Module 2 X Ray Diffraction

PHL654X-ray Diffraction (XRD)

Reading materials:-

Chapter 7:

T. L. Alfrod, L. C. Feldman and J. W. Mayer, Fundamentals of NanoscaleFilm Analysis, Springer, 2007.

Reference Book:

B. D. Cullity and S. R. Stocks, Elements of X-ray diffraction , Prentice-Hall.

Crystal structure determination.

Effect of temperature on crystal structure

Precise lattice parameter determination

Determination of crystallite sizes from macro-nano dimension.

Strain analysis.

Alloy formation.

Objectives..

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Source:http://www.ndt-ed.org/EducationResources/CommunityCollege/Materials/Graphics/QuartzGlass.jpgQuasicrystalIntroduction revisitedPHL654

Braggs law in real spacePHL654----- (1)

PHL654Crystal structure1. Lattice and Basis

PHL654TriclinicMonoclinicOrthorhombicHexagonalRhombohedralPrimitive (P): lattice points on the cell corners only. Body (I): one additional lattice point at the center of the cell. Face (F): one additional lattice point at the center of each of the faces of the cell. Base (A, B or C): one additional lattice point at the center of each of one pair of the cell faces.Cubic2. Bravais Lattices in 3D Crystal structureTetragonal

Exercise 1: XRD and data analysis of a powder sample (Cubic)PHL654Geometry..Typical spectrum

Continued..Analysis of BCC and FCC structurePHL654

Continued..PHL654---- (2)Does a crystal has many values of a0 ?

BCCFCCContinued..PHL654Allowed reflections: h+k+l:evenAllowed reflections: h,k,l unmixed(all even or all odd)

Exercise 2: XRD and data analysis of Hexagonal crystalPHL654Two lattice parameters: a, cAllowed reflections: h+2k = 3N (N: integer) and l: odd - AbsentAll others are present

Previous week..Importance of X-ray diffraction

Main objectives of XRD

Crystal structure (BCC, FCC and hexagonal) determination (for known samples)PHL654BCCFCCHexagonal

Crystal structure using JCPDS datasheet (For information only)PHL654

Continued..JCPDS of NaCl (For information only)PHL654

Continued..How to distinguish Cu2O and CuO? (For information only)PHL654

PHL654How to distinguish Cu2O and CuO? (For information only)

PHL654How to identify structure of a completely unknown sample?(For information only)Steps to be followed:

Exercise 3: Coefficient of thermal expansion PHL654---- (3)

Exercise 4: Precise determination of lattice parameterLattice spacing (d) and lattice Parameter (a) varies with Sin.

Sin varies with , having differenterror for different .

Leads to error in d and a.

Task: How to determine true valueof a?PHL654

Bradley Jeans functiona = a0 +a0K Cos2Ref: B. D. Cullity Shortcoming: Extrapolation of random data points varies from person to personCohens method PHL654

Exercise 5: Crystallite size and lattice strain analysisPHL654---Scherer FormulaBstrain = tanComment:-Both crystallite size andStrain leads to broadeningof XRD peak

Task:-How to decouple them?

BCC, FCC and Hexagonal structure reviewed.

Determination of crystal structure using JCPDS (for information only)

Temperature effect on lattice parameter.

Precise determination of lattice parameter.

Determination of crystallite size and lattice strain.

Previous week..PHL654

Exercise 6: Mixing of two compoundsFactors influencing XRD intensityPHL654Task: Take 100% pure MgO powder sample. Add 20, 40, 60 and 80mol% of NiO. Heat treat this mixtures at 1500 0C for 8 h and slowly cool this mixture to room temperature. How can you distinguish theseMixtures structurally?Structure factorMultiplicity factorTemperature factorLorentz polarization factor

Frequently asked questions (FAQs)Session 1What is the difference between a single crystal, a polycrystal, a nanocrystal and an amorphous material?

Define oriented structure and epitaxial growth.

Grain boundaries exist in amorphous materials. Yes/No.

Each plane of a crystal is uniquely defined by which quantity?

Why X-ray is suitable for crystal structure determination?

How XRD pattern look like for a single crystal, a polycrystal a nanocrystal and an amorphous form a same material?

7. How can you distinguish a simple cubic and a body centred cubic structure by looking at XRD patterns?

8. What do you exactly mean by the term Indexing of x-ray pattern?

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XRD Instrumentation (For information only)PHL654

A base-centered cubic crystal has two atoms per unit cell located at 000 and 0 positions. What will be the intensity of diffracted x-ray from this structure when miller indices are mixed? The two x-ray lines K and K are diffracted from a crystalline plane. If the diffraction angle corresponding to second one is known, how do you get the same for the first one?

Why the best value of a is expected at an angle close to 900?

XRD peak broadening is only due to instrumental error. Yes/No.

Suppose you dont know the error of the instruments in your XRD set up. Can you suggest an diffraction experiment only to obtain the instrumental error.

Frequently asked questions (FAQs)Session 2PHL654

Tutorial session based on Practical Examples:Q1. Determine a and c values of Mg (Hexagonal, c/a = 1.624) from the given first six reflections: 2 32.16, 34.38, 36.60, 47.80, 57.36, 63.05. [X-ray: CuK]

Q2. Using method of least squares, determine the best straight line through the followingfour points. x = 10 18 30 42 y = 15 11 11 8

Q3. Al crystal (FCC) is studied by CuK x-rays. The following reflections are observed.

hkl

56.017K133156.232K233158.291K142058.523K242068.735K142269.107K2422

Determine a for each reflection. Using Cohens method calculate the precise value of a.

Q4. An FCC crystal gives following first four reflections.2 38.51, 44.77, 65.15 78.26. Peak broadening dye to crystallite size and lattice strain(Br: in radians) corresponding to these lines are, (2.8, 3.4, 4.4, 5.5 )x 10-3 respectively.Calculate crystallite size (along z direction).

Q5. In a NaCl crystal (a cubic lattice) 4 Na and 4 Cl atoms per unit cells are located as follows:

Na000 0 0 0

Cl 0000 00

Show that the intensity of diffracted x-ray for mixed indices is zero and for unmixed indicesis finite.