the simple Bohr model of the atom.  In such a model, the nucleus of the atom containing the protons and neutrons is surrounded by shells of electrons.  The innermost shell, called the K- shell, is surrounded by the L- and M - shells.  When the energy of the electrons accelerated toward the target becomes high enough to dislodge  K- shell electrons, electrons from the L - and M - shells move in to take the place of those dislodged.

Each of these electronic transitions produces an X-ray with a wavelength that depends on the exact structure of the atom being bombarded.  A transition from the L - shell to the K- shell produces a Ka X-ray, while the transition from an M - shell to the K- shell produces a Kb X-ray.  

 

These characteristic X-rays have a much higher intensity than those produced by the continuous sprectra, with Ka X-rays having higher intensity than Kb X-rays.  The important point here is that the wavelength of these characteristic x-rays is different for each atom in the periodic table (of course only those elements with higher atomic number have L- and M - shell electrons that can undergo transitions to produce X-rays).  A filter is generally used to filter out the lower intensity Kb X-rays.

For commonly used target materials in X-ray tubes, the  X-rays have the following well-known experimentally determined wavelengths:

Element

KaWavelength (l) Å

Mo

0.7107

Cu

1.5418

Co

1.7902

Fe

1.9373

Cr

2.2909

Choice of Radiation

Most X-ray tubes used for diffraction studies have targets (anodes) made of copper or molybdenum metal. The characteristic wavelengths and excitation potentials for these materials are shown below. Copper radiation is preferred when the crystals are small or when the unit cells are large. Copper radiation (or softer) is required when the absolute configuration of a compound is needed and the compound only contains atoms with atomic numbers & 10. A copper source is preferred for most types of powder diffraction.

Molybdenum radiation is preferred for larger crystals of strongly absorbing materials and for very high resolution, sin (θ) / λ < 0.6 Å, data. The scintillation point detectors, often used in small molecule diffraction, have somewhat higher quantum efficiencies for molybdenum radiation than for copper radiation. Because the diffraction spots are closer together for molybdenum radiation than for copper radiation, molybdenum is the preferred radiation source when using area detectors to study small molecules. The solid angle coverage of most area detectors is such that with molybdenum radiation, it is usually possible to collect an entire data set with the detector sitting at a single position. However, because a brighter incident beam of X-rays is produced from a copper tube than from a molybdenum tube at the same power level, very small crystals of even strongly absorbing materials will often yield better diffracted intensities from copper radiation than from molybdenum radiation.

Occasionally, other types of target materials, e.g. Cr, Fe, W, or Ag, are chosen for specialized diffraction experiments. Sources with Cr or Fe targets are often chosen when protein crystals are very small or when anomalous differences need to be enhanced. When samples are very strongly absorbing or when extremely high resolution data are needed then X-ray tubes with sources such as W or Ag are usually selected.

Table 1. Selected X-Ray Wavelengths and Excitation Potentials.

Cr

Fe

Cu

Mo

Z

24

26

29

42

Kα1, Å

 2.28962 

 1.93597 

 1.54051 

 0.70932 

Kα2, Å

 2.29351 

 1.93991 

 1.54433 

 0.71354 

Kαave, Å

 2.29092 

 1.93728 

 1.54178 

 0.71073 

Kβ, Å

 2.08480 

 1.75653 

 1.39217 

 0.63225 

β filter

Ti

Cr

Ni

Nb

Resolution, Å

1.15

0.95

0.75

0.35

Excit. Pot. (kV)

5.99

7.11

8.98

20.0

K-beta emissions, similar to K-alpha emissions, result when an electron transitions to the innermost "K" shell (principal quantum number 1) from a 3p orbital of the second or "M" shell (with principal quantum number 3).

In X-ray spectroscopy, K-alpha emission lines result when an electron transitions to the innermost "K" shell (principal quantum number 1) from a 2p orbital of the second or "L" shell (with principal quantum number 2). The line is actually a doublet, with slightly different energies depending on spin-orbit interaction energy between the electron spin and the orbital momentum of the 2p orbital. K-alpha is typically by far the strongest X-ray spectral line for an element bombarded with energy sufficient to cause maximally intense X-ray emission.

Traditionally, either Mo or Cu X-ray wavelengths are used in most Small Molecule applications and Cu X-rays are used exclusively in Protein Crystallography. Agilent Technologies (formerly Oxford Diffraction) pioneered co-mounted dual wavelength systems to enable the user to carry out a range of diverse experiments, for a number of different applications. For an absolute configuration study, the information required is in the small differences in the anomalous scattering signal, usually observed in reflections collected at the highest resolution. The heavier the elements found in the sample, the bigger this difference becomes, and this is multiplied by using Cu radiation over Mo.

The Bohr Model has an atom consisting of a small, positively-charged nucleus orbited by negatively-charged electrons.

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