Chapter 3 (conclusion)

1. Chapter 3 (conclusion) • Silica-containing materials • X-ray diffraction • Applications of single crystals • Polycrystalline materials W.R. Wilcox, Clarkson University, last revised September 17, 2013

2. Silica • The most common elements on earth are Si & O • SiO2 (silica) has 14 polymorphic crystal structures, of which  quartz is the stable phase at room T & P. • http://en.wikipedia.org/wiki/Silicon_dioxide • http://en.wikipedia.org/wiki/Quartz • Also exists as an amorphous phase, "quartz glass" or "fused silica." • The strong Si-O bonds lead to high melting temperatures (>1600ºC) crystobalite (stable above 1470oC)

3. Silicates For example, quartz can be shown as: Bonding of adjacent SiO44- tetrahedra accomplished by the sharing of corners, edges, or faces • Multivalent cations Ca2+, Mg2+, Al3+ ionically bond SiO44- to one another. • Examples: • Mg2SiO4 (Forsterite) with 1895oC melting point. • Ca2MgSi2O7 (Åkermanite) with 1452oC melting point.

4. Layered Silicates • Layered silicates (e.g., clays, mica, talc) • SiO4 tetrahedra connected to form a two-dimensional plane • A net negative charge is associated with each (Si2O5)2- unit • This negative charge is balanced by anadjacent plane rich in positively charged cations

5. Layered Silicates (continued) • Kaolinite clay alternates (Si2O5)2- layers with Al2(OH)42+ layers Adjacent sheets of this type are loosely bound to one another by van der Waal’s forces, and so are easily separated.

6. Silica Glass Structure • Glasses are not crystalline; they are amorphous. • Silica glasses have short-range order, but not long-range order. • Common silica glasses contain Na, Ca, Al, B oxides added to SiO2. • The SiO4 remains the basic building block, but is portrayed in two dimensions as Si bonded to three O. • Fused silica has nothing added: Additives prevent some O from bonding to two Si. This lowers the melting point and the viscosity of the melt. Soda-lime glass is the most common, e.g. for windows.

7. Characterization by X-Ray diffraction • An important family of characterization methods. • They utilize x-ray diffraction for various applications, e.g., identification of a material, obtaining crystal orientation, determination of a structure, viewing defects. See, for example: http://en.wikipedia.org/wiki/X-ray_crystallography • All techniques use a beam of x-rays of a single wavelength λ to strike a sample and a detector for the x-rays coming from the sample. • First explanation was Bragg's Law in 1913 (http://en.wikipedia.org/wiki/Bragg%27s_law) • Consider that crystallographic planes reflect the x-rays:

8. Bragg's Law for X-Ray Diffraction • If diffracted beams from planes AA' and BB' are in phase, they reinforce one another. This occurs when the difference in the distances travelled by the two beams is a whole number n of wavelengths, nλ. The difference here is 2dhklsinθ where h, k and l are the Miller indices of the planes.

9. Bragg's Law • nλ = 2dhklsinθ • As with many "laws" explaining phenomena, this is a simplification of scattering by real atoms. • Nevertheless, it is an excellent first step in interpreting scattering of x-rays. • It is a necessary condition for diffraction, but not always sufficient. • For cubic structures only: • Note that for cubic structures the higher the indices for the planes, the smaller is dhkl, so the larger is θ. • One technique utilizes powder or a polycrystalline solid as the sample, so that very many orientations are exposed to the beam. • The motion of the beam and detector are synchronized:

10. z z z c c c y y y a a a b b b x x x X-Ray Powder Pattern (110) (211) Intensity (relative) (200) Diffraction angle 2q Diffraction pattern for polycrystalline a-iron (BCC)

11. Laue Methods for Single Crystals • Utilize photographic film. • Gives spots, each one of which is for a particular crystallographic plane. • Symmetry of spots reveals the symmetry of the plane normal to the beam.

12. Laue pattern for Mg (0001) Six-fold symmetry: As you go around, the same pattern repeats 6 times.  VMSE

13. http://minerva.union.edu/jonesc/scientific_photos%202010.htm

14. Crystals as Building Blocks • Many modern applications use synthetic single crystals, e.g. integrated circuits (computer chips), solar cells, infrared detectors, x-ray detectors, oscillators, solid-state lasers, light emitting diodes, magneto-optic memory devices, micro electromechanical systems, lenses, hard windows, etc. • Jet engine turbine blades • Many properties of crystals depend on crystallographicdirection, i.e. they are asymmetric. • Most engineering materials are polycrystalline, i.e. they consist of many separate crystals called "grains." • The grains may be randomly oriented or partially aligned, depending on how the material was produced. • Grain sizes range from nm to cm. Some properties depend on grain size. • For small randomly-oriented grains, the macroscopic properties are isotropic.

15. Polycrystalline Example • Electron-beam welded Nb-Hf-W plate. • The small equiaxed grains on the two sides are the original unaffected material. • The elongated grains in the middle result from being melted and refrozen by the electron beam (moved downward here). • The equiaxed grains near the elongated grains have grown larger because of being heated without melting (heat-affected zone). 1 mm