CRYSTAL STRUCTURE, MECHANICAL BEHAVIOUR & FAILURE OF MATERIALS
|
|
- Sybil Harvey
- 6 years ago
- Views:
Transcription
1 MODULE ONE CRYSTAL STRUCTURE, MECHANICAL BEHAVIOUR & FAILURE OF MATERIALS CRYSTAL STRUCTURE Metallic crystal structures; BCC, FCC and HCP Coordination number and Atomic Packing Factor (APF) Crystal imperfections: point, line and surface imperfections Atomic Diffusion: Phenomenon, Fick s laws, factors affecting diffusion. 1.1 INTRODUCTION The engineering materials (either metallic or non-metallic) can be identified as crystalline or amorphous structured. But most of the metals assume crystalline form with a systematic and regular arrangement of atoms as compared to amorphous structure that lacks regular atomic arrangement. A crystalline material is thus comprised of group of atoms with a specific atomic arrangement which repeats in a 3D pattern; the small group of atoms that repeats over a 3D array is termed as a unit cell. The geometry and the atomic positions of a unit cell define the crystal structure. Figure 1.1: Unit cell lattice parameters Based on unit cell geometry for different possible combinations of a, b, c and,, seven crystal systems were identified. Further, considering atomic arrangement within a crystal system A. Bravais showed that the seven crystal systems could be arranged in 14 independent ways to obtain the 14 Bravais lattices. Pruthvi Loy, Chiranth B.P. 1 SJEC, Mangalore
2 Table 1.1: Crystal systems and Bravais lattices Pruthvi Loy, Chiranth B.P. SJEC, Mangalore
3 1. METALLIC CRYSTAL STRUCTURES Inspite of the different possible crystal structures three relatively simple structures are found for most of the common metals. Body Centered Cubic (BCC) Face Centered Cubic (FCC) Hexagonal Close Packed (HCP) 1..1 Body Centered Cubic (BCC) A cubic unit cell with atoms located at all eight corners and a single atom at the cubic center. No of atoms per unit cell = i.e., 8x (8 corner atoms each shared by 8 neighboring unit cells) + 1 (1atom at the cubic center) = Example: Chromium, Tungsten, Iron, etc. 1.. Face Centered Cubic (FCC) It also has a cubic geometry with atoms located at each of the corners and the centers of all the cube faces. No of atoms per unit cell = 4 i.e., 8x (8 corner atoms each shared by 8neighboring unit cells) + 6 x (6 atoms at the cube faces shared by unit cells) = Example: Copper, Aluminium, Silver, Gold, etc. Pruthvi Loy, Chiranth B.P. 3 SJEC, Mangalore
4 1..3 Hexagonal Close Packed (HCP) No of atoms per unit cell = 6 i.e., 1 x (1 corner atoms each shared by 6 neighboring unit cells) + x ( atoms at the hexagonal faces each shared by unit cells) + 3 whole atoms = 6 Example: Titanium, Zinc, Cobalt, Magnesium, etc. 1.3 CHARACTERISTICS OF CRYSTAL STRUCTURE The type of structure and its characteristics has a profound influence on the material properties. Two of the important characteristics of a crystal structure are the coordination number and the atomic packing factor (APF); apart from these the other characteristic features of interest is the stacking of planes Coordination number For metals, each atom has the same number of nearest-neighbor or touching atoms, which is the coordination number. Unit Cell Coordination number 1. Simple Cubic 06. Body Centered Cubic Face Centered Cubic 1 4. Hexagonal Close Packed Atomic Packing Factor The Atomic Packing Factor (APF) is the fraction of volume in a crystal structure that is occupied by the atoms. i.e., APF = = = Pruthvi Loy, Chiranth B.P. 4 SJEC, Mangalore
5 a) Simple Cubic: Number of atoms per unit cell, = 1 Volume of each atom, = Volume of a unit cell, = Therefore, APF = = (because, = r) APF = 0.5 i.e., only 5 % of the space available inside a unit cell of simple cubic structure is occupied by atoms. b) BCC: From ADC, AC = AD + DC AC = + AC = From ABC, AB =AC + BC = ( ) + = 3 = Number of atoms per unit cell, = Volume of each atom, = Volume of a unit cell, = Pruthvi Loy, Chiranth B.P. 5 SJEC, Mangalore
6 Therefore, APF = = ( ) APF = 0.68 i.e., 68 % of the space available in a BCC unit cell is occupied by atoms. c) FCC: From ABC, AC +BC = AB + = = Number of atoms per unit cell, = 4 Volume of each atom, = Volume of a unit cell, = Therefore, APF = = ( ) APF = 0.74 i.e., 74 % of the space available in a FCC unit cell is occupied by atoms. Pruthvi Loy, Chiranth B.P. 6 SJEC, Mangalore
7 d) HCP: From ABD, = h + ( ) h = - = h = Number of atoms per unit cell, = 6 Volume of each atom, = Volume of a unit cell, = Area of hexagon x c = 6 x Area of ABC x c = 6 x ( ) x c = 6 x ( ) x c = 6 c Also, = r and c = Where, c is lattice constant, its value can be calculated as shown below(considering the atoms to be spherical in shape), Pruthvi Loy, Chiranth B.P. 7 SJEC, Mangalore
8 From AMN, AM = AN + MN = ( ) + ( ) cos 30 = a AN = = + AN= a = c = = Therefore, APF = = APF = 0.74 i.e., 74 % of the space available in a HCP unit cell is occupied by atoms. Pruthvi Loy, Chiranth B.P. 8 SJEC, Mangalore
9 Note: It is possible to compute the theoritical density of a metallic solids having the knowledge of its crystal ctructure. Where, = = n = number of atoms per unit cell A = atomic weight V C = volume of the unit cell N A = Avogadro s number (6.03 x 10 3 atoms/mol) Table 1.: BCC, FCC and HCP Unit cell parameters Atoms/unit cell, n Coordination number, Z edge length, lattice constant, c Unit cell volume, V c APF BCC 8 FCC HCP 6 1 r c 0.74 Example Problem: Copper has an atomic radius of 0.18 nm (1.8 Å), an FCC crystal structure, and an atomic weight of 63.5 g/mol. Compute its theoretical density and compare the answer with its measured density. SOLUTION: Given, n = 4, A= 63.5 g/mol, r = 0.18 x 10-9 m = 0.18 x 10-7 cm Volume of unit cell, = = ( ) = = 16 = 16 (0.18x10-7 ) 3 = 4.75x10-3 cm 3 Therefore, Density, = = = 8.89 From periodic table of elements, the literature value of density of copper is Pruthvi Loy, Chiranth B.P. 9 SJEC, Mangalore
10 1.3.3 Stacking of Planes During solidification the atoms within the solid pack together as tightly as possible, i.e., a layer of atoms stack one above the other to make up the solid material.although layers of atoms are stacked one above the other, their sequence of stacking varies for different crystal structures.the stacking sequence of few crystal strucures are as shown below. Figure 1.: Stacking of Planes in a crystal structure Pruthvi Loy, Chiranth B.P. 10 SJEC, Mangalore
11 1.4 CRYSTAL IMPERFECTIONS For the study of crystal structures we have assumed a perfect or ideal crystal. However, such an idealized crystal does not exist; all contain large number of various defects or imperfections. The properties of most of the metals are profoundly influenced by the presence of imperfections. Thus specific characteristics can be obtained in crystals by introducing crystalline defects. Adding alloying elements to the metal is one way of introducing a crystal defect. According to the geometry or dimensionality the defects may be classified as; Zero dimensional or Point defect o Vacancy o Interstitial defect o Substitutional defect One dimensional or Line defect o Edge dislocation o Screw dislocation Two dimensional or Surface defect o External surface o Grain boundary o Tilt boundary o Twin boundary o Stacking fault Three dimensional or Volume defect - Pores, cracks, foreign inclusions and other phases Point imperfections Vacancy: The simplest of the point defect is a vacancy, where in one or more atoms are missing from their respective location within the crystal lattice. The vacancies may occur as a result of imperfect packing during crystallization or they may also arise from thermal fluctuation of atoms at high temperature. Figure 1.3: Vacancy defect Pruthvi Loy, Chiranth B.P. 11 SJEC, Mangalore
12 Impurity: A pure metal consisting of only one type of atom is highly idealistic; impurity or foreign atoms will always be present. Most familiar metals are not highly pure rather they are alloys in which impurity atoms have been intentionally added to impart specific characteristics to the material. The addition of impurity atoms to a metal will result in the formation of either a solid solution and/or a new phase. A solid solution forms when as the solute atoms (impurity) are added to the solvent (host material) and the crystal structure of the parent material is retained with no new structures being formed. Impurity point defects in crystals can be, Interstitial impurity or Substitutional impurity Figure 1.4: Impurity defects Interstitial impurity: In this an interstitial foreign atom occupies a definite position in a nonlattice site within the crystal. Example: Addition of carbon atoms (0.071 nm) to iron (0.14 nm) where the carbon atoms occupy the interstitial space between the iron atoms. Substitutional impurity: When a foreign atom substitutes the parent atom and occupies its position in the lattice site, then it is known as a substitutional defect. Example: Addition of copper to nickel; copper atoms substitute the nickel atoms. Note: Point defect in ceramics may exist as both vacancies and interstitials. The atomic bonding is predominantly ionic in ceramics; i.e., their crystal structures may be thought of as being composed of electrically charged ions instead of atoms. The metallic ions, or cations, are positively charged, because they have given up their valence electrons to the nonmetallic ions, or anions, which are negatively charged. An ionic crystal possess electronegativity, i.e., there is equal number of positive and negative charges from ions; as a consequence, defects in ceramics do not occur alone rather defect for each ion type may occur; one such defect is Frenkel & Schottky defect. Figure 1.5: Frenkel and Schottky defects Pruthvi Loy, Chiranth B.P. 1 SJEC, Mangalore
13 Frenkel defect involves a cation vacancy - cation interstitial pair. It might be thought of as being formed by a cation leaving its normal position and moving into an interstitial site. There is no change in charge because the cation maintains the same positive charge as an interstitial. Schottky defect is a cation vacancy - anion vacancy pair. This defect might be thought of as being created by removing one cation and one anion from the interior of the crystal. Since for every anion vacancy there exists a cation vacancy, the charge neutrality of the crystal is maintained Line Imperfections Linear defects in crystalline solids are due to misalignent of atoms during the dislocation of atomic planes. Dislocations are of two types; Edge Dislocation and Screw Dislocation Figure 1.6: Line imperfections Edge Dislocation It is created in a crystal by insertion of an extra plane of atoms i.e., a half plane as shown in figure. The edge of the half plane terminates within the crystal, this is termed as dislocation line. The atoms above the dislocation line are squeezed together and are in a state of compression while the atoms below are pulled apart and are in a state of tension. Edge dislocation is represented by the symbol for positive dislocation and for negetive dislocation. Screw Dislocation It is said to be formed in perfect crystal when part of the crystal displaces angularly over the remaining part under the action of shear stress. The upper front region of the crystal is shifted one atomic distance to the right relative to the bottom portion. The screw dislocation derives its name from the spiral or helical path that is traced around the dislocation line by the atomic planes of atoms. Screw dislocation is represented by the symbol for clockwise or positive dislocation and for counterclockwise or negtive dislocation. Pruthvi Loy, Chiranth B.P. 13 SJEC, Mangalore
14 Table 1.3: Comparison of Edge and Screw dislocation Edge Dislocation It is created when a half plane of atoms is inserted in a crystal It moves in the direction of Burger s vector Burger s vector is perpendicular to the dislocation line Edge dislocation travels faster when loaded It requires less force to form and travels faster under loads. Atomic bonds around the dislocation line experiences tension and compression Symbolic representation: for positive dislocation for negetive dislocation Screw Dislocation It is created when a part of crystal displaces angularly over the remaining part It moves in the direction perpendicular to that of Burger s vector Burger s vector is parallel to the dislocation line Screw dislocation travels comparatively slower It requires comparatively high force to form and travels slower under loads Atomic bonds around the dislocation line experiences shear force. Symbolic representation: for positive dislocation for negtive dislocation Surface Imperfections External Surface: One of the most obvious surface defect is the external surface, along which the crystal structure terminates. Surface atoms are not bonded to the maximum number of nearest neighbors, and are therefore in a higher energy state than the atoms at interior positions. Grain Boundary: A grain boundary is formed when two adjoining growing crystals meet at their surface.the atoms are bonded less regularly along the grain boundary and are at a higher energy state as a result the impurity atoms preferentially segregate along these boundaries.also, grain boundary acts as a barrier for dislocation motion; the smaller the grains, larger is the grain boundary area and dislocations if any moves only a short distance and stops at the grain boundary. A polycrystalline solid contains numerous grains or crystals. Each crystal has nearly the same crystal structure but different orientations. The grain boundary is few atomic radius thick and contains crystallographic misalignment between adjacent grains; various degrees of crystallographic misalignments are possible. When this orientation mismatch is slight (of the order of few degrees), then it is termed as small angle grain boundary. A small angle of misorientation (less than 10) with the edge dislocations aligned in the manner as shown in figure 1.7(b), then it is called a tilt boundary. Pruthvi Loy, Chiranth B.P. 14 SJEC, Mangalore
15 Figure 1.7: (a) Grain boundary (b) Tilt boundary Twin Boundary: A twin plane or boundary is a special type of grain boundary across which there is a specific morror lattice symmetry; i.e., the atoms on one side of the boundary are located in mirror image positions of the atoms on the other side. The region of material between these boundaries is termed as twinned region. Figure 1.8: Twinning and twin boundary Stacking Faults: A crystal structure has a specific stacking sequence; any deviations from the actual stacking sequence of the plane of atoms is termed as a stacking fault. For example: The stacking sequence of a FCC structure is A, B, C, A, B, C, A, B, C,. Sometimes it may appear as A, B, C, A, B, A, B, C, with a missing C plane which is termed as a stacking fault. Pruthvi Loy, Chiranth B.P. 15 SJEC, Mangalore
16 1.4.4 Volume Imperfections These are three dimensional imperfections that are formed inside the solid material. These includes voids, cracks, foreign inclusions and other phases which are normally introduced during processing and fabrication. 1.5 ATOMIC DIFFUSION From an atomic perspective diffusion may be defined as the mass flow process by which atoms or molecules migrate from lattice site to lattice site within a material resulting in the uniformity of composition as a result of thermal agitation. The importance and various applications of diffusion phenomenon are; Diffusion occurs more rapidly with increasing temperature and is the basis for most metallurgical processes. Diffusion is fundamental to phase changes and is important aspect in heat treatment of metals. It is important in the formation of metallic bonds (soldering, welding, brazing, etc.) Diffusion Phenomenon Diffusion in solids can take place by the following methods; Vacancy diffusion Interstitial diffusion Vacancy diffusion involves the movement of an atom from original lattice position to an adjacent vacant lattice site. The extent to which vacancy diffusion can occur depends on the number of vacant sites present in the crystal; significant concentrations of vacancies may exist in metals at elevated temperature. Figure 1.9: Vacancy diffusion Interstitial diffusion involves the movement of interstitial atoms from an interstitial site to its neighbouring site without permanently displacing any of the parent atoms in a crystal lattice. With interstitial diffusion an activation energy is associated because to move into an adjacent interstitial site it must squeeze past the parent atoms in the crystal attice with the energy supplied by the vibrational energy of moving atoms. Pruthvi Loy, Chiranth B.P. 16 SJEC, Mangalore
17 Figure 1.10: Interstitial diffusion Interstitial diffusion occurs more rapidly than vacancy diffusion since interstitial atoms are smaller and as more empty interstitial positions are present than the vacancies Fick s Law of Diffusion Diffusion is a time dependent process; i.e., the quantity of an element that is transported within another is a function of time. Often it is necessary to know how fast diffusion occurs, or the rate of mass transfer. This rate is expressed as a diffusion flux (J), which is defined as the mass (m) diffusing through and perpendicular to a unit cross-sectional area of solid (A) per unit time (t). i.e., J = or J = kg/m -s or atoms/m -s The diffusion flux may or may not vary with time and accordingly we have two laws of diffusion: i. Fick s first law for steady state diffusion ii. Fick s second law for unsteady state diffusion Fick s first law of diffusion: It states that the flux of atoms (J), moving across a unit area in unit time is proportional to concentration gradient under steady state. Where, i.e., J or J = - D J diffusion flux, atoms/m -s concentration gradient D diffusivity or diffusion coefficient, m /s The negetive sign indicates that the direction of diffusion is down the concentration gradient, i.e., from a region of higher concenration to a region of lower concentration. Pruthvi Loy, Chiranth B.P. 17 SJEC, Mangalore
18 Concentration gradient is obtained as, = Figure 1.11: Steady state diffusion Fick s second law of diffusion: Most practical diffusion situations are usually of unsteady state. i.e., the diffusion flux and the concentration gradient at some particular point in solid vary with time resulting in net accumulation or depletion of diffusing species. Therefore, = * + Where, = rate of composition change = concentration gradient D = diffusivity, m /s Figure 1.1: Concentration profile for unsteady state diffusion Pruthvi Loy, Chiranth B.P. 18 SJEC, Mangalore
19 If diffusion coefficient is independent of concentration; = D i.e., the rate of composition change is equal to the diffusivity times the rate of concentration gradient. The solution to the above equation can be obtained by applying appropriate boundary conditions. For t = 0, C = C 0 (0 x ) For t > 0, C = C s (at x = 0) and C = C 0 (at x = ) Applying the above boundary conditions the solution can be obtained as, = 1 erf ( ) From the above equation and D are known. may be determined at any time and position if the parameters Factors Affecting Diffusion The various factors affecting diffusion are:. Grain size 3. Atomic radius 4. Temperature 5. Concentration Crystal Structure: The ease with which the atoms diffuse increases with decreasing density of packing. Example: Atoms have higher diffusion coefficients in BCC iron than FCC iron because the former has low atomic packing factor. Grain size: As we know grain boundary diffusion is faster than diffusion within the grains, it is to be expected that overall diffusion rate would be higher in fine grained material due to increased grain boundary. Atomic radius: Diffusion occurs more rapidly when the size of the diffusing atom is small. Example: diffusion of carbon atoms in iron. Concentration: a higher concentration gradient results in faster diffusion rates. Temperature: It has most profound influence on the coefficient and diffusion rate. The diffusion coefficient (D) is related to temperature by Arrhenius type of equation as shown below, Pruthvi Loy, Chiranth B.P. 19 SJEC, Mangalore
20 D = D 0 Where, D 0 temperature independent pre-exponential, m /s Q activation energy, J/mol R gas constant ( R = J/mol-K) T absolute temperature, K When the temperature increases, the diffusion coefficient increases and therefore the flow atoms also increase. Problems (Diffusion): 1. Calculate the diffusion coefficient for magnesium in aluminium at 570 C given that, D o = 1. x 10-4 m /s and Q = 131 kj/mole. Solution: D o = 1. x 10-4 m /s Q = 131 kj/mole = J/mole T = 570 C = = 843 K R = J/mol-K D = D 0 = 1. x 10-4 * + D = x m /s. It is proposed to enhance the surface wear resistance of a steel gear by carburizing treatment. The initial carbon content of steel is 0.15 wt%. After the treatment the surface concentration is to be maintained at 0.95 wt%. For the treatment to be effective a carbon content of 0.55 wt% must be established at 0.75mm below the surface. Specify appropriate heat treatment in terms of temperature and time for temperature 900 C to 1050 C. Take D o =.3x10-5 m /s, Q = J/mole. Solution: D o =.3x10-5 m /s Q = J/mole C 0 = 0.15 wt % C s = 0.95 wt % C x = 0.55 wt % X = 0.75 mm = m Pruthvi Loy, Chiranth B.P. 0 SJEC, Mangalore
21 WKT, = 1 erf ( ) = 1 erf, where, z = erf = Table 1.4: Error-function values From error-function value table, the value of z can be obtained by interpolation as follows, z z erf (z) i.e. = Therefore, z = 0.47 But z = = = 0.47 Dt = * + = 6.17 x 10-7 m Also, D = D 0 * + D = D 0 * + x For 900 C (1173 K) 6.17 x 10-7 =.3 x 10-5 * + x t = 9.6 hrs Similarly calculate for 950, 1000 and 1050 C Pruthvi Loy, Chiranth B.P. 1 SJEC, Mangalore
22 The following heat treatment parameters were calculated Temperature, C Time, hrs Steel gear, having carbon content of 0.% is to be gas carburized to achieve carbon content of 0.9% at the surface and 0.4% at 0.5mm depth from the surface. If the process is to be carried out at 97 C, find the time required for carburization. Take diffusion coefficient of carbon in given steel = 10.8x10-11 m /s. Given data: Z erf(z) Z Solution: D = 10.8x10-11 m /s C 0 = 0. % C s = 0.95 % C x = 0.4 % x = 0.5 mm = m WKT, = 1 erf ( ) = 1 erf ( ) = 1 erf ( ) = erf ( ) Let z = Equation (1) Therefore, erf(z) = Pruthvi Loy, Chiranth B.P. SJEC, Mangalore
23 From the given error-function value table, the value of z can be obtained by interpolation as follows, i.e. = Therefore, z = Substituting the value on z in equation (1), z = t = t = sec = 14.8 min References: 1. Fundamentals of Materials Science & Engineering William D. Callister. Material Science and Metallurgy K. R. Phaneesh 3. Material Science and Metallurgy Kesthoor Praveen 4. Mechanical Metallurgy G. E. Dieter Pruthvi Loy, Chiranth B.P. 3 SJEC, Mangalore
Defects and Diffusion
Defects and Diffusion Goals for the Unit Recognize various imperfections in crystals Point imperfections Impurities Line, surface and bulk imperfections Define various diffusion mechanisms Identify factors
More informationMaterials and their structures
Materials and their structures 2.1 Introduction: The ability of materials to undergo forming by different techniques is dependent on their structure and properties. Behavior of materials depends on their
More informationLearning Objectives. Chapter Outline. Solidification of Metals. Solidification of Metals
Learning Objectives Study the principles of solidification as they apply to pure metals. Examine the mechanisms by which solidification occurs. - Chapter Outline Importance of Solidification Nucleation
More informationImperfections, Defects and Diffusion
Imperfections, Defects and Diffusion Lattice Defects Week5 Material Sciences and Engineering MatE271 1 Goals for the Unit I. Recognize various imperfections in crystals (Chapter 4) - Point imperfections
More informationDefect in crystals. Primer in Materials Science Spring
Defect in crystals Primer in Materials Science Spring 2017 11.05.2017 1 Introduction The arrangement of the atoms in all materials contains imperfections which have profound effect on the behavior of the
More informationCHAPTER 5: DIFFUSION IN SOLIDS
CHAPTER 5: DIFFUSION IN SOLIDS ISSUES TO ADDRESS... How does diffusion occur? Why is it an important part of processing? How can the rate of diffusion be predicted for some simple cases? How does diffusion
More informationTOPIC 2. STRUCTURE OF MATERIALS III
Universidad Carlos III de Madrid www.uc3m.es MATERIALS SCIENCE AND ENGINEERING TOPIC 2. STRUCTURE OF MATERIALS III Topic 2.3: Crystalline defects. Solid solutions. 1 PERFECT AND IMPERFECT CRYSTALS Perfect
More informationSingle vs Polycrystals
WEEK FIVE This week, we will Learn theoretical strength of single crystals Learn metallic crystal structures Learn critical resolved shear stress Slip by dislocation movement Single vs Polycrystals Polycrystals
More informationImperfections in the Atomic and Ionic Arrangements
Objectives Introduce the three basic types of imperfections: point defects, line defects (or dislocations), and surface defects. Explore the nature and effects of different types of defects. Outline Point
More informationIMPERFECTIONSFOR BENEFIT. Sub-topics. Point defects Linear defects dislocations Plastic deformation through dislocations motion Surface
IMPERFECTIONSFOR BENEFIT Sub-topics 1 Point defects Linear defects dislocations Plastic deformation through dislocations motion Surface IDEAL STRENGTH Ideally, the strength of a material is the force necessary
More informationImperfections: Good or Bad? Structural imperfections (defects) Compositional imperfections (impurities)
Imperfections: Good or Bad? Structural imperfections (defects) Compositional imperfections (impurities) 1 Structural Imperfections A perfect crystal has the lowest internal energy E Above absolute zero
More informationStudent Name: ID Number:
Student Name: ID Number: DEPARTMENT OF MECHANICAL ENGINEERING CONCORDIA UNIVERSITY MATERIALS SCIENCE - MECH 1/ - Sections T & X MIDTERM 003 Instructors: Dr. M.Pugh & Dr. M.Medraj Time Allowed: one (1)
More information10/7/ :43 AM. Chapter 5. Diffusion. Dr. Mohammad Abuhaiba, PE
10/7/2013 10:43 AM Chapter 5 Diffusion 1 2 Why Study Diffusion? Materials of all types are often heat-treated to improve their properties. a heat treatment almost always involve atomic diffusion. Often
More informationN = N A ρ Pb A Pb. = ln N Q v kt. 지난문제. Below are shown three different crystallographic planes for a unit cell of some hypothetical metal.
지난문제. Below are shown three different crystallographic planes for a unit cell of some hypothetical metal. The circles represent atoms: (a) To what crystal system does the unit cell belong? (b) What would
More informationCHAPTER 5 IMPERFECTIONS IN SOLIDS PROBLEM SOLUTIONS
CHAPTER 5 IMPERFECTIONS IN SOLIDS PROBLEM SOLUTIONS Vacancies and Self-Interstitials 5.1 Calculate the fraction of atom sites that are vacant for copper at its melting temperature of 1084 C (1357 K). Assume
More informationLecture # 11 References:
Lecture # 11 - Line defects (1-D) / Dislocations - Planer defects (2D) - Volume Defects - Burgers vector - Slip - Slip Systems in FCC crystals - Slip systems in HCP - Slip systems in BCC Dr.Haydar Al-Ethari
More informationMaterials Science. Imperfections in Solids CHAPTER 5: IMPERFECTIONS IN SOLIDS. Types of Imperfections
In the Name of God Materials Science CHAPTER 5: IMPERFECTIONS IN SOLIDS ISSUES TO ADDRESS... What are the solidification mechanisms? What types of defects arise in solids? Can the number and type of defects
More informationDept.of BME Materials Science Dr.Jenan S.Kashan 1st semester 2nd level. Imperfections in Solids
Why are defects important? Imperfections in Solids Defects have a profound impact on the various properties of materials: Production of advanced semiconductor devices require not only a rather perfect
More information10/8/2016 8:29 PM. Chapter 5. Diffusion. Mohammad Suliman Abuhaiba, Ph.D., PE
Chapter 5 Diffusion 1 2 Home Work Assignments 10, 13, 17, 21, 27, 31, D1 Due Tuesday 18/10/2016 3 rd Exam on Sunday 23/10/2016 3 Why Study Diffusion? Materials of all types are often heattreated to improve
More informationLecture # 11. Line defects (1D) / Dislocations
Lecture # 11 - Line defects (1-D) / Dislocations - Planer defects (2D) - Volume Defects - Burgers vector - Slip - Slip Systems in FCC crystals - Slip systems in HCP - Slip systems in BCC References: 1-
More informationIntroduction to Engineering Materials ENGR2000 Chapter 4: Imperfections in Solids. Dr. Coates
Introduction to Engineering Materials ENGR000 Chapter 4: Imperfections in Solids Dr. Coates Learning Objectives 1. Describe both vacancy and self interstitial defects. Calculate the equilibrium number
More informationDr. Ali Abadi Chapter Three: Crystal Imperfection Materials Properties
Dr. Ali Abadi Chapter Three: Crystal Imperfection Materials Properties A perfect crystal, with every atom of the same type in the correct position, does not exist. There always exist crystalline defects,
More information11/2/2018 7:57 PM. Chapter 5. Diffusion. Mohammad Suliman Abuhaiba, Ph.D., PE
Chapter 5 Diffusion 1 2 Bonus Outsource a software for heat treatment Install the software Train yourself in using the software Apply case studies on the software Present your work in front of your colleagues
More informationENGINEERING MATERIALS LECTURE #4
ENGINEERING MATERIALS LECTURE #4 Chapter 3: The Structure of Crystalline Solids Topics to Cover What is the difference in atomic arrangement between crystalline and noncrystalline solids? What features
More informationChapter Outline. How do atoms arrange themselves to form solids?
Chapter Outline How do atoms arrange themselves to form solids? Fundamental concepts and language Unit cells Crystal structures! Face-centered cubic! Body-centered cubic! Hexagonal close-packed Close packed
More informationEx: NaCl. Ironically Bonded Solid
Ex: NaCl. Ironically Bonded Solid Lecture 2 THE STRUCTURE OF CRYSTALLINE SOLIDS 3.2 FUNDAMENTAL CONCEPTS SOLIDS AMORPHOUS CRYSTALLINE Atoms in an amorphous Atoms in a crystalline solid solid are arranged
More informationDiffusion phenomenon
Module-5 Diffusion Contents 1) Diffusion mechanisms and steady-state & non-steady-state diffusion 2) Factors that influence diffusion and nonequilibrium transformation & microstructure Diffusion phenomenon
More informationChapter Outline How do atoms arrange themselves to form solids?
Chapter Outline How do atoms arrange themselves to form solids? Fundamental concepts and language Unit cells Crystal structures Face-centered cubic Body-centered cubic Hexagonal close-packed Close packed
More informationTwo marks questions and answers. 1. what is a Crystal? (or) What are crystalline materials? Give examples
UNIT V CRYSTAL PHYSICS PART-A Two marks questions and answers 1. what is a Crystal? (or) What are crystalline materials? Give examples Crystalline solids (or) Crystals are those in which the constituent
More informationCrystal Defects. Perfect crystal - every atom of the same type in the correct equilibrium position (does not exist at T > 0 K)
Crystal Defects Perfect crystal - every atom of the same type in the correct equilibrium position (does not exist at T > 0 K) Real crystal - all crystals have some imperfections - defects, most atoms are
More informationCHAPTER 5 IMPERFECTIONS IN SOLIDS PROBLEM SOLUTIONS ev /atom = exp. kt ( =
CHAPTER 5 IMPERFECTIONS IN SOLIDS PROBLEM SOLUTIONS Vacancies and Self-Interstitials 5.1 Calculate the fraction of atom sites that are vacant for copper at its melting temperature of 1084 C (1357 K). Assume
More informationMaterial Science. Prof. Satish V. Kailas Associate Professor Dept. of Mechanical Engineering, Indian Institute of Science, Bangalore India
Material Science Prof. Satish V. Kailas Associate Professor Dept. of Mechanical Engineering, Indian Institute of Science, Bangalore 560012 India Chapter 3. Imperfections in Solids Learning objectives:
More informationCrystal structure of the material :- the manner in which atoms, ions, or molecules are spatially.
Crystal structure A crystalline material :- is one in which the atoms are situated in a repeating or periodic array over large atomic distances. Crystal structure of the material :- the manner in which
More informationPoint Defects. Vacancies are the most important form. Vacancies Self-interstitials
Grain Boundaries 1 Point Defects 2 Point Defects A Point Defect is a crystalline defect associated with one or, at most, several atomic sites. These are defects at a single atom position. Vacancies Self-interstitials
More informationPoint Defects in Metals
CHAPTER 5 IMPERFECTIONS IN SOLIDS PROBLEM SOLUTIONS Point Defects in Metals 5.1 Calculate the fraction of atom sites that are vacant for lead at its melting temperature of 327 C (600 K). Assume an energy
More informationChapter-3 MSE-201-R. Prof. Dr. Altan Türkeli
Chapter-3 MSE-201-R Prof. Dr. Altan Türkeli The Structure of Crystalline Solids FUNDAMENTAL CONCEPTS Solid materials may be classified according to the regularity with which atoms or ions are arranged
More informationOrder in materials. Making Solid Stuff. Primary Bonds Summary. How do they arrange themselves? Results from atomic bonding. What are they?
Making Solid Stuff Primary Bonds Summary What are they? Results from atomic bonding So the atoms bond together! Order in materials No long range order to atoms Gases little or no interaction between components
More informationMaterial Science. Prof. Satish V. Kailas Associate Professor Dept. of Mechanical Engineering, Indian Institute of Science, Bangalore India
Material Science Prof. Satish V. Kailas Associate Professor Dept. of Mechanical Engineering, Indian Institute of Science, Bangalore 560012 India Chapter 5. Diffusion Learning objectives: - To know the
More informationImperfections in atomic arrangements
MME131: Lecture 9 Imperfections in atomic arrangements Part 2: 1D 3D Defects A. K. M. B. Rashid Professor, Department of MME BUET, Dhaka Today s Topics Classifications and characteristics of 1D 3D defects
More informationDefects in solids http://www.bath.ac.uk/podcast/powerpoint/inaugural_lecture_250407.pdf http://www.materials.ac.uk/elearning/matter/crystallography/indexingdirectionsandplanes/indexing-of-hexagonal-systems.html
More informationChapter 5. Imperfections in Solids
Chapter 5 Imperfections in Solids Chapter 5 2D Defects and Introduction to Diffusion Imperfections in Solids Issues to Address... What types of defects arise in solids? Can the number and type of defects
More informationMETALLIC CRYSTALS. tend to be densely packed. have several reasons for dense packing: have the simplest crystal structures.
METALLIC CRYSTALS tend to be densely packed. have several reasons for dense packing: -Typically, only one element is present, so all atomic radii are the same. -Metallic bonding is not directional. -Nearest
More informationChapter 3 Structure of Crystalline Solids
Chapter 3 Structure of Crystalline Solids Crystal Structures Points, Directions, and Planes Linear and Planar Densities X-ray Diffraction How do atoms assemble into solid structures? (for now, focus on
More informationPoint coordinates. x z
Point coordinates c z 111 a 000 b y x z 2c b y Point coordinates z y Algorithm 1. Vector repositioned (if necessary) to pass through origin. 2. Read off projections in terms of unit cell dimensions a,
More informationStacking Oranges. Packing atoms together Long Range Order. What controls the nearest number of atoms? Hard Sphere Model. Hard Sphere Model.
{ Stacking atoms together Crystal Structure Stacking Oranges Packing atoms together Long Range Order Crystalline materials... atoms pack in periodic, 3D arrays typical of: -metals -many ceramics -some
More informationStructure of Metals 1
1 Structure of Metals Metals Basic Structure (Review) Property High stiffness, better toughness, good electrical conductivity, good thermal conductivity Why metals have these nice properties - structures
More informationThe Science and Engineering of Materials, 4 th ed Donald R. Askeland Pradeep P. Phulé. Chapter 3 Atomic and Ionic Arrangements
The Science and Engineering of Materials, 4 th ed Donald R. Askeland Pradeep P. Phulé Chapter 3 Atomic and Ionic Arrangements 1 Objectives of Chapter 3 To learn classification of materials based on atomic/ionic
More information(a) Would you expect the element P to be a donor or an acceptor defect in Si?
MSE 200A Survey of Materials Science Fall, 2008 Problem Set No. 2 Problem 1: At high temperature Fe has the fcc structure (called austenite or γ-iron). Would you expect to find C atoms in the octahedral
More informationDensity Computations
CHAPTER 3 THE STRUCTURE OF CRYSTALLINE SOLIDS Fundamental Concepts 3.1 What is the difference between atomic structure and crystal structure? Unit Cells Metallic Crystal Structures 3.2 If the atomic radius
More informationPoint coordinates. Point coordinates for unit cell center are. Point coordinates for unit cell corner are 111
Point coordinates c z 111 Point coordinates for unit cell center are a/2, b/2, c/2 ½ ½ ½ Point coordinates for unit cell corner are 111 x a z 000 b 2c y Translation: integer multiple of lattice constants
More informationDislocations and Plastic Deformation
Dislocations and Plastic Deformation Edge and screw are the two fundamental dislocation types. In an edge dislocation, localized lattice distortion exists along the end of an extra half-plane of atoms,
More informationEnergy and Packing. typical neighbor bond energy. typical neighbor bond energy. Dense, regular-packed structures tend to have lower energy.
Energy and Packing Non dense, random packing Energy typical neighbor bond length typical neighbor bond energy r Dense, regular packing Energy typical neighbor bond length typical neighbor bond energy r
More informationPacking of atoms in solids
MME131: Lecture 6 Packing of atoms in solids A. K. M. B. Rashid Professor, Department of MME BUET, Dhaka Today s topics Atomic arrangements in solids Points, directions and planes in unit cell References:
More informationProblems. 104 CHAPTER 3 Atomic and Ionic Arrangements
104 CHAPTER 3 Atomic and Ionic Arrangements Repeat distance The distance from one lattice point to the adjacent lattice point along a direction. Short-range order The regular and predictable arrangement
More informationImpurities in Solids. Crystal Electro- Element R% Structure negativity Valence
4-4 Impurities in Solids 4.4 In this problem we are asked to cite which of the elements listed form with Ni the three possible solid solution types. For complete substitutional solubility the following
More informationModule 10. Crystal Defects in Metals I. Lecture 10. Crystal Defects in Metals I
Module 10 Crystal Defects in Metals I Lecture 10 Crystal Defects in Metals I 1 NPTEL Phase II : IIT Kharagpur : Prof. R. N. Ghosh, Dept of Metallurgical and Materials Engineering Introduction Keywords:
More informationIntroduction to Engineering Materials ENGR2000 Chapter 3: The Structure of Crystalline Solids. Dr. Coates
Introduction to Engineering Materials ENGR2000 Chapter 3: The Structure of Crystalline Solids Dr. Coates Learning Objectives I 1. Describe difference in atomic/molecular structure between crystalline/noncrystalline
More informationMaterials Science ME 274. Dr Yehia M. Youssef. Materials Science. Copyright YM Youssef, 4-Oct-10
ME 274 Dr Yehia M. Youssef 1 The Structure of Crystalline Solids Solid materials may be classified according to the regularity with which atoms or ions are arranged with respect to one another. A crystalline
More informationFundamental concepts and language Unit cells Crystal structures! Face-centered cubic! Body-centered cubic! Hexagonal close-packed Close packed
Fundamental concepts and language Unit cells Crystal structures! Face-centered cubic! Body-centered cubic! Hexagonal close-packed Close packed crystal structures Density computations Crystal structure
More informationChrystal Structures Lab Experiment 1. Professor Greene Mech Submitted: 4 February, 2009 Max Nielsen Trevor Nickerson Ben Allen Kushal Sherpa
Chrystal Structures Lab Experiment 1 Professor Greene Mech 496-02 Submitted: 4 February, 2009 Max Nielsen Trevor Nickerson Ben Allen Kushal Sherpa Abstract: The study of materials science requires an understanding
More informationdiffusion is not normally subject to observation by noting compositional change, because in pure metals all atoms are alike.
71 CHAPTER 4 DIFFUSION IN SOLIDS 4.1 INTRODUCTION In the previous chapters we learnt that any given atom has a particular lattice site assigned to it. Aside from thermal vibration about its mean position
More informationبسم هللا الرحمن الرحیم. Materials Science. Chapter 3 Structures of Metals & Ceramics
بسم هللا الرحمن الرحیم Materials Science Chapter 3 Structures of Metals & Ceramics 1 ISSUES TO ADDRESS... How do atoms assemble into solid structures? How does the density of a material depend on its structure?
More informationLecture 3: Description crystal structures / Defects
Lecture 3: Description crystal structures / Defects Coordination Close packed structures Cubic close packing Hexagonal close packing Metallic structures Ionic structures with interstitial sites Important
More informationMSE 170 Midterm review
MSE 170 Midterm review Exam date: 11/2/2008 Mon, lecture time Place: Here! Close book, notes and no collaborations A sheet of letter-sized paper with double-sided notes is allowed Material on the exam
More informationatoms = 1.66 x g/amu
CHAPTER 2 Q1- How many grams are there in a one amu of a material? A1- In order to determine the number of grams in one amu of material, appropriate manipulation of the amu/atom, g/mol, and atom/mol relationships
More informationStructure of silica glasses (Chapter 12)
Questions and Problems 97 Glass Ceramics (Structure) heat-treated so as to become crystalline in nature. The following concept map notes this relationship: Structure of noncrystalline solids (Chapter 3)
More informationChapter Outline Dislocations and Strengthening Mechanisms. Introduction
Chapter Outline Dislocations and Strengthening Mechanisms What is happening in material during plastic deformation? Dislocations and Plastic Deformation Motion of dislocations in response to stress Slip
More informationStrengthening Mechanisms
ME 254: Materials Engineering Chapter 7: Dislocations and Strengthening Mechanisms 1 st Semester 1435-1436 (Fall 2014) Dr. Hamad F. Alharbi, harbihf@ksu.edu.sa November 18, 2014 Outline DISLOCATIONS AND
More informationChapter 4: Imperfections (Defects) in Solids
Chapter 4: Imperfections (Defects) in Solids ISSUES TO ADDRESS... What types of defects exist in solids? How do defects affect material properties? Can the number and type of defects be varied and controlled?
More information9/29/2014 8:52 PM. Chapter 3. The structure of crystalline solids. Dr. Mohammad Abuhaiba, PE
1 Chapter 3 The structure of crystalline solids 2 Home Work Assignments HW 1 2, 7, 12, 17, 22, 29, 34, 39, 44, 48, 53, 58, 63 Due Sunday 12/10/2014 Quiz # 1 will be held on Monday 13/10/2014 at 11:00 am
More informationSOLIDIFICATION, PHASE DIAGRAM & STEELS
MODULE TWO SOLIDIFICATION, PHASE DIAGRAM & STEELS 4. SOLIDIFICATION Introduction Mechanism of solidification - crystallization and development of cast structure - nucleation and grain growth - dendritic
More informationChapter 3: Atomic and Ionic Arrangements. Chapter 3: Atomic and Ionic Arrangements Cengage Learning Engineering. All Rights Reserved.
Chapter 3: Atomic and Ionic Arrangements 3-1 Learning Objectives 1. 2. 3. 4. 5. 6. 7. 8. Short-range order versus long-range order Amorphous materials Lattice, basis, unit cells, and crystal structures
More information9/28/2013 9:26 PM. Chapter 3. The structure of crystalline solids. Dr. Mohammad Abuhaiba, PE
Chapter 3 The structure of crystalline solids 1 2 Why study the structure of crystalline solids? Properties of some materials are directly related to their crystal structure. Significant property differences
More informationChapter 7 Dislocations and Strengthening Mechanisms. Dr. Feras Fraige
Chapter 7 Dislocations and Strengthening Mechanisms Dr. Feras Fraige Chapter Outline Dislocations and Strengthening Mechanisms What is happening in material during plastic deformation? Dislocations and
More informationChapter 5: Diffusion. Introduction
Chapter 5: Diffusion Outline Introduction Diffusion mechanisms Steady-state diffusion Nonsteady-state diffusion Factors that influence diffusion Introduction Diffusion: the phenomenon of material transport
More information4-Crystal Defects & Strengthening
4-Crystal Defects & Strengthening A perfect crystal, with every atom of the same type in the correct position, does not exist. The crystalline defects are not always bad! Adding alloying elements to a
More informationEnergy and Packing. Materials and Packing
Energy and Packing Non dense, random packing Energy typical neighbor bond length typical neighbor bond energy r Dense, regular packing Energy typical neighbor bond length typical neighbor bond energy r
More informationCRYSTAL STRUCTURE TERMS
CRYSTAL STRUCTURE TERMS crystalline material - a material in which atoms, ions, or molecules are situated in a periodic 3-dimensional array over large atomic distances (all metals, many ceramic materials,
More informationMovement of edge and screw dislocations
Movement of edge and screw dislocations Formation of a step on the surface of a crystal by motion of (a) n edge dislocation: the dislocation line moves in the direction of the applied shear stress τ. (b)
More informationChapter1: Crystal Structure 1
Chapter1: Crystal Structure 1 University of Technology Laser Engineering & Optoelectronic Department Glass: 3 rd year Optoelectronic Engineering Subject: Solid state physics & material science Ass. Prof.
More informationFrom sand to silicon wafer
From sand to silicon wafer 25% of Earth surface is silicon Metallurgical grade silicon (MGS) Electronic grade silicon (EGS) Polycrystalline silicon (polysilicon) Single crystal Czochralski drawing Single
More informationME 254 MATERIALS ENGINEERING 1 st Semester 1431/ rd Mid-Term Exam (1 hr)
1 st Semester 1431/1432 3 rd Mid-Term Exam (1 hr) Question 1 a) Answer the following: 1. Do all metals have the same slip system? Why or why not? 2. For each of edge, screw and mixed dislocations, cite
More informationmuch research (in physics, chemistry, material science, etc.) have been done to understand the difference in materials properties.
1.1: Introduction Material science and engineering Classify common features of structure and properties of different materials in a well-known manner (chemical or biological): * bonding in solids are classified
More informationMME 2001 MATERIALS SCIENCE
MME 2001 MATERIALS SCIENCE 1 20.10.2015 crystal structures X tal structure Coord. # Atoms/ unit cell a=f(r) APF % SC 6 1 2R 52 BCC 8 2 4R/ 3 68 FCC 12 4 2R 2 74 HCP 12 6 2R 74 Theoretical Density, knowing
More informationThese metal centres interact through metallic bonding
The structures of simple solids The majority of inorganic compounds exist as solids and comprise ordered arrays of atoms, ions, or molecules. Some of the simplest solids are the metals, the structures
More informationSolid State Device Fundamentals
Solid State Device Fundamentals ENS 345 Lecture Course by Alexander M. Zaitsev alexander.zaitsev@csi.cuny.edu Tel: 718 982 2812 Office 4N101b 1 Interatomic bonding Bonding Forces and Energies Equilibrium
More informationChapter 2. Ans: e (<100nm size materials are called nanomaterials)
Chapter 2 1. Materials science and engineering include (s) the study of: (a) metals (b) polymers (c) ceramics (d) composites (e) nanomaterials (f) all of the above Ans: f 2. Which one of the following
More information12/10/09. Chapter 4: Imperfections in Solids. Imperfections in Solids. Polycrystalline Materials ISSUES TO ADDRESS...
Chapter 4: ISSUES TO ADDRESS... What are the solidification mechanisms? What types of defects arise in solids? Can the number and type of defects be varied and controlled? How do defects affect material
More informationThe structures of pure metals are crystalline (crystal lattice) with regular arrangement of metal atoms that are identical perfect spheres.
HW#3 Louisiana Tech University, Chemistry 481. POGIL (Process Oriented Guided Inquiry Learning) Exercise on Chapter 3. Metals and Alloys. Why? Metals What is the structure of a metallic solid? What is
More informationCHAPTER 6 OUTLINE. DIFFUSION and IMPERFECTIONS IN SOLIDS
CHAPTER 6 DIFFUSION and IMPERFECTIONS IN SOLIDS OUTLINE 1. TYPES OF DIFFUSIONS 1.1. Interdiffusion 1.2. Selfdiffusion 1.3.Diffusion mechanisms 1.4.Examples 2. TYPES OF IMPERFECTIONS 2.1.Point Defects 2.2.Line
More information9/16/ :30 PM. Chapter 3. The structure of crystalline solids. Mohammad Suliman Abuhaiba, Ph.D., PE
Chapter 3 The structure of crystalline solids 1 Mohammad Suliman Abuhaiba, Ph.D., PE 2 Home Work Assignments HW 1 2, 7, 12, 17, 22, 29, 34, 39, 44, 48, 53, 58, 63 Due Sunday 17/9/2015 3 Why study the structure
More informationSOLID STATE
SOLID STATE Short Answer Questions: 1. Derive Bragg s equation? Ans. Bragg s equation: W.H. Bragg has proposed an equation to explain the relation between inter planar distance (d) and wave length ( λ
More informationCHAPTER 3. Crystal Structures and Crystal Geometry 3-1
CHAPTER 3 Crystal Structures and Crystal Geometry 3-1 The Space Lattice and Unit Cells 3-2 Atoms, arranged in repetitive 3-Dimensional pattern, in long range order (LRO) give rise to crystal structure.
More informationVLSI Technology Dr. Nandita Dasgupta Department of Electrical Engineering Indian Institute of Technology, Madras
VLSI Technology Dr. Nandita Dasgupta Department of Electrical Engineering Indian Institute of Technology, Madras Lecture - 5 Crystal Structure contd So far, we have discussed about the crystal structure
More informationTutorial 2 : Crystalline Solid, Solidification, Crystal Defect and Diffusion
Tutorial 1 : Introduction and Atomic Bonding 1. Explain the difference between ionic and metallic bonding between atoms in engineering materials. 2. Show that the atomic packing factor for Face Centred
More informationSolid State Device Fundamentals
Solid State Device Fundamentals ENS 345 Lecture Course by Alexander M. Zaitsev alexander.zaitsev@csi.cuny.edu Tel: 718 982 2812 Office 4N101b 1 Solids Three types of solids classified according to atomic
More informationCHAPTER 3: CRYSTAL STRUCTURES & PROPERTIES
CHAPTER 3: CRYSTAL STRUCTURES & PROPERTIES ISSUES TO ADDRESS... How do atoms assemble into solid structures? (for now, focus on metals) How does the density of a material depend on its structure? When
More informationTwins & Dislocations in HCP Textbook & Paper Reviews. Cindy Smith
Twins & Dislocations in HCP Textbook & Paper Reviews Cindy Smith Motivation Review: Outline Crystal lattices (fcc, bcc, hcp) Fcc vs. hcp stacking sequences Cubic {hkl} naming Hcp {hkil} naming Twinning
More informationGeneral Objective. To develop the knowledge of crystal structure and their properties.
CRYSTAL PHYSICS 1 General Objective To develop the knowledge of crystal structure and their properties. 2 Specific Objectives 1. Differentiate crystalline and amorphous solids. 2. To explain nine fundamental
More informationChapter 7: Dislocations and strengthening mechanisms
Chapter 7: Dislocations and strengthening mechanisms Introduction Basic concepts Characteristics of dislocations Slip systems Slip in single crystals Plastic deformation of polycrystalline materials Plastically
More information