Imperfections in Crystalline Structures

• Imperfections in crystalline solid-state materials are often also called “defects”. Defects play a major role in determining the physical properties of materials.

• Defects can be 0 dimension (0-d), 1-dimension (1-d), 2-dimension (2-d).

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Imperfections in crystalline structures

• Point defects or 0-dimension defects appear as lattice vacancies, substitutional or interstitial atoms as shown in Fig. 2-8. The interstitial or substitutional are often called alloying elements if inserted intentionally, and are called impurities if they are unintentional.

• What causes line defects?Line defects or 1-d defects are created when an extra plane of atoms is displaced or dislocated out of its normal lattice space coordinations. See Fig. 2-9.

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Point Defects

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Line Defects

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• Creation of line defects results in lowering the strength of the solid crystal significantly, since it takes much less energy to now displace or move a row or plane of atoms one unit distance in a given time rather than all at once. These defects are also called dislocations.

• However, the creation of a lot of defects or dislocations increases the strength of the solid. The dislocations entangle impeding their movement. Ex. Blacksmith pounding on a horse shoe.

• 2-d defects or planar defects: Ex are grain boundaries, stacking faults. Grain boundaries are created when two or more crystals are mismatched at the boundaries. This normally happens when the material undergoes crystallization.

Imperfections in crystalline structures

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• In a given grain all of the atoms are in a lattice but the orientation of the atoms are specific to one direction. Other neighboring grains also have the same crystal lattice but are arranged in different directions. This creates a region of mismatch, called the grain boundary. Grain boundary (gb) contains less number of atoms and is hence less dense and thus represents a high energy site compared to the bulk. As a result, gbs are sites where the impact of any change or external force occurs.

Imperfections in crystalline structures

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Microstructure

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Microstructure of a hip joint

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• Gbs can be seen by polishing and subsequent etching of a polycrystalline (several) material. The high energy of the gbs make them easy chemically reactive. Fig. 2-10 shows the polished surface of a metal hip joint implant.

• The size of the grains also plays an important role in determining the physical properties of the material.

• A fine grained material is stronger and harder than the material exhibiting a coarse grained structure. This is because the former contains more grain boundaries which interferes with the movement of atoms during deformation leading to a stronger and harder material.

Imperfections in crystalline structures

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Cell adhesion on Metal Compacts

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Webster et al. Biomaterials 2004, 4731-4739 11Kumta-BIOENG-2016

Webster et al. Biomaterials 2004, 4731-4739

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Webster et al. Biomaterials 2004, 4731-4739

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Webster et al. Biomaterials 2004, 4731-4739 14

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Webster et al. Biomaterials 2004, 4731-4739 15

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Surface Area and Reactivity

• Surface Area: Measure of reactivity of the surface. – Gives an indication of the area of a material

surface in contact or exposed to a given environment.

– Very useful parameter for studying catalysis, bioactivity in relation to the surface exposed to physiological fluid environment.

• Measured as m2/gKumta-MEMS-0040 16

Surface Area and Reactivity• If we assume spherical particles of radius

‘r’– Volume = 4/3 πr3; density = ρ– Mass = [Vol][density] = [4/3πr3][ρ]– Surface area = 4πr2

– SSA = 4πr2/[4/3πr3][ρ] = 3/rρ– As radius decreases, SSA increases– Smaller the particle, larger area exposed– Smaller the crystal size, larger number of

atoms exposedKumta-MEMS-0040 17

‘r’

Reactivity

• Free Energy ΔG = VdP –SdT– At constant temperature, ΔG α dP;

• For two particles in contact, ΔP = 2γ/r• Hence ΔG α 1/r; smaller the particle, higher is the

reactivity.

• Hence nanocrystalline materials and nanoparticles exhibit higher SSA and higher reactivity.

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Some Relevant Examples

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Examples

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Examples

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The average R of Mg atom is 0.161 nm. However XRD show that Mgatoms are compressed by almost 1% to oblate spheroids. This is because of The c/a ratios departing from the normal values of 1.63.

Example

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Polymers

• Long chain molecules formed by covalent bonding along the backbone chain. Chains are held together either by secondary bonding forces such as van der Waals and hydrogen bonds or by primary bonds through cross links between chains.

• Chains are flexible and can be tangled easily. In addition, each chain can have side groups, branches and copolymeric chains or blocks. These blocks can interfere with the long-range ordering of chains.

• Short chain polymers will tend to crystallize completely. Ex. Paraffin wax and polyethylene have same formula but differ in the chain length. [(CH2CH2)n] but will crystallize completely because of the short length.

• Long chain polyethylene with 40-50 repeat units –CH2CH2- to several thousands chain to form the linear polyethylene do not crystallize completely only upto 80-90% is normally possible.

• Branched polymers in which side chains are attached to the main backbone will also not crystallize due to steric hindrance of the side chains resulting in a noncrystalline structure.

• Partial crystallinity is called semi-crystalline which is very common for linear polymers. Semicrystalline structure contains

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Polymers

MMWWW/.MWW iiiii ==∑∑∑

DP = degree of polymerization = average number of repeating units per molecule, i.e. chain. If average molecular weight is M, then the DP is:M = DP x molecular weight of mer

Average molecular weight is given according to weight fraction as:

Since 1Wi =∑ which is the weight average molecular weight 24

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Types of Polymer Chains

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Characteristics of Polymer Chains

• Long chains-decreases mobility-higher strength and greater thermal stability.

• Linear polymers-polyesters, polyvinyls, polyamides, and polyesters are easy to crystallize than branched polymers.

• Branched polymers are semicrystalline.• Typical polymer chains are arranged in a combination of

folded and extended chains. Fringed micelle regions contain amorphous and crystalline regions. Folded chain structures are characteristic of single crystals.

• Cross linked network polymers do not crystallize and tend to be non-crystalline or amorphous.

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Polymer Chains

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Polymer Chains

• Vinyl polymers have repeat units –CH2-CHX-; where X is a monovalent side group.

• Three possible arrangements:1. atactic-random arrangement2. Isotactic-groups are on one side of the

main chain3. Syndiotactic-groups are on alternating

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PolymerSmall side groups like polyethy-lene (X =H) and linear chainlike polyethylene---> they tendto crystallize easily.

Large side groups such as PVCX = Cl and Polystyrene (X = C6H6)

Random distribution ---- > noncrystalline

Isotactic and syndiotactic tend to crystallize easily.

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Polymers

Copolymers: two or more homopolymers(same type of repeat unit) are chemicallycombined. Disrupts the structure promoting noncrystalline structure

Addition of plasticizers prevent cyrstallizationby keeping the chains separated from one another resulting in noncrystalline structureof a polymer that normally is prone tocrystallization.

Nitrocellulose plasticized with camphor to formcelluloid.

Plasticizers make rigid noncrystalline polymerslike PVC to form a more flexible solid (Tygon)

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Polymer chains

• Elastomers or rubbery polymers exhibit large extension characteristics at room temperature and can snap back to their original dimensions when the load is released. Elastomers are noncrystalline polymers that have an intermediate structure comprising long chain molecules in 3-d networks. Chains have kinks or bends that straighten when a load is applied.

• Examples: cis polyisoprene (natural rubber) are bent at the double bond due to methyl group acting as a steric hindrance preventing crystallization.

• If the methyl group is on the opposite side of the hydrogen, you have trans-polyisoprene which will crystallize due to the absence of the steric hindrance present in the cis-form. Resulting polymer is a very rigid solid called gutta percha which is not an elastomer.[-CH2-C(CH3)=CH-CH2-]

• Below the glass transition temperature Tg, temperature at which the liquid transforms to a viscous solid that is amorphous, natural rubber loses its elasticity and becomes a glasslike material. To be flexible, all elastomers should have Tg below room temperature. Elastomers that are cross linked do not behave like liquids above Tgsince the cross link points act as pinning sites. Without cross links, the polymer would deform easily. Ex latex which is like a glass and upon cross linking with sulfur called vulcanization, the glass becomes rigid.

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Amorphous Materials

• Glasses or amorphous materials are formed by supercooling the liquid to preserve the structure of the liquid at room temperature. This happens if the liquid is cooled sufficiently rapidly to prevent the nucleation and growth of crystals. This point is called the glass transition temperature, Tg.

• As a result the density of glass is always lower than the crystal due to the presence of voids or free volume.

• The metastable state of glass make them prone to crystallization. • They are also brittle, and less strong, also exhibit higher resistivity.• Ceramics and polymers become glasses relatively easily due to the slow

diffusion and sluggish nature of the elements due to the covalent bonding.• Metals are more resistant to form glasses because of the mobile state of the

atoms. • Ceramics form 3-d networks, the rigidity of the subunits prevent them from

crystallizing. • Common examples, silica, phenolformaldehyde (bakelite) formed by

network bridging with O linking two Si while phenol rings are cross linked by formaldehyde. These 3-d structures do not flow easily.

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Note the higher volume of glass and the lower density.

Glass Formation

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Network Structures

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Composites

• Composed of two or more distinct components.• Term implies distinct phases separated on a

larger scale than the atomic level which lead to significantly altered properties.

• Bone and fiberglass are examples of composites.

• Alloys such as brass, steel containing carbide is not.

• All natural materials tend to be composites.• Most biomaterials are not composites.

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Composites• Properties of composites:

– Shape of second phase material– Volume fraction– Stiffness and integrity of the interface between the constituents.– Shape classified as

• Inclusion shapes– Particles– Fibers– Platelet with two dimensions

• Cellular solids are those in which the inclusions are voids, filled with air or liquid. Cells here refer to structure and not biological cells which occur in living systems.

• Examples:– Dental composite filling material-2-18. has a particulate sructure. It is normally packed

into the tooth cavity while still soft, and the resin is polymerized in situ. Silica additions serve to provide hardness and wear resistance superior to the resin.

– Typical fibrous solid is seen in 2-19. Fibers serve to stiffen the system and strengthen the polymer matrix. Pull-out of fiber during fracture helps to absorb energy resulting in a tough material. Fibers have been added to total joint replacement prostheses to improve mechanical properties, particularly strength and toughness.

• Properties of a composite are controlled by:– Microstructure– Structure of the composite– Structure and properties can be tailored easily by controlling the structure-

microstructure depending on the processing method.36

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Silica-polymer composite

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Glass-fiber epoxy composite

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LaminateIs fibrous

Laminate composite

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Cellular Solids(Synthetic)

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Cellular Solids(Natural)

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Unit Cell Geometry

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Unit Cell Geometry

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