Materials Science Chapter 4 Disorder in solid Phases

Imperfections in Crystalline Phases Nothing is perfect. Imperfection can be due to: Atom in wrong place – missing or foreign atoms (contamination) But in some cases: Some impurities are added to improve the properties of materials, e.g. Cu is added to Au or Ag to increase the hardness and durability of the objects. Zinc when mixed with copper forms brass, an alloy with better mechanical properties.

Point Defects The simplest defects are point defects. e.g. a vacancy, due to a missing atom. Results from imperfect packing during crystallization or thermal vibrations at high temperatures, or 2 vacancies combine to form a divacancy or 3 to form tri- vacancy In ceramics vacancies occur in such a way that electro- neutrality must be maintained. i.e. whenever a positive ion is missing, (-ve) ions with a corresponding charge must be missing too. The absence of a positive or (-ve) ions from a crystal is called Shottky Defect

Point Defects When an extra atom is lodged in the crystal in a position that does not belong to the crystal lattice, this defect is called Interstitalcy When an ion leaves its normal place and lodges itself into interstitial site, the compound defect is known as Frenkel defect (Vacancy + interstitalcy)

Point Defects Point Defects. (a) Vacancy, D. (b) Di-vacancy (two missing atoms). (c) Ion-pair vacancy (Schottky defect). (d) Interstitialcy. (e) Displaced ion (Frenkel defect).

Line Defects (Dislocations) The most common type of line defects is a dislocation. An edge dislocation (┴) is shown below. Edge Dislocation,  A linear defect occurs at the edge of an extra plane of atoms. The slip vector b is the resulting displacement.

Line Defects (Dislocations) Zones of compression and tension accompany an edge dislocation: The dislocation of atoms around the dislocation line is called Burger’s Vector b Dislocation Energy. Atoms are under compression (dark) and tension (light) near the dislocation

Line Defects (Dislocations) Burger’s vector is parallel to the linear defect. Crystal growth is facilitated by screw dislocations Screw Dislocation. The slip vectore (b) is parallel to the linear defect.

Line Defects (Dislocations) Dislocation Formation by Shear. (a) The dislocation line. D, expands through the crystal until displacement is complete. (b) This defect forms a screw dislocation where the line is parallelto the shear direction. (c) The linear defect is an edge dislocation where the lineis perpendicular to the shear direction.

Grains and Grain boundaries Surface Atoms (Schematic). These atoms are not entirely surrounded by others, so they possess more energy than do the internal atoms.

Grain Boundaries. Note the disorder at the boundary. Grains and Grain Boundaries (Iron, X500). Each grain is a single crystal. The boundaries between grains are surfaces of mismatch.

Example 4.1 Accurate measurements can be made to four significant figures of the density of aluminum. When cooled rapidly from 650 o C,  Al = Mg/m 3. Compare that value with the theoretical density obtained from diffraction analyses where a was determined to be nm. Procedure: use the method for density determination based on the fact that aluminum is fcc contains 4 atoms/unit cell.

Noncrystalline Materials Long range order in is absent in some materials of major importance e.g. liquids, glass and Majority of plastics Few metals when rapidly cooled form non-crystalline solids Non –crystalline solids are called amorphous solids Liquids: fluids (flow under their own mass) Many liquids of technical importance can become very viscous and even solids without crystallizing

Melting of Metals Providing of heat energy not only results thermal vibrations but also vacancies, e.g. Lead Melting of Metals: (a) Crystalline metals with CN = 12 and (b) Liquid metal. CN<12

Crystalline lead contains 0.1% vacancies which increase to 1% by heating. This results in destruction of the 12-fold coordination and disappearance of the long-range order. Energy is required to disrupt the crystalline structure upon melting. This energy I called the heat of fusion (  H f ). It differs from one material to another according to the following table.

Melting increases volume of most metals and ionic solids By melting the CN drops e.g. from 12 to 11 or 10 in fcc and hcp crystals In materials with network structures with stereo-specific i.e. low PF e.g. diamond and silicon Volume decrease by melting Volume Changes with Temperature (Sodium - bcc, Lead - fcc, Magnesium-hcp). Metals with these structures expand on melting.

Volume Changes with Temperature. (a) Ice (hydrogen-bridge bonding). (b) Silicon (covalently-bonded). The coordination number is low for both bondings. Therefore, the packing factors of the solids are low. The structures collapse into smaller volumes as they melt.

GLASSES Glasses are very viscous liquids and non-crystalline At high temperatures glasses form true liquids and respond to shear stress Thermal contraction is formed by solidification. Extensive cooling leads to abrupt change is thermal expansion coefficient Below certain temperature called Glass transition temperature or more simply the glass temperature, there is no further arrangement of the atoms and further cooling results only in reduction of thermal vibrations

Volume Changes in Supercooled Liquids and Glasses. When a liquid is cooled, it contracts rapidly and continuously because, with decreased thermal agitation, the atoms develop more efficient packing arrangements. In the absence of crystallization, the contraction continues below T m to the glass-transition temperature, T g, where the material becomes a rigid glass. Below Tg, no further rearrangements occur, and the only further contraction is caused by reduced thermal vibrations of the atoms in their established locations.