# Chapter 3. Crystalline Structure Seven Systems and Fourteen Lattices Metal Structures Ceramic Structures Polymeric Structures Semiconductor Structures.

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Chapter 3. Crystalline Structure Seven Systems and Fourteen Lattices Metal Structures Ceramic Structures Polymeric Structures Semiconductor Structures Lattice Positions, Directions, and Planes X-Ray Diffractions

Structure Review In solid state, particles are bonded together in rigid, crystalline structure. Seven basic crystalline structures are: –cubic: BCC, and FCC –tetragonal: Simple T and BCT –orthorhombic: simple, Body CO, Base CO, and FCO –rhombohedral –hexagonal: hexagonal close packed, FCC closed packed, complex cubic structure (diamond structure) –monoclinic: simple and base-centered –triclinic Each crystal system has a different axis length and angles that separate the atoms –Table 3.1

Structure Review Defining components of a general crystal system –lengths of the axes (lattice constants) are a, b, and c –angles between the atom planes are  (alpha),  (beta), and  (gamma) Components of the crystalline structure z x y b a c   

Miller Index Defining particular plane of the atom with Miller Index 3 steps to determine the Miller Index –Find the intercepts x = 2, y = 3, and z = 2 from figure –Take the reciprocal of the axis length, 1/2, 1/3, and 1/2 –Find the lowest common multiplier and then multiply the reciprocal –Then, the Miler Index is (3, 2, 3)…… 6*1/2, 6*1/3, 6*1/2.. Note ( ) Example, z x y b=3 a=2 c=2

Crystalline Structures Every crystal lattice structure has its own unit cell –Smallest unit into which a lattice structure can be broken down that sill retains the properties of the whole structure –Table 3.2. Fourteen Crystal (Bravais) Lattices Simple Cubic, Body-Centered Cubic, Face-Centered Cubic Simple Tetragonal, BCT Simple Orthorhombic, BCO, Base CO, FCO, Rhombohedral Hexagonal Simple Monoclinic, BCM, Triclinic

Metal Crystalline Structures Body centered cubic- atom centered in the cube –Atomic packing factor (APF) is 0.68 and represents the fraction of the unit cell occupied by the two atoms. –Ba, Ce, Li, K, molybdenum (less ductile metals) Face centered cubic- atom centered on each of the faces –Atomic packing factor (APF) is 0.74 and represents the fraction of the unit cell occupied by the two atoms. –Regular stackings of close-packed planes Fourth close pack layer lies precisely above the first one –Al, Cu, Au, Pb, Ni, Platinum, Ag (soft metals) Hexagonal close packed (HCP) –Two atoms are associated with each Bravais lattice point One atom centered within the unit cell and various fractional atoms at unit cells (four 1/6 th atoms and four 1/12 th atoms) –Close pack is efficient packing shperes as is the fcc structure. –Atomic packing factor (APF) is 0.74 and represents the fraction of the unit cell occupied by the two atoms. –Regular stackings of close-packed planes The third close-packed layer lies precisely above the first. –Be, Mg, Ti, Zn, Zr

Metal Crystalline Structures Hexagonal Close-packed structure (continued) –the distance between atoms in the bases are equal in the hexagonal structure. The bases are perpendicular to the sides. The angle between the sides is 120°. –Graphite has Close-packed hexagonal structure of Carbon –diamond has a form of face-centered closed -pack cubic structure, or complex cubic structure (diamond structure) –other materials with closed-packed hexagonal structure include Be, Cadmium, Co, Mg, Titanium, Zn, Zirconium Simple tetragonal and body centered tetragonal structures –all atomic planes are still at right angles to each other,as in cubic structure, however, one dimension is longer than the other two –pure tin: natural tetragonal stucture

Metal Crystalline Structures Simple orthorhombic –Lengths of all three axis are different. The places of atoms are perpendicular. –Can have body centered, face centered, base centered Rhombohedral –None of the planes are perpendicular Monoclinic structure –two atoms of the atomic planes are perpendicular, but the third angle is not 90°. Triclinic structure –no two places are perpendicular to each other, the distances between the atoms are different, and the angles are not equal –elongated, thin crystal formation

Metal Crystalline Structures Allotropes –some materials exist in two or more crystalline structures and depends upon temperature and pressure changes. –e.g., pure iron is BCC at normal temp and pressure conditions. Change to FCC if temperature is raised to 1670 F –allotropes are also known as polymorphs Freezing point of material –As the energy in a liquid system decreases, the forces that are grouping the atoms tend to form distinct patterns which become the characteristic lattice structure of the material. –Formation of lattice crystals produces heat. Lattice grows until it meets another energy block, e.g., lattice structure or container. –Grain Boundary- point at which two lattice structures collide. Grains Boundaries

Crystalline Structures For lattice growth to start, a nucleus (seed), must be present. –Very pure metals, rapid cooling restricts time for nucleus growth. –Supercooling occurs if the temperature falls below the melting temperature. The temperature increases as the nucleus forms and levels off as the lattice structure evolves. –Crystal size depends upon: metal type, temperature, Cooling rate: Rapid cooling = smaller crystals Lattice growth occurs more rapidly in directions perpendicular to each other, called Dendritic nature of crystals

Ceramic Crystalline Structures Wide variety of chemical compositions of ceramics is reflected in their structures –Ionic packing factor- the fraction of the unit cell volume occupied by various cations and anions Simplest chemical formula, MX, where M is the metallic element and X is the non-metallic element –CsCl structure Fig 3-8 –BCC- built with two ions associated with each lattice point –Does not represent any important ceramic materials NaCl is shown in Figure 3-9 –Shares structure of many ceramic materials –Two intertwining FCC structures, one of Na ions and one of Cl ions. –Other important ceramic oxides with FCC are MgO, CaO, FeO, and NiO

Ceramic Crystalline Structures Other chemical formula, MX 2, where M is the metallic element and X is the non-metallic element –Shares structure of importantceramic materials, Figure 3-10 CaF 2 –Built with an FCC Bravais lattice with three ions (on Ca and two F). 12 ions (four Ca and 8 F) per unit cell. –Other important ceramic oxides with this structure are UO 2, ThO 2, TeO 2 [Uranium, Thorium, Tellurium Oxides] Ref: http://www-tech.mit.edu/Chemicool/http://www-tech.mit.edu/Chemicool/ –Silica is the most important ceramic of this form, MX 2. Structure is not simple because it is not one structure but many depending upon temperature and pressure (like iron phase diagram) Example, cristobalite (fig 3-11) –Built upon an FCC Bravais lattice with 6 ions (two Si and 4 O ions) –24 ions per unit cell –Continuously connected network of SiO 4 tetrahedra (Note: the sharing of O 2 ions by adjacent tetrahedra gives the overall chemical formula, SiO 2

Ceramic Crystalline Structures Other chemical formula, M 2 X 3, where M is the metallic element and X is the non-metallic element –Important material- Corundum (Al 2 O 3 ) –Rhombohedral Bracais lattice, Fig 3-13, but closely approximated hexagonal lattice. –30 ions per lattice with 12 Al and 18 O. –Stucture similar to HCP Close-packed O – sheets with two-thirds of the small interstices between sheets filled with Al +++. Cr 2 O 3 and Fe 2 O 3 have corundum structure

Ceramic Crystalline Structures Other chemical formula, M’M”X 3, where M’ and M” are the metallic elements and X is the non-metallic element –Important material- Perovskite (CaTiO 3 ) –Simple cubic Bracais lattice, Fig 3-14, Different atoms occupy the corner (Ca ++ ), body centered (Ti 4+ ), and face centered (O -- ) positions –5 ions per lattice point with one Ca, one Ti, and three O per unit cell. –Properties Have important ferroelectric and piezoelectric properties –Related to the relative locations of cations and anions as a function of T Other chemical formula, M’M” 2 X 4, involves magnetic ceramics based on the spinel structure (MgAl 2 O 4 )- Figure 3-15 –56 ions per unit cell with 8 Mg, 16 Al, and 32 O –Important materials- NiAl 2 O 4, ZnAl 2 O 4, and ZnFe 2 O 4 –Mg are in tetrahedral positions that are coordinated by 4 oxygens with the Al in octrahedral positions Other chemical formula, M’’(M’M”)X 4, include Fe(MgFe)O 4, FeFe 2 O 4 Fe(NiFe)O 4, and many other commercially important ferrites or ceramics

Silicate Structures Chemical reaction of SiO 2 with other ceramic oxides –Nature of silicate structures is the traditional oxides tend to break up the continuity of the SiO 4 tetrahedra connections. The remaining connectedness of tetrahedra may be in the form of silicate chains or sheets. Example, Fig 3-16. –Kaolinite structure, [2(OH) 4 Al 2 Si 2 O 5 ] is a hydrated aluminosilicate and a good example of clay mineral –Structure is typical of sheet silicates –Built on triclinic Bravais lattice and two laolinite molecules per unit cell –Many clay minerals have a platelike or flaky structure (fig 3-17) due to the crystal structure. Graphite- Exceptions to general description of ceramics as compounds. –Layered crystal structure of carbon at room temperature- Fig 3-18 –Graphite is monoatomic it is more ceramic than metallic –Hexagonal rings of C are bonded strongly with covalent bonds. »Bonds between layers are of van der Waals type accounting for graphite’s friable nature and use as dry lubricant. Diamond is cubic structure of C (Fig 3-23

Carbon/Graphite Fibers Need for reinforcement fibers with strength and modulii higher than those of glass fibers has led to development of carbon Thomas Edison used carbon fibers as a filament for electric light bulb High modulus carbon fibers first used in the 1950s Carbon and graphite are based on layered structures of hexagonal rings of carbon Graphite fibers are carbon fibers that –Have been heat treated to above 3000°F that causes 3 dimensional ordering of the atoms and –Have carbon contents GREATER than 99% –Have tensile modulus of 344 Gpa (50Mpsi)

Carbon/Graphite Fibers Manufacturing Process –Current preferred methods of producing carbon fibers are from polyacrylonitrile (PAN), rayon (regenerated cellulose), and pitch. PAN –Have good properties with a low cost for the standard modulus carbon –High modulus carbon is higher in cost because high temperatures required PITCH –Lower in cost than PAN fibers but can not reach properties of PAN –Some Pitch based fibers have ultra high modulus (725 GPa versus 350GPa) but low strength and high cost (Table 3-2)

Carbon/Graphite Fibers PAN Manufacturing Process Figures 3-3 and 3-4 –Polyacrylonitrile (PAN) is commercially available textile fiber and is a ready made starting material for PAN-based carbon fibers –Stabilized by thermosetting (crosslinking) so that the polymers do not melt in subsequent processing steps. PAN fibers are stretched as well –Carbonize: Fibers are pyrolyzed until transformed into all-carbon Heated fibers 1800°F yields PAN fibers at 94% carbon and 6% nitrogen Heated to 2300°F to remove nitrogen yields carbon at 99.7% Carbon –Graphitize: Carried out at temperatures greater than 3200° F to Improve tensile modulus by improving crystalline structure and three dimensional nature of the structure. –Fibers are surface treated Sizing agent is applied Finish is applied Coupling agent is applied –Fibers are wound up for shipment

Carbon/Graphite Fibers PITCH Manufacturing Process Figure 3-3 –Pitch must be converted into a suitable fiber from petroleum tar Pitch is converted to a fiber by going through a meso-phase where the polymer chains are somewhat oriented though is a liquid state (liquid crystal phase) Orientation is responsible for the ease of consolidation of pitch into carbon –Stabilized by thermosetting (crosslinking) so that the polymers do not melt in subsequent processing steps –Carbonize: Fibers are pyrolyzed until transformed into all-carbon Heated fibers 1800°F Heated to 2300°F –Graphitize: Carried out at temperatures greater than 3200° F to Improve tensile modulus by improving crystalline structure and three dimensional nature of the structure. –Fibers are surface treated Sizing agent is applied Finish is applied Coupling agent is applied –Fibers are wound up for shipment

Carbon Fiber Mechanical Properties Table 3-2

Diamond Ceramic Crystalline Structures

Amorphous- Molecular structure is incapable of forming regular order (crystallizing) with molecules or portions of molecules regularly stacked in crystal-like fashion. A - morphous (with-out shape) Molecular arrangement is randomly twisted, kinked, and coiled States of Thermoplastic Polymers

Amorphous Materials PVCAmorphous PSAmorphous AcrylicsAmorphous ABSAmorphous Polycarbonate Amorphous PhenoxyAmorphous PPOAmorphous SANAmorphous PolyacrylatesAmorphous

Crystalline- Molecular structure forms regular order (crystals) with molecules or portions of molecules regularly stacked in crystal-like fashion. Very high crystallinity is rarely achieved in bulk polymers Most crystalline polymers are semi-crystalline because regions are crystalline and regions are amorphous Molecular arrangement is arranged in a ordered state States of Thermoplastic Polymers

Crystalline Materials LDPECrystalline HDPECrystalline PPCrystalline PETCrystalline PBTCrystalline PolyamidesCrystalline PMOCrystalline PEEKCrystalline PPSCrystalline PTFECrystalline LCP (Kevlar)Crystalline

Factors Affecting Crystallinity Cooling Rate from mold temperatures Barrel temperatures Injection Pressures Drawing rate and fiber spinning: Manufacturing of thermoplastic fibers causes Crystallinity Application of tensile stress for crystallization of rubber Processing can produce an amorphous structure from a semi-crystalline material –Clear PET bottles for soda –Clear Polyethylene plastic bags

X-Ray Diffraction X-ray diffraction is used to determine the crystalline structure of materials. Diffraction is the result of radiation’s being scattered by a regular array of scattering centers whose spacing is about the same as the wavelength of the radiation. –Example, parallel scratch lines spaced repeatedly about 1  m apart causes diffraction of the visible light (electromagnetic radiation with a wavelength just under 1  m. –The diffraction grating causes the light to be scattered with a strong intensity in a few directions (Fig. 3-33) Phenomenon in which the atoms of a crystal, by virtue of their uniform spacing, cause an interference pattern of the waves in an incident beam of X rays. –The crystal's atomic planes act on the X rays in the same way a uniformly ruled grating acts on a beam of light (see polarization). –The interference pattern is specific to each substance and gives information on the structure of the atoms or molecules in the crystal.

X-Ray Diffraction Appendix 2 shows that atoms and ions are on the order of 0.1 nm in size –Crystal structures as being diffraction gratings on a sub nm scale. –X-ray diffraction characterizes crystalline structures, because Fig 3-34. Portion of electromagnetic spectrum with a wavelength in this range is x-radiation (compared to 1000-nm range for visible light. –In x-rays, atoms are the scattering centers. Mechanism is the interaction of photon of electromagnetic radiation with an orbital electron in the atom. A crystal acts as a 3-dimensional diffraction grating, repeated stacking of crystal planes serves the same function serves the same purpose as the parallel scratch lines in Fig 3-33. –For diffraction to occur, x-ray beams scattered off adjacent crystal planes must be in phase. Otherwise, destructive interference of waves occurs which blocks the scattering pattern. (no intensity)

Miller Index Defining particular plane of the atom with Miller Index 3 steps to determine the Miller Index –Find the intercepts x = 2, y = 3, and z = 2 from figure –Take the reciprocal of the axis length, 1/2, 1/3, and 1/2 –Find the lowest common multiplier and then multiply the reciprocal –Then, the Miler Index is (3, 2, 3)…… 6*1/2, 6*1/3, 6*1/2.. Note ( ) Example, z x y b=3 a=2 c=2

X-Ray Diffraction Bragg equation relates the spacing between adjacent crystal planes and the  angle of diffraction (Bragg angle). –n = 2d sin , Bragg’s Law, Where d is the spacing between adjacent crystal planes and  is the angle of scattering. is the wavelength of the x-ray beam. 2  is the diffraction angle. Note: William Bragg (1862-1942) and son were first to demonstrate the power of x-ray diffraction by identifying the chemical structure of NaCl. Today over 70,000 materials have been identified. –Magnitude of interplanar spacing, d, is a direct function of the Miller indices for the plane For a cubic system, the relationship is simple. The spacing between adjacent hkl planes is d hkl = a…  (h 2 +k 2 +l 2 ) –Where a is the lattice parameter )edge of the unit cell

X-Ray Diffraction Crystal structures with nonprimitive unit cells have atoms at additional lattice sites located along a unit cell edge, within a unit cell face, or in the interior of the unit cell. –Extra scattering can cause out-of phase scattering which will eliminate the diffraction. Table 3.4 Example, Fig 3-39 –Diffraction pattern for a specimen of aluminum powder. »Each peak represents a solution to Bragg’s law. »Powder consists of many small crystal grains of oriented randomly, single wavelength of radiation is used. »The pattern is compared with a database of known diffraction patterns.

X-Ray Diffraction Corrosion and scale analysis by XRD (X-ray diffraction) –This involves qualitative identification of corrosion products. The peaks in the diffraction pattern are checked against a database of previously identified phases using a search match program. Any chemical data you have available helps to narrow the search scope http://www.ktgeo.com/tCS.html

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