1 APPLIED PHYSICS CODE : 07A1BS05 I B.TECH CSE, IT, ECE & EEE UNIT-1: CHAPTER 2.2 NO. OF SLIDES : 20

2 S.No.ModuleLecture No. PPT Slide No. 9Braggs law.L Laue methodL powder method.L UNIT INDEX UNIT-I

3 X-Ray Powder Diffraction Lecture-10

4 Diffraction Methods X-Ray Powder diffraction Instrument geometries Lecture-10

5 X-Ray Powder Diffraction (XRPD) is one of the most powerful techniques for analyzing the crystalline nature of solids. XRPD capabilities include micro- diffractometry, flat plate or capillary sample configuration, spinning and rocking methods, variable temperature and humidity conditions, and a unique sample conveyor system to overcome sample inhomogeneity effects. Lecture-10

6 XRPD is perhaps the most widely used X-ray diffraction technique for characterizing materials. As the name suggests, the sample is usually in a powdery form, consisting of fine grains of single crystalline material to be studied. The technique provides information that cannot be obtained any other way. The information obtained includes types and nature of crystalline phases present, structural make-up of phases, degree of crystallinity, amount of amorphous content, microstrain & size and preferred orientation of crystallites. The technique is also used for studying particles in liquid suspensions or polycrystalline solids (bulk or thin film materials). Lecture-10

7 The term 'powder' means that the crystalline domains are randomly oriented in the sample. Therefore, when the 2-D diffraction pattern is recorded, it shows concentric rings of scattering peaks corresponding to the various d spacings in the crystal lattice. The positions and the intensities of the peaks are used for identifying the underlying structure (or phase) of the material. This phase identification is important because the material properties are highly dependent on structure (think, for example, of graphite and diamond). Lecture-10

8 Powder diffraction data can be collected using either transmission or reflection geometry, as shown below. If the particles in the powder sample are randomly oriented, both methods will yield the same results. Lecture-10

9 Single crystal diffraction Laues method - variable, fixed. Rotating crystal method - fixed, variable to some extent. Why not single crystal methods? It may be difficult to obtain a single crystal. The usual form of a material may be polycrystalline. Problems with twinning or phase transitions complicate structural assignments. Lecture-10Lecture-10 Lecture-10

10 Powder diffraction In this method the crystal is reduced to a fine powder and is placed in a beam of monochromatic X-rays. Each particle is a tiny crystal or an assemblage of smaller crystals randomly oriented with respect to the the incident beam. Powder methods - fixed, variable. Lecture-11

11 The diagram shows only two scattering planes, but implicit here is the presence of many parallel, identical planes, each of which is separated from its adjacent neighbor by a spacing d. Constructive interference occurs when (A+B)/ = n, coinciding with Braggs law, n = 2dsin. The integer n refers to the order of diffraction. For n = 1, (A+B) = and for n = 2, (A+B) = 2 etc. Lecture-11

12 Angles are used to calculate the interplanar atomic spacings (d-spacings). Because every crystalline material will give a characteristic diffraction pattern and can act as a unique fingerprint, the position (d) and intensity (I) information are used to identify the type of material by comparing them with patterns for over 80,000 data entries in the International Powder Diffraction File (PDF) database, complied by the Joint Committee for Powder Diffraction Standards (JCPDS). By this method, identification of any crystalline compounds can be made even in complex samples. Lecture-11

13 Lecture-11 The position (d) of the diffracted peaks also provides information about how the atoms are arranged within the crystalline compound (unit cell size or lattice parameter). The intensity information is used to assess the type and nature of atoms. Determination of lattice parameter helps understand extent of solid solution (complete or partial substitution of one element for another, as in some alloys) in a sample. The d and I from a phase can also be used to quantitatively estimate the amount of that phase in a multi-component mixture. The width of the diffracted peaks is used to determine crystallite size and micro-strain in the sample.

14 If the sample consists of tens of randomly oriented single crystals, the diffracted beams are seen to lie on the surface of several cones. Lecture-11

15 Instrument geometries There are several ways of collecting XRPD patterns: Camera methods: Guinier, Debye-Scherrer, Gandolfi, Lecture-11

16 The Debye – Scherrer powder camera A photographic film is placed around the inner circumference of the camera body. The incident beam enters through a pinhole and almost the whole diffraction pattern is recorded simultaneously. At the point of entrance the angle is 180 and at the exit the angle is 0. Lecture-12

17 Pinhole source Film located on camera body Rod shaped sample Sample rotates to give better randomness Almost complete angular range covered Lecture-10Lecture-10 Lecture-12

18 View of an instrument Lecture-12

19 Lecture-10 Lecture-12

20 X-Ray Powder Diffraction Instruments Lecture-10Lecture-10 Lecture-12