Characteristic X-ray, x-ray diffraction and spectrometer

Introduction:

Whenever the fast moving electrons strike the metal target of high atomic weight, the electromagnetic radiations coming out, called x-rays.The emitted x-rays can be analysed by the following two ways.

(1) By varying the accelerating potential and keeping the same target.

(2) By keepingg the same acccelerating potential and changing the target.

Taking Tungsten as the target and applied potential of 30kv, 40kv, 50kv and 70kv, the nature of variation of intensity and the wavelenght of emitted x-ray is shown in the figure below. For the applied potential 30kv, 40kv and 50kv, we observe the smooth curve which corresponds to the continuous x-ray spectra. At 70kv, we observe the two peaks over the smooth curve.These peaks corresponds to the characteristic of the atom. The smooth curve represents the continuous x-ray spectra and the curve containing peaks represents the characteristic x-ray spectra.

Fig:-1:X-ray spectra of tungsten at various accelarating potentials

Origin of continuous x-ray spectra:

Whenever the fast moving electrons strike the metal target, then there is the interaction between the electrons and the atom of the target. At approaching the electrons towards the atomic core, it gets deaccelerate. However an accelerated or deaccelerated charge particle lose the energy in the form of radiations. The same principle is applied here. The deaccelerated electrons lose the energy in the form of radiation which corresponds to the continuous x-ray spectra.

The origin of continuous x-ray spectra is the inverse of photoelectric effect. Here, the electrons emits the radiation.

Origin of characteristic x-ray spectra

Whenever the fast moving electrons with an energy equivalent to binding energy of an electron then there is the possibility of ejecting electrons from any of the orbit. Thus, the vaccency is created and this vaccency is filled up by the transition of electrons from any of the highest orbit corresponds to the characteristic x-ray spectra.

For example; after collision of electrons to the atomic target, the gap is created in the shell. These gap is fitted by the transition of electrons from any of the L,M,N,O,..etc orbits. If the gap is filled by the transition of electrons from L shell then this is called \(k_\alpha\)-line.If the gap is filled by the transition of electrons from M shell then this line is called \(k_\beta\)-line and if from N shell then this line is called \(k_\gamma\)-line as in figure above. And similar be the case of \(L_\alpha\),\(L_\beta\),\(L_\gamma\) and so on.

Bragg's Law For X-ray Diffraction

When monochromatic x-ray fall on a crystal, it is scattered by the individuals atoms which are scattered by the individuals atoms which are arranged in the sets of parallel layers. The crystal acts as a series of parallel reflecting planes the. The intensity of the reflected beam at certain angle will be maximum when the path difference betweeen two reflected waves from different planes is an integral multiple of \(\lambda\) .

Consider a set of parallel planes of atom points at a spacing d between two succesive planes. Let a narrow monochromatic x-ray beam of wavelength \(\lambda\) be incident on the first plane at a glancing angle \(\theta\). Consider the ray AB incident on the first plane. The corresponding reflected ray BC must also be inclined at the same angle \(\theta\) to the plane xy. Since x-rays are much more penetrating than ordinary light, there is only partial reflection at each plane. The complete absorbtion takes place only after penetrating several layer. Consider two parallel rays ABC and A'B'C' in the beam which are refeclected by two atoms \(\theta\) and \(\theta\)'. \(\theta\)' is vertically below \(\theta\). The ray A'B'C' has longer path than they ABC. To calculate path difference between two rays from B draw normals BT & BS on A'B' & B'C' respectively.

Then, path difference=TB'+B'S=dsin\(\theta\)+dsin\(\theta\)=2dsin\(\theta\)

Hence,for maximum intensity the path difference between two two reflected rays should be integral multiple of \(\lambda\),then $$2dsin\theta=n\lambda$$where n=1,2,3,4,.....

This is Bragg's law.

Bragg X-ray spectrometer:

The spectometer is a device which is used to analyze the spectra .The Bragg's spectrometer is an X-ray spectrometer which is used to analyze the X-ray spectra. The conservation of X-ray spectrometer similar to that of optical X-ray spectrometer,

The essential part of X-ray spectrometer are

1) The X-ray source

2) A crystal which is held on the circular table of evacuated and which is provided with vernier.

3) An ionisation chamber (Detector)

The X- ray coming from X-ray source are collimated by two narrow slit \(s_1\) & \( s_2 \). Then it entered into the chamber table T in which the X- ray strike with the crystal so that it gets defracted. The defraacted X-ray are then passed to the ionization chamber after passing through the slit \(s_3\) and \(s_4\) as shown in figure above.The ionization current or intensity of diffrated X-ray is measured by electrometer E.

Working:

The x-ray from X-ray tube are incident upon the crystal by galancing angle \(\theta\) . By varying the the galancing angle, the intensity of refracted X-ray is measured by electrometre. As we have known that when a crystal is rotated through an angle \(\theta\), the defracted X-rays are shifted by an angle 2\(\theta\). A graph between the intensity of diffrated X-ray & the galancing angle should be plotted.The nature of grpah is as shown in figure below.This graph is called x-ray spectrum .The prominent peaks \(A _1\), \(A_2\), \(A_3\) refers to the X- ray of wavelength in \(\lambda\).The value of galancing angle \(\theta1\), \(\theta2\), \(\theta3\) corresponding to prominent peaks \(A_1\), \(A_2\), \(A_3\) are measured from the graph.It is found that $$sin\theta1:sin\theta2:sin\theta3:1:2:3$$

This indicates that the prominent peaks \(A_1\), \(A_2\), \(A_3\) coressponds to the primary,secondar,tertiary maximum.The peaks \(B_1\), \(B_2\), \(B_3\) coresspondence to the first order ,second order and third order maximum for the x-ray of wavelength \(\lambda2\).

CALCULATION OF WAVELENGTH:

As we know, from the Bragg's law;$$2dsin\theta=n\lambda$$where;d=Bragg's spacing or lattice spacing,\(\theta\)=galancing angle corresponding to order of diffration n, \(\lambda\)=wavelength of diffrated X-ray

If the value of d is known,then the value of \(\theta\) can be easily calculated by uisng the formula $$2dsin\theta=n\lambda$$Hence, by using the Bragg's X-ray spectrometer,the wavelength of X-ray can be calculated.

References:

Adhikari, P.B, Daya Nidhi Chhatkuli and Iswar Prasad Koirala. A Textbook of Physics. Vol. II. Kathmandu: Sukunda Pustak Bhawan, 2012.

Jenkins, F.A and H.E White. Fundamental of optics. New York (USA): McGraw-Hill Book Co, 1976.

wood, R.W. Physical Optics. New York (USA): Dover Publication , 1934.