Crystalline Arrangement of atoms

Chapter 4 IMPERFECTIONS IN SOLIDS The atomic arrangements in a crystalline lattice is almost always not perfect. The atomic arrangements in a crystalline lattice is almost always not perfect. There are defects in the way atoms are arranged in the crystalline solids. There are defects in the way atoms are arranged in the crystalline solids. So we can say that in crystalline solids some Lattice Irregularities are always present. So we can say that in crystalline solids some Lattice Irregularities are always present. These crystalline defects are not bad. Some are intentionally introduced to improve the material. These crystalline defects are not bad. Some are intentionally introduced to improve the material.

Types of Crystalline Defects POINT DEFECTS are classified on the basis of their geometry and dimensionallity. POINT DEFECTS (Vacancies, self interstitials, impurity atoms) LINE DEFECTS (one dimensional) (Dislocations) INTERFACIAL DEFECTS (two dimensional) (Grain Boundaries)

VACANCY i.e. an atom missing from lattice position

IMPURITY ATOMS

POINT DEFECTS

Interstitials

Crystalline Defects

Vacancies Vacancies are always present in the crystalline solids. Vacancies are always present in the crystalline solids. Vacancies are created during process of solidification or due to thermal agitations of lattice atoms. Vacancies are created during process of solidification or due to thermal agitations of lattice atoms. At a given temperature there is always present an EQUILIBRIUM CONCENTRATION of VACANCIES. At a given temperature there is always present an EQUILIBRIUM CONCENTRATION of VACANCIES.

EQUILIBRIUM CONCENTRATION OF VACANCIES Equilibrium concentration of vacancies increase with temperature! Boltzmann's constant (1.38 x J/atom K) (8.62 x eV/atom K)  N v N  exp  Q v kT       Equilibrium No. of vacancies No. of atomic sites. Activation energy Temperature Each lattice site is a potential vacancy site

5 We can get Q from an experiment. Measure this... Replot it... MEASURING ACTIVATION ENERGY  N v N  exp  Q v kT       N v N T exponential dependence! defect concentration 1/T N N v ln 1 -Q v /k slope

6 Find the equil. # of vacancies in 1 m of Cu at 1000 o C. Given: 3 Answer: ESTIMATING VACANCY CONC x eV/atom-K 0.9eV/atom 1273K  N v N  exp  Q v kT       For 1m 3, N = N A A Cu  x x1m 3 = 8.0 x sites = 2.7 · N v =(2.7 · ) (8.0 x ) =2.2x vacancies

Impurities in Solids Pure metal containing only one type of atoms Not Possible Pure metal containing only one type of atoms Not Possible Impurity atoms are always present. Impurity atoms are always present. These atoms exists as point defects. These atoms exists as point defects. In alloys, impurity atoms (alloying element atoms) are intentionally added. In alloys, impurity atoms (alloying element atoms) are intentionally added. An alloy is usually a solid solution of two or more types of atoms. An alloy is usually a solid solution of two or more types of atoms. e.g. Fe + C  Steel e.g. Fe + C  Steel SOLVENT SOLUTE SOLID SOLUTION

TYPES OF SOLID SOLUTIONS SOLID SOLUTION SOLID SOLUTION SUBSTITUTIONAL SOLID SOLUTION Solute atoms replace (substitute) the solvent atoms in the solvent lattice INTERSTITIAL SOLID SOLUTION Solute atoms occupy the interstitial sites of the solvent lattice

Solid Solutions

Conditions For Substitutionl Solid Solubility Four Conditions must be satisfied for obtaining appreciable (large) solubility of the substitutional solute in a given solvent lattice. Four Conditions must be satisfied for obtaining appreciable (large) solubility of the substitutional solute in a given solvent lattice. 1. Atomic Size Factor: The atomic size difference between the solute and solvent atoms must be less than  15%. 2. Crystal Structure: Crystal structure of both solute and solvent must be same. 3. Electronegative: The electro negativity difference must be small. If this difference is large ionic compound will form instead of solid solution. 4. Valence: Higher valance metals will dissolve easily than low valance metals.

Ni + Cu Will they have large Solid Solubility? Check! 4 conditions Ni Cu Atomic Size nm nm Crystal structure FCC FCC Electronegativity Valence Answer: Yes they will

HOW about CU + Zn Zn Cu Atomic Size nm nm Crystal structure HCP FCC Electronegativity Valence Answer: No they won’t

Two most common ways to specify the composition or concentration are Two most common ways to specify the composition or concentration are Weight or mass percent: weight of a particular element relative to the total alloy weight. Weight or mass percent: weight of a particular element relative to the total alloy weight. Atom percent: number of moles of an element in relation to the total moles of the elements in the alloy. Atom percent: number of moles of an element in relation to the total moles of the elements in the alloy. Weight %: Weight %: where m 1 and m 2 represent the weight or mass of elements. Atom %: Atom %: where No. of moles (n m ) = {(mass in grams) / Atomic weight SPECIFICATION OF COMPOSITION

SPECIFICATION OF COMPOSITION (Contd.) COMPOSITION CONVERSIONS COMPOSITION CONVERSIONS Weight% to Atom% Weight% to Atom% Atom% to Weight% Atom% to Weight%

SPECIFICATION OF COMPOSITION (Contd.) Weight% to Kg/m3 ( mass of one component per unit volume of material) Weight% to Kg/m3 ( mass of one component per unit volume of material)

Example 4.2 Derive Equation 4.6a Derive Equation 4.6a Solution: Solution: Total alloy mass, Total alloy mass, Atom % of element 1, Simplifies to

DISLOCATIONS Dislocations are LINEAR DEFECT and represent a line around which atoms in the crystalline lattice are misaligned. Dislocations are LINEAR DEFECT and represent a line around which atoms in the crystalline lattice are misaligned. Two Types of Dislocations Two Types of Dislocations EDGE DISLOCATION EDGE DISLOCATION SCREW DISLOCATION SCREW DISLOCATION Also MIXED DISLOCATION Also MIXED DISLOCATION

EDGE DISLOCATION Represented by a half atomic plane the edge of which ends within the crystal

EDGE DISLOCATION

SCREW DISLOCATION

MIXED DISLOCATION

BURGERS VECTOR Burgers Vector b represents the magnitude and direction of lattice distortion created by the dislocation. Burgers Vector b represents the magnitude and direction of lattice distortion created by the dislocation. FOR EDGE DISLOCATION b is perpendicular to dislocation line. FOR EDGE DISLOCATION b is perpendicular to dislocation line. FOR SCREW DISLOCATION b is parallel to dislocation line. FOR SCREW DISLOCATION b is parallel to dislocation line.

BURGERS VECTOR FOR METALLIC MATERIALS FOR METALLIC MATERIALS The BURGERS VECTOR for a dislocation lies along a closed packed direction. The BURGERS VECTOR for a dislocation lies along a closed packed direction. The Magnitude of the BURGERS VECTOR is equal to the interatomic or interpalnar spacing. The Magnitude of the BURGERS VECTOR is equal to the interatomic or interpalnar spacing.

BURGERS VECTOR

DISLOCATIONS

4.5 Interfacial Defects Interfacial defects are boundaries that have two dimensions and normally separate regions of the materials that have different crystal structures and/or crystallographic orientations. Interfacial defects are boundaries that have two dimensions and normally separate regions of the materials that have different crystal structures and/or crystallographic orientations. These imperfections include external surfaces, grain boundaries, twin boundaries, stacking faults, and phase boundaries. These imperfections include external surfaces, grain boundaries, twin boundaries, stacking faults, and phase boundaries. EXTERNAL SURFACES EXTERNAL SURFACES One of the most obvious imperfection boundaries is the external surface One of the most obvious imperfection boundaries is the external surface The crystal structure terminates The crystal structure terminates Surface atoms are not bonded to the maximum number of nearest neighbors  higher energy state than interior atoms. Surface atoms are not bonded to the maximum number of nearest neighbors  higher energy state than interior atoms. To reduce this energy, if possible materials tend to minimize surface area  not possible for solids. To reduce this energy, if possible materials tend to minimize surface area  not possible for solids.

INTERFACIAL DEFECTS (GRAIN BOUNDARIES) Boundary separating two small grains or crystals having different crystallographic orientations in polycrystalline materials. Boundary separating two small grains or crystals having different crystallographic orientations in polycrystalline materials. Within the boundary region, which is probably just several atom distances wide, there is some atomic mismatch in a transition from the crystalline orientation of one grain to that of an adjacent one. Within the boundary region, which is probably just several atom distances wide, there is some atomic mismatch in a transition from the crystalline orientation of one grain to that of an adjacent one. Various degrees of crystallographic misalignment between adjacent grains are possible ( Figure 4.7). Various degrees of crystallographic misalignment between adjacent grains are possible ( Figure 4.7).

4.5 Interfacial Defects (Contd.) Tilt boundary Tilt boundary One simple small-angle grain boundary One simple small-angle grain boundary Figure demonstrates how a tilt boundary having an angle of misorientation  results from an alignment of edge dislocations. Figure demonstrates how a tilt boundary having an angle of misorientation  results from an alignment of edge dislocations. Twist boundary Twist boundary When the angle of misorientation is parallel to the boundary When the angle of misorientation is parallel to the boundary Due to an array of screw dislocations Due to an array of screw dislocations

The atoms are bonded less regularly along a grain boundary  interfacial or grain boundary energy similar to surface energy. The atoms are bonded less regularly along a grain boundary  interfacial or grain boundary energy similar to surface energy. Grain boundaries are more chemically reactive than the grains themselves as a consequence of this boundary energy. Grain boundaries are more chemically reactive than the grains themselves as a consequence of this boundary energy. Impurity atoms often preferentially segregate along these boundaries because of their higher energy state. Impurity atoms often preferentially segregate along these boundaries because of their higher energy state. Because of less total boundary area, the total interfacial energy is lower in large or coarse- grained materials than in fine-grained ones. Because of less total boundary area, the total interfacial energy is lower in large or coarse- grained materials than in fine-grained ones. Grains grow at elevated energy to reduce the total boundary energy Grains grow at elevated energy to reduce the total boundary energy