Atomic and Nuclear Physics LEYBOLD Physics X-ray physics Leaflets P6.3.3.1 Physics of the atomic shell Bragg reflection: diffraction of x-rays at a monocrystal Objects of the experiment To investigate Bragg reflection at an NaCI monocrystal using the characteristic x-ray radiation of molybdenum. To determine the wavelength for the characteristic K and Kg x-ray radiation of molybdenum. To confirm Bragg's law of reflection. To verify the wave nature of x-rays. Principles In 1913.H.W.and W.L.Bragg realized that the regular arrangement of atoms and/or ions in a crystal can be under- stood as an array of lattice elements on parallel lattice planes. When we expose such a crystal to parallel x-rays,additionally assuming that these have a wave nature,then each element in nλ=2dsin9 a lattice plane acts as a "scattering point",at which a spherical wavelet forms.According to Huygens,these spherical wave- 9 lets are superposed to create a "reflected"wavefront.In this model,the wavelength A remains unchanged with respect to the "incident"wave front,and the radiation directions which are perpendicular to the two wave fronts fulfill the condition "angle of incidence angle of reflection". Constructive interference arises in the rays reflected at the individual lattice planes when their path differences A are integral multiples of the wavelength A. △=n-λwith n=1,2,3, 0 As Fig.1 shows for two adjacent lattice planes with the spacing 10 30 d,we can say for the path differences A1 and A2 of the incident and reflected rays with the angle △1=△2=d.sin8 so that the total path difference is △=2.d.sin8. 0 (1)and(lI)give us Bragg's law of reflection: n.λ=2.d.sin8 0 The angle is known as the glancing angle In this experiment,we verify Bragg's law of reflection by investigating the diffraction of x-rays at an NaCl monocrystal in which the lattice planes are parallel to the cubic surfaces of the unit cells of the crystal.The lattice spacing d of the cubic eObjects of the experiment To investigate Bragg reflection at an NaCl monocrystal using the characteristic x-ray radiation of molybdenum. To determine the wavelength for the characteristic Ka and Kβ x-ray radiation of molybdenum. To confirm Bragg’s law of reflection. To verify the wave nature of x-rays. Bragg reflection: diffraction of x-rays at a monocrystal 0308-Ste Atomic and Nuclear Physics X-ray physics Physics of the atomic shell P6.3.3.1 LEYBOLD Physics Leaflets Principles In 1913, H. W. and W. L. Bragg realized that the regular arrangement of atoms and/or ions in a crystal can be under￾stood as an array of lattice elements on parallel lattice planes. When we expose such a crystal to parallel x-rays, additionally assuming that these have a wave nature, then each element in a lattice plane acts as a “scattering point”, at which a spherical wavelet forms. According to Huygens, these spherical wave￾lets are superposed to create a “reflected” wavefront. In this model, the wavelength l remains unchanged with respect to the “incident” wave front, and the radiation directions which are perpendicular to the two wave fronts fulfill the condition “angle of incidence = angle of reflection”. Constructive interference arises in the rays reflected at the individual lattice planes when their path differences D are integral multiples of the wavelength l. D = n ⋅ l with n = 1, 2, 3, … (I) As Fig. 1 shows for two adjacent lattice planes with the spacing d, we can say for the path differences D1 and D2 of the incident and reflected rays with the angle q: D1 = D2 = d ⋅ sin q so that the total path difference is D = 2 ⋅ d ⋅ sin q. (II) (I) and (II) give us Bragg’s law of reflection: n ⋅ l = 2 ⋅ d ⋅ sin q (III) The angle q is known as the glancing angle. In this experiment, we verify Bragg’s law of reflection by investigating the diffraction of x-rays at an NaCl monocrystal in which the lattice planes are parallel to the cubic surfaces of the unit cells of the crystal. The lattice spacing d of the cubic 1