BME - lecture 2

Basic Materials Engineering Course Notes

Overview

  • Instructor: Łukasz Kołodziejczyk, Prof. TUL

  • Institution: Politechnika Łódzka, Institute of Materials Science & Engineering

  • Email: lukasz.kolodziejczyk@p.lodz.pl

1. Crystalline Solids

A. Structure of Crystalline Solids

  1. Imperfections in Solids

    • Defects in materials that can influence physical properties.

  2. Dislocations and Strengthening Mechanisms

    • A focus on how dislocation dynamics can affect material strength.

2. Short-Range Order (SRO) vs. Long-Range Order (LRO)

A. Short-Range Order (SRO)

  • Found in monoatomic gases or plasma in types of light.

  • Atoms or ions lack orderly arrangement and randomly fill available space.

  • Related to amorphous materials (e.g., liquid crystals).

B. Long-Range Order (LRO)

  • Seen in materials like metals, alloys, ceramics, semiconductors, and some polymers.

  • Atoms or ions maintain a repetitive, grid-like pattern in three dimensions.

  • Characterized by an orderly arrangement extending over a length scale of greater than 100 nm.

3. Single Crystal vs. Polycrystalline Materials

  • Single Crystal Material: Contains only one crystal; properties depend on chemical composition and directional characteristics.

  • Polycrystalline Material: Composed of multiple crystal grains with different orientations.

    • Grain Boundaries are regions of misalignment between adjacent crystals.

    • Properties depend on the characteristics of both the grains and grain boundaries.

4. Amorphous Materials

  • Defined as materials that exhibit only a short-range order.

  • Form when the kinetics of manufacturing do not allow periodic arrangements.

  • Examples: Glass, certain polymers, colloidal gels.

  • Unique properties arise from their irregular atomic arrangements.

5. Basic Crystallography Terms

A. Lattice

  • A collection of points in a periodic arrangement, where each point has identical surroundings.

  • Can be 1D, 2D, or 3D.

B. Motif (Basis)

  • Group of one or more atoms associated with each lattice point.

C. Crystal Structure

  • Formed by combining the lattice and motif.

D. Unit Cell

  • The smallest subdivision of a lattice that retains lattice characteristics; can be stacked to create the whole lattice.

6. Bravais Lattices

  • There are seven unique crystal systems for three-dimensional space filling:

    1. Cubic

    2. Tetragonal

    3. Orthorhombic

    4. Rhombohedral (Trigonal)

    5. Hexagonal

    6. Monoclinic

    7. Triclinic

  • There are 14 distinct arrangements known as Bravais lattices.

7. Lattice Parameters

  • Describe the size and shape of the unit cell:

    • Dimensions of the sides of the unit cell

    • Angles between the sides.

8. Metallic Crystal Structures

A. Common Metallic Structures

  • Most metals are found in three crystal structures: FCC (Face-Centered Cubic), BCC (Body-Centered Cubic), and HCP (Hexagonal Close-Packed).

B. Examples of Metallic Crystals

  1. Aluminum (FCC), Atomic Radius: 0.1431 nm

  2. Molybdenum (BCC), Atomic Radius: 0.1363 nm

  3. Cadmium (HCP), Atomic Radius: 0.1490 nm

  4. Nickel (FCC), Atomic Radius: 0.1246 nm

  5. Chromium (BCC), Atomic Radius: 0.1249 nm

  6. Platinum (FCC), Atomic Radius: 0.1387 nm

  7. Cobalt (HCP), Atomic Radius: 0.1253 nm

  8. Silver (FCC), Atomic Radius: 0.1445 nm

  9. Copper (FCC), Atomic Radius: 0.1278 nm

  10. Tantalum (BCC), Atomic Radius: 0.1430 nm

  11. Gold (FCC), Atomic Radius: 0.1442 nm

  12. Titanium (α) (HCP), Atomic Radius: 0.1445 nm

  13. Iron (α) (BCC), Atomic Radius: 0.1241 nm

  14. Tungsten (BCC), Atomic Radius: 0.1371 nm

  15. Lead (FCC), Atomic Radius: 0.1750 nm

  16. Zinc (HCP), Atomic Radius: 0.1332 nm

9. Number of Atoms per Unit Cell

  • Each unit cell's definition includes specific numbers of lattice points, with identifiable positions:

    • Corner atoms

    • Body-centered atoms

    • Face-centered atoms

  • Each corner point can be shared by multiple unit cells.

A. Calculation Formula

N = Ni + rac{Nf}{2} + rac{N_c}{8}

  • Where:

    • $N_i$ = number of interior atoms

    • $N_f$ = number of face atoms

    • $N_c$ = number of corner atoms

    • $X$ = 8 for cubic and 6 for hexagonal forms.

10. Allotropic or Polymorphic Transformations

  • Materials having more than one crystal structure are categorized as allotropic or polymorphic.

  • This applies to both pure elements and compounds.

11. Isotropic and Anisotropic Behavior

A. Definitions

  • Isotropic Material: Properties are identical in all directions.

  • Anisotropic Material: Properties depend on the crystallographic direction measured.

B. General Trends

  • Most polycrystalline materials display isotropic properties.

  • Single crystals or oriented grains exhibit anisotropic mechanical, optical, magnetic, and dielectric properties.

12. Imperfections in Atomic and Ionic Arrangements

  • Engineered materials contain defects which impact properties:

    • Point Defects

    • Line Defects (Dislocations)

    • Surface Defects

13. Point Defects

  • Localized disruptions in the crystal structure.

  • Three significant types include:

    1. Vacancy: An atom or ion missing from its normal site.

    2. Interstitial Atom: An extra atom inserted into vacant positions in the crystal.

    3. Substitutional Atom: An atom replaced by a different type.

A. Impurities and Dopants

  • Impurities: Naturally present elements or compounds.

  • Dopants: Elements added intentionally in known concentrations for beneficial effects.

14. Vacancies

  • Defined as when an atom or ion is absent.

  • Produce increased randomness, raising entropy and boosting thermodynamic stability.

A. Formation

of vacancies can occur during phase transitions, such as melting or solidification, which allow materials to adapt to changing environmental conditions.

15. Interstitial Defects

  • Form when an extra atom is inserted into a normally unoccupied crystal position.

  • They hinder dislocation movement, thereby enhancing material strength.

  • Their concentration stays relatively steady regardless of temperature changes.

16. Substitutional Defects

  • Arise from replacing one atom with a different type in the lattice.

  • May alter surrounding interatomic distances, often enhancing the material's strength.

17. Dislocations

  • Line imperfections formed during solidification or plastic deformation.

  • Crucial for understanding deformation and strength in materials, especially metals.

A. Types of Dislocations

  1. Screw Dislocation

  2. Edge Dislocation

  3. Mixed Dislocation

18. Edge Dislocations

  • Conceptualized by cutting a perfect crystal and filling a space with an extra atomic plane.

A. Burgers Vector

  • The Burgers vector ($ extbf{b}$) indicates displacement created by an edge dislocation, and is perpendicular to the edge dislocation line.

19. Screw Dislocations

  • Formed by skewing a crystal, creating a displacement indicated by the Burgers vector ( extbf{b}) parallel to the dislocation's axis.

20. Mixed Dislocations

  • Characteristics of both edge and screw dislocations, with a Burgers vector neither perpendicular nor parallel.

21. Surface Defects

  • Defects that separate areas with different structures or orientations:

    • Interfacial Defects

    • External Surfaces

    • Grain Boundaries

    • Phase Boundaries

    • Twin Boundaries

    • Stacking Faults

22. Dislocations and Strengthening Mechanisms

  • Understanding these mechanisms is essential for designing properties such as strength and toughness in metals and composites.

23. Plastic Deformation vs. Dislocation Motion

  • Plastic deformation involves the movement of numerous dislocations.

  • The process of deformation termed slip occurs along slip planes.

24. Analogy with Caterpillar

  • The motion of dislocations can be likened to a caterpillar moving.

25. Formation of a Step

  • Illustrated by the motion of edge and screw dislocations with respect to applied shear stress ($ au$).

26. Dislocation Density

  • Refers to the number of dislocations per unit area or volume of a material.

A. Expression

  • Measured in millimeters of dislocation per cubic millimeter or equivalent to dislocations per square millimeter.

  • Values include:

    • Carefully solidified metals: approx. $10^3$ dislocations/mm$^3$

    • Heavily deformed metals: $10^9$ to $10^{10}$ dislocations/mm$^3$

    • Deformed metals post-heat treatment: $10^5$ to $10^6$ dislocations/mm$^3$

    • Ceramic materials: $10^2$ to $10^4$ dislocations/mm$^3$

    • Silicon single crystals: $0.1$ to $1$ dislocations/mm$^3$

27. Case Study: Dislocation Interactions

  • Focus on dislocation annihilation in a perfect crystal structure.

28. Slip Systems

  • Dislocations have preferred planes for movement due to atomic arrangements.

A. Definitions

  • Slip Plane: Plane with highest atomic packing density.

  • Slip Direction: Direction along the plane that is most densely packed with atoms.

29. Conclusion

  • On a microscopic level, plastic deformation corresponds to the MOTION OF DISLOCATIONS in reaction to applied shear stress.