CRYSTAL A crystal is a solid in which the constituent atoms, molecules , or ions are packed in an ordered UNIT CELLS It is the smallest arrangement of an atom, molecules which is a true representation of crystal structure as observed along all three axes. The unit cell is building block for crystal. Repetition of unit cell generates entire crystal. CRYSTAL STRUCTURE It is a unique arrangement of atoms in an ordered condition in a crystal.

TYPES OF CRYSTAL STRUCTURE Simple cubic crystal structure Body centered crystal structure Face centered crystal structure Hexagonal closed packed system

Face centered crystal structure Atoms located at corners and on centers of faces Cu, Al, Ag, Au have this crystal structure Number of atoms per unit cell, n = 4. FCC unit cell: 6 face atoms shared by two cells: 6 x 1/2 = 3 8 corner atoms shared by eight cells: 8 x 1/8 = 1

Body centered crystal structure Number of atoms per unit cell, n = 2 Center atom not shared: 1 x 1 = 1 8 corner atoms shared by eight cells: 8 x 1/8 = 1 Atoms located at corners and one atom at the centers of atructure

Hexagonal closed packed system Six atoms form regular hexagon surrounding one atom in center Another plane is situated halfway up unit cell (c-axis) with 3 additional atoms situated at interstices of hexagonal (close-packed) planes Cd, Mg, Zn, Ti have this crystal structure

IMPERFECTIONS OF CRYSTALS POINT IMPERFECTIONS LINE IMPERFECTIONS SURFACE IMPERFECTIONS VOLUME IMPERFECTIONS The term “defect” or “imperfection” is generally used to describe any deviation from the perfect periodic array of atoms in the crystal.

POINT IMPERFECTIONS They are imperfect point- like regions, one or two atomic diameters in size and hence referred to as ‘zero dimensional imperfections’. There are different kinds of point imperfections. VACANCIES If an atom is missing from its normal site in the matrix, the defect is called a vacancy defects. When the temperature is sufficiently high, as the atoms vibrate around their regular positions, some acquire enough energy to leave the site completely.

SUBSTITUTIONAL IMPURITY It refers to a foreign atom that substitutes for or replaces a parent atom in the crystal. INTERSTITIAL IMPURITY An interstitial defect arises when an atom occupies a definite position in the lattice that is not normally occupied in the perfect crystal.

LINE IMPERFECTIONS The defects, which take place due to dislocation or distortion of atoms along a line, in some direction are called as ‘line defects’. Line defects are also called dislocations. In the geometric sense, they may be called as ‘one dimensional defects’. The two types of dislocations are, Edge dislocation Screw dislocation If one of these vertical planes does not extend to the full length, but ends in between within the crystal it is called ‘edge dislocation’.

SCREW DISLOCATION In this dislocation, the atoms are displaced in two separate planes perpendicular to each other. It forms a spiral ramp around the dislocation.

SURFACE IMPERFECTIONS Surface imperfections arise from a change in the stacking of atomic planes on or across a boundary. The change may be one of the orientations or of the stacking sequence of atomic planes. In geometric concept, surface imperfections are two- dimensional. They are of two types external and internal surface imperfections. GRAIN BOUNDARIES TWIN BOUNDARIES They are the imperfections which separate crystals or grains of different orientation in a poly crystalline solid during nucleation or crystallization. It is a two dimensional imperfection. During crystallization, new crystals form in different parts and they are randomly oriented with respect to one another.

TWIN BOUNDARIES If the atomic arrangement on one side of a boundary is a mirror reflection of the arrangement on the other side, then it is called as twin boundary. VOLUME IMPERFECTIONS Volume defects such as cracks may arise in crystals when there is only small electrostatic dissimilarity between the stacking sequences of close packed planes in metals. Presence of a large vacancy or void space, when cluster of atoms are missed is also considered as a volume imperfection.

CONSTITUTION OF ALLOYS AND PHASE DIAGRAMS ALLOYS are composed of two or more elements, at least one of which is a metal

Solid Solutions A solid solution occurs when we alloy two metals and they are completely soluble in each other. If a solid solution alloy is viewed under a microscope only one type of crystal can be seen just like a pure metal. Solid solution alloys have similar properties to pure metals but with greater strength but are not as good as electrical conductors. The common types of solid solutions are 1) Substitutional solid solution 2) Interstitial solid solutions

Substitutional solid solutions Interstitial solid solutions The size of the solute atom is similar to the solvent atom (example: brass alloy of zinc & copper) The size of the solute atom is much smaller than that of the solvent (example: steel alloy iron & carbon)

:

Hume-Rothery conditions Extent of solid solubility in a two element system can be predicted based on Hume-Rothery conditions. If the system obeys these conditions, then complete solid solubility can be expected. Hume-Rothery conditions:- Crystal structure of each element of solid solution must be the same. Size of atoms of each two elements must not differ by more than 15%. Elements should not form compounds with each other i.e. there should be no appreciable difference in the electro-negativities of the two elements. Elements should have the same valence.

Crystal structure factor: For complete solid solubility, the two elements should have the same type of crystal structure i.e., both elements should have either F.C.C. or B.C.C. or H.C.P. structure. Relative size factor: As the size (atomic radii) difference between two elements increases, the solid solubility becomes more restricted. For extensive solid solubility the difference in atomic radii of two elements should be less than about 15 percent. If the relative size factor is more than 15 percent, solid solubility is limited. For example, both silver and lead have F.C.C. structure and the relative size factor is about 20 percent. Therefore the solubility of lead in solid silver is about 1.5 percent and the solubility of silver in solid lead is about 0.1 percent. Copper and nickel are completely soluble in each other in all proportions. They have the same type of crystal structure (F.C.C.) and differ in atomic radii by about 2 percent.

Chemical affinity factor: Solid solubility is favoured when the two metals have lesser chemical affinity. If the chemical affinity of the two metals is greater then greater is the tendency towards compound formation. Generally, if the two metals are separated in the periodic table widely then they possess greater chemical affinity and are very likely to form some type of compound instead of solid solution. Relative valence factor: It is found that a metal of lower valence tends to dissolve more of a metal of higher valence than vice versa. For example in aluminium-nickel alloy system, nickel (lower valance) dissolves 5 percent aluminium but aluminium (higher valence) dissolves only 0.04 percent nickel.

Component Pure metal or compound (e.g., Cu, Zn in Cu-Zn alloy, sugar, water.) Solvent Host or major component in solution. Solute Dissolved, minor component in solution Phases A phase can be defined as a physically distinct and chemically homogeneous portion of a system that has a particular chemical composition and structure. Water in liquid or vapor state is single phase. Ice floating on water is an example two phase system.

P = number of phases that coexist in a system Gibbs Phase rule The number of degrees of freedom, F (no. of independently variable factors), number of components, C, and number of phases in equilibrium, P, are related by Gibbs phase rule as P+F = C+2 P = number of phases that coexist in a system C = Number of component F = Degrees of freedom Phase diagram A graph showing the phase or phases present for a given composition as a function of temperature.

The lever rule 1) All material must be in one phase or the other: Wα + WL = 1 2) Mass of a component that is present in both phases equal to the mass of the component in one phase +mass of the component in the second phase: WαCα + WLCL = Co 3) Solution of these equations gives us the lever rule. WL = (Cα - Co) / (Cα- CL) Wα = (Co - CL) / (Cα- CL)

Cooling curves

Cooling curve for pure iron

Eutectic System In the eutectic system between two metals A(α) and B(β), two solid solutions, one rich in A and another rich in B form. In addition to liquids and solidus lines there are two more lines on A and B rich ends which define the solubility limits B in A and A in B respectively. These are called solvus lines. Three phases (L+α+β) coexist at point E. This point is called eutectic point or composition. Left of E is called hypoeutectic whereas right of E is called hypereutectic. A eutectic composition solidifies as a eutectic mixture of αand β phases. The melting point at the eutectic point is minimum

Eutectic System

Peritectic System In the peritectic ,a solid and liquid phases combine to form another solid solution

Eutectoid Reactions The eutectoid (eutectic-like in Greek) reaction is similar to the eutectic reaction but occurs from one solid phase to two new solid phases. Invariant point (the eutectoid) – three solid phases are in equilibrium. Upon cooling, a solid phase transforms into two other solid phases (δ ↔ γ + ε ) Looks as V on top of a horizontal tie line (eutectoid isotherm) in the phase diagram. Eutectoid

Peritectoid System It is a three-phase reaction similar to peritectic but occurs from two solid phases to one new solid phase α + β = γ. α + γ γ α + β γ + β

Iron-Carbon System Ferrite Pearlite Ferrite. Alpha ferrite. α-ferrite BCC iron It exists at room temperature. The solubility of carbon in iron is only 0.008%at room temperature which increases to 0.025% at 727 ⁰ C It is strongly magnetic upto 768 ⁰ C above which on heating it becomes non magnetic Delta ferrite. δ-ferrite. Stable only at high temperatures thus no practical engineering use Soft and ductile. The solubility of carbon in iron is only 0.51%at 1495 ⁰C At 723 ⁰C, austenite transforms into alpha ferrite and cementite Eutectoid reaction-single solid phase is transformed into two other solid phases It shows better strength and hardness.

Iron-Carbon System Austenite Cementite Gamma iron, γ-iron Polymorphic transformation from BCC to FCC More solid solubility than ferrite Denser than ferrite Its single phase FCC structure is ductile at high temperatures (good formability) Large amounts of Ni and Mangenese can be dissolved in FCC iron The maximum solubility of carbon in iron is only 2.0% at 1147 ⁰ C Carbide-An another name of cementite 100% iron carbide, Fe3C 6.67% Carbon Hard Brittle Can include other alloying elements such as chromium, molybdenum, mangenese.

Iron-Carbon System The following phases are involved in the transformation, occurring with iron-carbon alloys: L - Liquid solution of carbon in iron; δ-ferrite – Solid solution of carbon in iron. Maximum concentration of carbon in δ-ferrite is 0.09% at 2719 ºF (1493ºC) – temperature of the peritectic transformation. The crystal structure of δ-ferrite is BCC (cubic body centered). Austenite – interstitial solid solution of carbon in γ-iron. Austenite has FCC (cubic face centered) crystal structure, permitting high solubility of carbon – up to 2.06% at 2097 ºF (1147 ºC). Austenite does not exist below 1333 ºF (723ºC) and maximum carbon concentration at this temperature is 0.83%.

Iron-Carbon System α-ferrite – solid solution of carbon in α-iron. α-ferrite has BCC crystal structure and low solubility of carbon – up to 0.25% at 1333 ºF (723ºC). α-ferrite exists at room temperature. Cementite – iron carbide, intermetallic compound, having fixed composition Fe3C. Cementite is a hard and brittle substance, influencing on the properties of steels and cast irons. The following phase transformations occur with iron-carbon alloys: Alloys, containing up to 0.51% of carbon, start solidification with formation of crystals of δ-ferrite. Carbon content in δ-ferrite increases up to 0.09% in course solidification, and at 2719 ºF (1493ºC) remaining liquid phase and δ-ferrite perform peritectic transformation, resulting in formation of austenite.

Iron-Carbon System Alloys, containing carbon more than 0.51%, but less than 2.06%, form primary austenite crystals in the beginning of solidification and when the temperature reaches the curve ACM primary cementite stars to form. Iron-carbon alloys, containing up to 2.06% of carbon, are called steels. Alloys, containing from 2.06 to 6.67% of carbon, experience eutectic transformation at 2097 ºF (1147 ºC). The eutectic concentration of carbon is 4.3%. In practice only hypoeutectic alloys are used. These alloys (carbon content from 2.06% to 4.3%) are called cast irons. When temperature of an alloy from this range reaches 2097 ºF (1147 ºC), it contains primary austenite crystals and some amount of the liquid phase. The latter decomposes by eutectic mechanism to a fine mixture of austenite and cementite, called ledeburite. All iron-carbon alloys (steels and cast irons) experience eutectoid transformation at 1333 ºF (723ºC). The eutectoid concentration of carbon is 0.83%. When the temperature of an alloy reaches 1333 ºF (733ºC), austenite transforms to pearlite (fine ferrite-cementite structure, forming as a result of decomposition of austenite at slow cooling conditions). Iron above 1390 degrees is known as delta iron Iron between 1390 and 910 degrees is known as gamma iron Iron below 910 degrees is known as alpha iron

Iron-Carbon System Fe-Fe3C phase diagram is characterized by five individual phases,: α–ferrite (BCC) Fe-C solid solution, γ-austenite (FCC) Fe-C solid solution, δ-ferrite (BCC) Fe-C solid solution, Fe3C (iron carbide) orcementite -an inter-metallic compound and liquid Fe-C solution andfour invariant reactions: peritectic reaction at 1495°C and 0.16%C, δ-ferrite + L↔ γ-iron (austenite) monotectic reaction 1495°C and 0.51%C, L↔ L+ γ-iron (austenite) eutectic reactionat 1147°C and 4.3 %C, L↔ γ-iron + Fe3C (cementite) [ledeburite] eutectoid reactionat 723°C and 0.8%C, γ-iron ↔ α–ferrite + Fe3C (cementite) [pearlite]