material science dr. mohammad sobuh. material science involves investigating the relationships that...

Material science Dr. Mohammad Sobuh

Material science involves investigating the relationships that exist between the structures and properties of materials. Material engineering is to create new products or systems using existing materials, and/or to develop techniques for processing materials.

The structure of a material is the arrangement of internal components of the material. Structure levels: Subatomic structure (electrons and nucleus interactions). Atomic structure (organisation of atoms/ molecules relative to one another). Microscopic structure (atoms agglomerated together and can be observed by a microscope). Macroscopic structure (structure viewed with the naked eye). Material property is a material trait in terms of the kind and magnitude of response to a specific imposed stimulus ( ex. forging metal/glass)

A single crystal Aluminium oxide may be transparent, translucent, or opaque depending on the martial structure Polycrystal: low porosity Polycrystal: high porosity

Properties of solid materials: Mechanical Electrical Thermal Magnetic Optical Deteriorative

Classification of materials Based on chemical makeup and atomic structure materials can be subdivided into: Metals. Ceramics. Polymers. Composite. Advanced materials

Metals Contain one or more metallic elements and often also non-metallic elements in a small amount (alloys). Atoms are arranged in orderly manner, thus metals are usually dense. Are relatively stiff and strong yet are ductile and resistant to fracture. Metallic materials have large numbers of non- localized electrons. Are extremely good conductors of electricity and heat and are not transparent to visible light.

Of the 110 elements, 89 are classified as metals. Nonmetallic elements: Oxygen, Chlorine, Iodine, Bromine, Nitrogen, Fluorine Hydrogen, Phosphorus, Astatine. The inert gases: helium, neon, argon, krypton, xenon, and radon. Intermediate elements (metalloids): Boron, Carbon, Sulphur, Silicon, Arsenic, Germanium, Tellurium

The most widely used metallic elements: Iron, copper, lead, zinc, aluminium, tin, nickel, and magnesium. Metals can be used in the pure state, but by far the largest amount is used in the form of alloys. An alloy is a combination of elements that exhibits the properties of a metal. The properties of alloys differ appreciably from those of the underlying elements: Improvement of strength, ductility, hardness, wear resistance, and corrosion resistance

Ceramics Compounds between metallic and non-metallic elements; most frequently oxides, nitrides, and carbides (aluminium oxide (or alumina)). Relatively stiff, strong (like metals), and very hard. However, they are extremely brittle (lack ductility) and highly subjected to fracture. Typically, insulative to the passage of heat and electricity, and are more resistant to high temperatures and harsh environments than metals and polymers. The traditional ceramics: Clay minerals (i.e., porcelain), cement, and glass.

Polymers Include the familiar plastic and rubber materials. Chain-like very large molecular structures, with carbon atoms as backbone. Consist of organic compounds (i.e. carbon, hydrogen), and other non-metallic elements (O,N, and Si). Low densities, and are not as stiff nor as strong as metals and ceramics but they are extremely ductile and pliable. They are relatively inert chemically and un-reactive, however they have tendency to soften and/or decompose at modest temperatures. Familiar polymers: Polyethylene (PE), nylon, poly(vinyl chloride) (PVC), polycarbonate (PC), polystyrene (PS), and silicone rubber. Polyethylene

Composites Composed of two (or more) individual materials (metals, ceramics, and polymers). Used to: Achieve a combination of properties that is not displayed by any single material. Incorporate the best characteristics of each of the component materials. Examples: Bone, wood and fibreglass, carbon fibres.

Fibreglass Small glass fibres are embedded within a polymeric material (normally an epoxy or polyester). The glass fibres are relatively strong and stiff, but also brittle. The polymer is ductile, but also weak and flexible and has low density. The resulting fibreglass is relatively stiff, strong, flexible, ductile and it has a low density.

ADVANCED MATERIALS Materials that are utilized in high-technology applications. Advanced materials are typically: Traditional materials whose properties have been enhanced. Newly developed high-performance materials. They may be of all material types (e.g., metals, ceramics, polymers), and are normally expensive. Examples: liquid crystal displays (LCDs), and fibre optics Categories: Semiconductors: have electrical properties that are intermediate between the electrical conductors (viz. metals and metal alloys) and insulators (viz. ceramics and polymers). Biomaterials: materials employed in components implanted into the human body for replacement of diseased or damaged body parts. Smart Materials: materials are able to sense changes in their environments and then respond to these changes in predetermined manners. Example: Memory alloys

Properties of solid materials Mechanical, electrical, thermal, magnetic, optical, deteriorative. The mechanical behavior of a material reflects the relationship between its response or deformation to an applied load or force. Deformation: Shaping materials by applying forces by various means. The term plastic relates to permanent changes, whereas elastic relates to reversible changes.

Strain: The degree of deformation to which the material is subjected. Types of strain: tensile, compressive, shear. Stress

Important mechanical properties: Strength, ductility, stiffness. Proportional (linear) change Yield point (Hookes law) Modulus of resilience

Engineering stress ()= Applied load (P)/ original cross-sectional area (A 0 ) Modulus of elasticity or Youngs modulus (E)= /e. and E have a unit of pressure; Pascal (Pa or N/m or m 1 kgs 2 ) E is a measure of the stiffness of an elastic material. Stiffness is the rigidity of an object - the extent to which it resists deformation in response to an applied force.

Poissons ratio (v): The absolute value of the ratio of the lateral strain to longitudinal strain.

Modulus of resilience: The area under stressstrain curve up to the yield point Y. Resilience is the ability of a material to absorb energy when it is deformed elastically, and release that energy upon unloading. Modulus of resilience =Y 2 /2E. Modulus of resilience has the units of energy per unit volume (N-m/m 3 ). In words Modulus of resilience is the specific energy that the material can store.

With increasing load beyond Y: Plastic deformation begins to take place. the relationship between stress and strain is no longer linear. Yield strength: is the stress at Y point. Yielding does not necessarily mean failure; yielding is necessary in metalwork (forging and bending).

Yield strength is a measure of its resistance to plastic deformation. Increasing load beyond Y results first in a continuous elongation in which the A 0 decreases permanently and uniformly through the whole length.

Further elongation requires increased load (thus stress), up to a maximum stress point after which less stress is required for further deformation. The maximum stress is known as ultimate tensile strength (UTS). UTS is a practical measure of the overall strength of a material. Elongation before reaching UTS is uniformed. Strain up to the UTS is called uniform strain. Increased load beyond the UTS results in a change in the A 0 that is no longer uniformed but is concentrated locally in a neck.

Following necking, the stress required for elongation deceases further. Finally, fracture happens within the necked region. Breaking or fracture stress is the final stress level in the stress/strain curve at which fracture takes place. Ductility is how large a strain the material withstands before fracture. A material that experiences A material that experiences very little or no plastic deformation upon fracture is termed brittle. Strain at fracture is a measure of ductility. The elongation at fracture is the total elongation.

Two quantities are used to defined ductility: Percent Elongation. Percent Reduction of area. Elongation = (l f -l 0 )/l 0 x 100 Reduction of area = (A 0 -A f )/A 0 x100 Elongation percentage has a inversed relationship with the original length. Toughness is a mechanical term that is a measure of the ability of a material to absorb energy up to fracture. It is the area under the stressstrain curve up to the point of fracture. Hardness is a measure of a materials resistance to localized plastic deformation (e.g., a small dent or a scratch)

Engineering stressstrain behavior for iron at three temperatures.

Crystal Structures Solid materials may be classified according to the regularity with which atoms or ions are arranged with respect to one another into: Crystaline materials Non-Crystaline materials A crystalline material is one in which the atoms are positioned in a repetitive 3D pattern, in which each atom is bonded to its nearest-neighbour atoms. Crystalline structure: the manner in which atoms, ions, or molecules are spatially arranged. All metals form crystalline structures under normal solidification conditions. Some of the properties of crystalline solids depend on the crystal structure of the material.

When describing crystalline structures: Atoms (or ions) are thought of as being solid spheres having well-defined diameters. Spheres touch one another. Lattice means a three-dimensional array of points coinciding with atom positions (or sphere centres). Unit cells: Small groups of atoms form a repetitive pattern within the crystal. All the atom positions in the crystal may be generated by translations of the unit cell integral distances along each of its edges. The unit cell is the basic structural unit or building block of the crystal structure. Atomic hard sphere model Crystal Unit cell

METALLIC CRYSTAL STRUCTURES Three relatively simple crystal structures are found for most of the common metals: Face-centred cubic, body-centred cubic, and hexagonal close-packed. The Face-Centred Cubic Crystal Structure (FCC): A unit cell of cubic geometry, with atoms located at each of the corners and the centres of all the cube faces.

In the FCC, spheres or ion cores touch one another across a face diagonal. The cube edge length (unit cell length) a and the atomic radius R are related through: For the FCC crystal structure: Each corner atom is shared among eight unit cells. A face-centred atom belongs to only two. One-eighth of each of the eight corner atoms and one-half of each of the six face atoms, or a total of four whole atoms, may be assigned to a given unit cell. Some of the familiar metals with FCC crystal structure: Copper, aluminium, silver, and gold.

Coordination number: The number of nearest- neighbour or touching atoms. For metals, each atom has the same coordination number. In FCC structure, the coordination number is 12. Atomic packing factor (APF): is the fraction of volume in a crystal structure that is occupied by atoms. APF = the sum of the sphere volumes of all atoms within a unit cell/ the unit cell volume. For the FCC structure, APF is 0.74, which is the maximum packing possible for spheres all having the same diameter. Metals typically have relatively large atomic packing factors

The Body-Centred Cubic Crystal Structure (BCC): Has a cubic unit cell with atoms located at all eight corners and a single atom at the cube centre. Centre and corner atoms touch one another along cube diagonals. Unit cell length a and atomic radius R are related through:

Examples of metals with BCC structure: Chromium, iron (), tungsten, and tantalum. Two atoms are associated with each BCC unit cell. The coordination number for the BCC crystal structure is 8. The atomic packing factor for BCC is 0.68.

The Hexagonal Close-Packed Crystal Structure (HCP): The top and bottom faces of the unit cell consist of six atoms that form regular hexagons and surround a single atom in the centre. Another plane that provides three additional atoms to the unit cell is situated between the top and bottom planes.

The equivalent of six atoms is contained in each unit cell: One-sixth of each of the 12 top and bottom face corner atoms. One-half of each of the 2 centre face atoms All 3 midplane interior atoms. If a and c represent, respectively, the short and long unit cell dimensions, the c/a ratio should be 1.633. However, for some HCP metals this ratio deviates from the ideal value. Coordination number and the atomic packing factor for the HCP crystal structure are the same as for FCC. The HCP metals include: Cadmium, magnesium, titanium (), zinc and cobalt.

DENSITY COMPUTATIONS A knowledge of the crystal structure of a metallic solid permits computation of its theoretical density () through: Where: n = number of atoms associated with each unit cell. A = atomic weight V C = volume of the unit cell N A = Avogadros number (6.023 10 23 atoms/mol)

Polymorphisms Some metals may have more than one crystal structure, a phenomenon known as polymorphism. In elemental solids, the condition is often termed allotropy. Crystal structure depends on both the temperature and the external pressure Pure iron has a BCC crystal structure at room temperature, which changes to FCC iron at 912C. A modification of the density and other physical properties accompanies a polymorphic transformation.

CRYSTAL SYSTEMS Crystal can be divided into groups according to unit cell configurations (unit cell geometry) and/or atomic arrangements. In the unit cell geometry based system, the shape of the appropriate unit cell parallelepiped without regard to the atomic positions in the cell. The unit cell geometry is completely defined in terms of six parameters (sometimes termed the lattice parameters): The three edge lengths a, b, and c. The three interaxial angles ,,and .

There are seven different possible combinations of a, b, and c, and ,,and ; each of which represents a distinct crystal system. The cubic system, for which and has the greatest degree of symmetry. Least symmetry is displayed by the triclinic system, since a b c and .

Crystallographic Points, Directions, and Planes The basis for determining index values is the unit cell, with a right-handed coordinate system consisting of three (x, y, and z) axes situated at one of the corners and coinciding with the unit cell edges.

POINT COORDINATES: The position of any point located within a unit cell may be specified in terms of its coordinates as fractional multiples of the unit cell edge lengths The position of P is designated using coordinates q r s with values that are less than or equal to unity. Coordinates are not separated by commas or any other punctuation marks

CRYSTALLOGRAPHIC DIRECTIONS Crystallographic direction is defined as a line between two points, or a vector. The following steps are utilized in the determination of the three directional indices: 1.A vector of convenient length is positioned such that it passes through the origin of the coordinate system. Any vector may be translated throughout the crystal lattice without alteration, if parallelism is maintained. 2.The length of the vector projection on each of the three axes is determined; these are measured in terms of the unit cell dimensions a, b, and c. 3.These three numbers are multiplied or divided by a common factor to reduce them to the smallest integer values. 4.The three indices, not separated by commas, are enclosed in square brackets, thus: [uvw]. The u, v, and w integers correspond to the reduced projections along the x, y, and z axes, respectively. 5.For each of the three axes, there will exist both positive and negative coordinates. Negative indices are represented by a bar over the appropriate index ex.

Lets derive the following directions: [010], [011], [012], [10], [212], [021]

To draw the direction vector 1.Draw x, y and z axes 2.Determine the origin as the tail of your direction vector (if there is a negative number in the direction vector move the origin in the positive direction of this axis). 3.Determine the endpoint of the vector (remove the a common factor if any of the indices are larger than 1)

For some crystal structures, several nonparallel directions with different indices are actually equivalent. For example, in cubic crystals, all the directions represented by the following indices are equivalent: [100], [010], [00], [001], [00]. The indices are equivalent because the spacing of atoms along each direction is the same. Equivalent directions are grouped together into a family, which are enclosed in angle brackets 100. directions in cubic crystals having the same indices without regard to order or sign, for example, [123] and [23 ], are equivalent.

CRYSTALLOGRAPHIC PLANES In all but the hexagonal crystal system, crystallographic planes are specified by three Miller indices as (hkl). Each index denotes a plane orthogonal to a direction [hkl]. Any two planes parallel to each other are equivalent and have identical indices.

Determining indices from a given plane 1.Choose origin (O) in unit cell OR a new O with axes x, y, z. 2.Find intercepts from O to (a) intercept; from O to (b) int.; from O to (c) int. 3.Take reciprocals of intercept position 4.Clean up: a.Reduce multiples; b.Eliminate fractions; c.Put above negative integer in indices; d.Place round brackets around integers.

1. Choose Origin Unit Cellabc 2. Intercept 3. Reciprocal 4. Reciprocal Value 5. Miler indices (001) (110) (111) (???) 1.Plane cannot touch the origin. 2.Choose the closest corner. (121)

Determining plane from a given indices 1.Select origin O at 000 Or if there is nigatives at O xyz. 2.Take the reciprocal of the indices which will be the intercepts. 3.Mark intercepts along x,y,z axes

Plot the plane of the given indices: (011) (100) 1. Choose Origin 2. Reciprocal 3. Reciprocal Value Unit Cellabc 4. Mark intercepts 5. Draw

Atomic Arrangements The atomic arrangement for a crystallographic plane depends on the crystal structure. A family of planes contains all those planes that are crystallographically equivalent; having the same atomic packing. A family is designated by indices that are enclosed in braces {}. (110) Reduced-sphere unit cells

For example, in cubic crystals (111), (111), (111), (111), (111), (111), (111), (111) planes all belong to the {111} family. In the cubic system only, planes having the same indices, irrespective of order and sign, are equivalent. For example, both (123) and (312 ) belong to the {123} family.

How the crystal structures arrive (Stacking sequence) (52%) (68%) = = (74%) A A A A A B A A CB A C B

FCC HCP

LINEAR AND PLANAR DENSITIES Linear and planar densities are important considerations relative to the process of slip. Slip is the mechanism by which metals plastically deform. Slip occurs on the most densely packed crystallographic planes and, in those planes, along directions having the greatest atomic packing.

Linear density (LD) is the number of atoms per unit length whose centres lie on the direction vector for a specific crystallographic direction; that is The units of linear density are reciprocal length i.e. nm -1

Example Determine the linear density of the [110] direction for the FCC crystal structure. There is an equivalence of two atoms along the [110] direction vector in the unit cell. The direction vector length is equal to 4R LD 110 = 2/4R = 1/2R atom 1 atom

Planar density (PD) is taken as the number of atoms per unit area that are centred on a particular crystallographic plane, or The units for planar density are reciprocal area i.e. nm -2

Example Determine the planner density of the direction shown in the following figure for the FCC crystal structure. 2 atoms in the plane Length = 4R Width= (110)

Crystallisation Single crystal: All unit cells interlock in the same way and have the same orientation. Single crystal has regular geometric shape having flat faces.

Polycrystalline: A collection of many small crystals (grains). Grain boundary: The region where two crystallographically mismatched grains meet (see (3) in the following slide). Sometimes the grains in polycrystalline materials have a preferential crystallographic orientation (not randomly oriented); this material is said to have a texture.

Stages of solidification Small crystals or nuclei form at various positions in random crystallographic orientations. The small grains grow by the successive addition from the surrounding liquid of atoms to the structure of each grain. The extremities of adjacent grains impinge on one another as the solidification process approaches completion. 1 2 3

ANISOTROPY The physical properties of single crystals of some substances depend on the crystallographic direction in which measurements are taken. This is due to the variance of atomic or ionic spacing with crystallographic direction. For example, the elastic modulus and the electrical conductivity may have different values in the [100] and [111] directions. This directionality of properties is termed anisotropy

Isotropic substances: are these in which measured properties are independent of the direction of measurement. The degree of anisotropy increases with decreasing structural symmetry. Triclinic vs. cubic structure.

Imperfections in Solids Perfect order throughout crystalline materials on an atomic scale does not exist. All contain large numbers of various defects or imperfections. Crystalline defect is referred to the lattice irregularity at one or more of its dimensions. Classification of crystalline imperfections (based on geometry or dimensionality of the defect): Point defects: those associated with one or two atomic positions). Linear defects: one-dimensional defects interfacial defects: two-dimensional defects

Point Defects The simplest of the point defects is a vacancy (vacant lattice site). All crystalline solids contain vacancies. The equilibrium number of vacancies (N v ) for a given quantity of material depends on and increases with temperature (exponential). Self-interstitial: the presence of an extra atom in an otherwise complete lattice.

In metals, a self-interstitial introduces relatively large distortions in the surrounding lattice.

IMPURITIES IN SOLIDS A pure metal consisting of only one type of atom just is not possible! Impurity (existence of foreign atoms) will always be present. Most familiar metals are not highly pure; rather, they are alloys. In alloys impurity atoms have been added intentionally to impart specific characteristics to the material. The addition of impurity atoms to a metal will result in the formation of a solid solution.

Solvent represents the element or compound that is present in the greatest amount. Solvent atoms are also called host atoms. Solute is used to denote an element or compound present in a minor concentration. A solid solution forms when the solute atoms are added to the host material. In solid solution, the crystal structure is maintained, and no new structures are formed. Solid solution is homogeneous (the impurity atoms are randomly and uniformly dispersed within the solid).

Impurity point defects: Substitutional solid solutions,: Solute or impurity atoms replace or substitute for the host atoms. Interstitial solid solutions: impurity atoms fill the voids or interstices among the host atoms.

Features of the solute and solvent atoms that determine the degree to which the solute dissolves: 1.Atomic size factor: Appreciable quantities of a solute may be accommodated in the solid solution only when the difference in atomic radii between the two atom types is less than about 15%. 2.Crystal structure: For appreciable solid solubility the crystal structures for metals of both atom types must be the same. 3.Electronegativity: The more electropositive one element and the more electronegative the other, the greater is the likelihood that they will form an intermetallic compound instead of a substitutional solid solution. 4.Valences: A metal will have more of a tendency to dissolve another metal of higher valency than one of a lower valency.

Interstitial solid solutions For metallic materials that have relatively high atomic packing factors, these interstitial positions are relatively small (thus smaller atomic diameter is required). the maximum allowable concentration of interstitial impurity atoms is low (less than 10%). Even very small impurity atoms introduce some lattice strains on the adjacent host atoms.

Miscellaneous Imperfections DISLOCATIONSLINEAR DEFECTS: A dislocation is a linear or one-dimensional defect around which some of the atoms are misaligned. Virtually all crystalline materials contain some dislocations introduced: During solidification During plastic deformation Consequence of thermal stresses that result from rapid cooling.

Types of dislocation Edge dislocation: An extra portion of a plane of atoms, or half-plane, the edge of which terminates within the crystal. The defect centres around the line that is defined along the end of the extra half-plane of atoms (dislocation line). The atoms above the dislocation line are squeezed together, and those below are pulled apart. The magnitude of this distortion decreases with distance away from the dislocation line. The magnitude and direction of the lattice distortion associated with a dislocation is expressed in terms of a Burgers vector (b) (perpendicular).

Screw dislocation: A dislocation formed by a shear stress in which the upper front region of the crystal is shifted (ex. one atomic distance to the right) relative to the bottom portion. The screw dislocation is linear and along a dislocation line (line AB).

Mixed dislocations: Most dislocations found in crystalline materials exhibit components of both edge and screw dislocation. Though a dislocation changes direction and nature within a crystal (e.g. from edge to mixed to screw), the Burgers vector will be the same at all points along its line. For metallic materials, the Burgers vector for a dislocation will point in a close-packed crystallographic direction and will be of magnitude equal to the interatomic spacing.

The nature of a dislocation (i.e., edge, screw, or mixed) is defined by the relative orientations of dislocation line and Burgers vector: For an edge, they are perpendicular. For a screw, they are parallel. They are neither perpendicular nor parallel for a mixed dislocation, but lies somewhere in between.

High-magnification transmission electron micrograph Dislocations can be observed in crystalline materials using electron-microscopic techniques.

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 include: External surfaces. Grain boundaries. Twin boundaries. Stacking faults. Phase boundaries

External Surfaces Surfaces along which the crystal structure terminates. Surface atoms are not bonded to the maximum number of nearest neighbours, therefore in a higher energy state than the atoms at interior positions. To reduce this energy, materials tend to minimize, if at all possible, the total surface area.

Grain Boundaries The boundary separating two small grains or crystals having different crystallographic orientations in polycrystalline materials. Various degrees of crystallographic misalignment between adjacent grains are possible: Small- (or low- ) angle grain boundary: When this orientation mismatch is slight, on the order of a few degrees. high-angle boundaries. Tilt boundary: When several edge dislocations are aligned. Twist boundary: An array of screw dislocations (The angle of misorientation is parallel to the boundary).

Angle of misorientation Tilt boundary Twist boundary

The atoms are bonded less regularly along a grain boundary (high grain boundary energy). The magnitude of this energy is a function of the degree of misorientation. This results in: Grain boundaries are more chemically reactive than the grains themselves. Impurity atoms often preferentially segregate along these boundaries The total energy is lower in large or coarse- grained materials than in fine-grained ones: Grains grow at elevated temperatures to reduce the total boundary energy

Twin Boundaries A special type of grain boundary across which there is a specific mirror lattice symmetry. The region of material between these boundaries is termed a twin. Twins result from atomic displacements that are produced from: Mechanical shear forces (mechanical twins) During annealing heat treatments following deformation (annealing twins) Twinning occurs on a definite crystallographic plane and in a specific direction depending on the crystal structure: Annealing twins are typically found in metals that have the FCC crystal structure. Mechanical twins are observed in BCC and HCP metals

ATOMIC VIBRATIONS Every atom in a solid material is vibrating very rapidly about its lattice position within the crystal. At any instant of time not all atoms vibrate at the same frequency and amplitude, nor with the same energy. Therefore these atomic vibrations may be thought of as imperfections or defects. At room temperature, a typical vibrational frequency is on 10 13 Hz, whereas the amplitude is a few thousandths of a nanometer.

BULK OR VOLUME DEFECTS These include pores, cracks, and foreign inclusions. They are normally introduced during processing and fabrication steps. Some of these defects and their effects on the properties of materials

Dislocations mechanisms Plastic deformation corresponds to the net movement of large numbers of atoms in response to an applied stress. Thus plastic deformation corresponds to the motion of large numbers of dislocations. During this process, interatomic bonds must be ruptured and then reformed.

Shear stress

The process by which plastic deformation is produced by dislocation motion is termed slip The crystallographic plane along which the dislocation line traverses is the slip plane. An edge dislocation: Moves in response to a shear stress applied in a direction perpendicular to its line. The direction of movement is parallel to the stress direction. A screw dislocation: Moves in response to a shear stress applied in a direction parallel to its line. The direction of movement is perpendicular to the stress direction.

The number of dislocations, or dislocation density: The total dislocation length per unit volume or, equivalently, the number of dislocations that intersect a unit area of a random section. For heavily deformed metals, the density may run as high as 10 9 to 10 10 mm -2. Dislocation densities as low as 10 3 mm -2 are typically found in carefully solidified metal crystals. typical dislocation density for ceramic materials is between 10 2 and also 10 4 mm -2

CHARACTERISTICS OF DISLOCATIONS When metals are plastically deformed, some fraction of the deformation energy (~ 5%) is retained internally; the remainder is dissipated as heat. The major portion of this stored energy is as strain energy associated with dislocations. As a consequence of dislocation, there are regions in which compressive, tensile, and shear lattice strains are imposed on the neighbouring atoms. The strains extend into the surrounding atoms, and their magnitude decreases with radial distance from the dislocation.

The strain fields surrounding dislocations may interact Forces are imposed on each dislocation by the combined interactions of all its neighbouring dislocations. Same plane Same direction Same plane Different direction

Dislocation interactions are possible between edge, screw, and/or mixed dislocations, and for a variety of orientations. During plastic deformation, the number of dislocations increases dramatically due to: Existing dislocations, which multiply Grain boundaries Internal defects and surface irregularities such as scratches and nicks

SLIP SYSTEMS Dislocations do not move with the same degree of ease on all crystallographic planes of atoms and in all crystallographic directions. There is a preferred plane (slip plane), and in that plane there are specific directions (slip direction) along which dislocation motion occurs. This combination of the slip plane and the slip direction is termed the slip system.

The slip system depends on: The crystal structure of the metal The atomic distortion that accompanies the motion of a dislocation (minimal). For a particular crystal structure : The slip plane is the plane that has the most dense atomic packing. The slip direction corresponds to the direction, in this plane, that is most closely packed with atoms. The number of independent slip systems represents the different possible combinations of slip planes and directions. Ex. there are 12 slip systems in FCC: four unique {111} planes and, within each plane, three independent directions.

{111} 110

Metals with FCC or BCC crystal structures have a relatively large number of slip systems (at least 12). These metals are quite ductile because extensive plastic deformation is normally possible along the various systems. Conversely, HCP metals, having few active slip systems, are normally quite brittle.

material science dr. mohammad sobuh. material science involves investigating the relationships that...

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