Beware of potential confusion: students will have met the formula for diffraction by a (transmission) grating. (Alternatively, use gratings with different spacing.)ĭiscussion – optional: Deriving Bragg’s law Observe that the separations of the diffracted beams increase as the effective slit width decreases. Now rotate the grating about a vertical axis. Shine a laser beam at normal incidence onto a grating and note the separation of the diffracted beams. Demonstration: Diffraction of laser light crystal models You could also point out that a single crystal gives a pattern of discrete dots a polycrystalline material or powder gives rings (because all orientations are present), and an amorphous material gives blurred rings or dots. This means that diffraction patterns can be used to determine the arrangement of atoms within a solid, and their separations. Emphasise the idea that, the narrower the spacing, the greater the diffraction. Hence X-rays will be diffracted by planes of atoms in crystalline solids. The wavelengths of X-rays are comparable to the atomic spacing in solid matter. To investigate matter on a smaller scale requires that we look at it using shorter wavelengths. This limit comes about because of diffraction effects, when the wavelength is comparable to physical dimensions. The shortest wavelength of visible light ~ 450 nm ( 450 × 10 -9 m) sets a limit for the smallest thing that can be seen using visible light. Students can learn about how X-rays were discovered, and how they are used.Įpisode 530-1: What are X-rays? (Word, 28 KB) Discussion: Diffraction and the limits of resolution If a typical wavelength is 1 nm, what is the frequency of such an X-ray? Rehearse students’ assumed knowledge of X-rays. Discussion and student questions: Students’ knowledge of X-rays Note that students who are also studying chemistry may already have come across Bragg’s law. Student activity: Chemical composition by X-ray analysis (20 minutes).Demonstrations: Various analogues of X-ray diffraction (30 minutes).Demonstration: Crystal spacing by X-rays (30 minutes).Discussion – optional: Deriving Bragg’s law (20 minutes).Demonstrations: Diffraction of laser light crystal models (20 minutes).Discussion: Diffraction and the limits of resolution (20 minutes).Discussion and student questions: Students’ knowledge of X-rays (30 minutes). ![]() A 4-peak comparison (2 ferrite/2 austenite) can also be made giving a standard deviation of the 4 comparisons.Most schools will not have an X-ray set, but there are plenty of effective analogue demonstrations using other types of waves (laser light, microwaves, and water waves). ![]() This comparison can be done on as little as one peak from each phase. Γ-iron: a FCC (face centered cubic) austenite phase.īy measuring the integrated intensity of the diffracted peaks from each phase and correcting by the diffracting conditions using R-factors, a direct comparison can be made between the corrected integrated intensity ratios and the ratio of Austenite to ferrite/martensite. Α-iron: a combination of BCC (body centered cubic) ferrite and/or a BCT (Body centered tetragonal) martensite, the two phases are generally indistinguishable by X-ray diffraction In the case of heat treated low alloy steels, there are 2 phases present The irradiated area affects the measurement time using a larger collimator reduces the needed time to make measurements. Measurements are usually fast lasting from few minutes to an hour. These can be used to calculate the planar principal stresses. This slope along with the materials linear elastic parameters (Modulus and Poisson’s ratio) allows for the calculation of the residual stress in the direction parallel to the plane we are tilting in.īy then rotating the goniometer or the sample around the measurement location in 2 additional direction (usually 0˚, 45˚ and 90˚) will give three stress values known directions. This gives linear distribution of d vs sin 2c. Using a combination of a material’s known crystal structure and the X-ray tubes characteristic radiation, a suitable diffracted peak with a favorable diffraction intensity and a high 2θ value (2θ>130˚) can be selected for performing measurements.Īssuming a planar stress state in the measured volume, the d-spacing normal to the surface can be used as an unstrained spacing, eliminating the need for an unstrained d value of the sample.Ĭomparing this 2θ/d-spacing information as the measuring head is tilted away from normal shows us the strain through the change in d-spacing in that direction. Residual stress determination from the X-ray diffraction data
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