Defects in Crystals Chapter 4

The Structure of Steel looks simple

If you look at a piece of metal through a microscope, you start to see structure -called grains These grains of steel are on the microscopic level and are approximately 10*10 -6 meters across Each grain is a single crystal

Go even deeper, and you start to see the crystal structure  Atomic Force Microscope image of the surface of an artificial opal  Notice the hexagonal packing of the surface layer

Imperfections  Most atoms are in ideal locations  Small number are out of place  Defects  Line Defects  Point Defects  Surface Defects  Dominate the material properties All real materials have defects

How can we affect the strength of metals inside a grain?  Ductility (ability to change shapes) is affected by many factors  It is the result of planes of atoms slipping past each other If we can make it hard for slip to happen, we make the material stronger

If we disrupt the crystal structure, the ability to slip is affected  Some “defects” in the crystal occur naturally.  They include planes of atoms that are misaligned,  and atoms that for some reason are not at the lattice points  Alloying has been used for centuries to add “impurities” to metallic crystals that make it harder for slip to occur.

Strength of a Material  Based on the bond strength most materials should be much stronger than they are  From Chapter Two we know that the strength for an ionic bond should be about 10 6 psi  More typical strength is 40*10 3 psi  Why?  Materials must not usually fail by breaking bonds!!

Slip

Slip is easiest along dislocations  Line imperfections in a 3D lattice  Edge  Screw  Mixed

Real materials have lots of dislocations, therefore the strength of the material depends on the force required to make the dislocation move, not the bonding energy

Deformation  Deformation of materials occurs when a line defect (dislocation) moves through the material  Be sure to watch the video from the CD that came with your book

Edge Dislocation  Extra plane of atoms  See the animations on the text CD  Burgers vector  Deformation direction  For edge dislocations it is perpendicular to the dislocation line

Edge Dislocation

A 3D way to visualize an edge dislocation

Screw Dislocation  A ramped step  Burgers vector  Direction of the displacement of the atoms  For a screw dislocation it is parallel to the line of the dislocation  Harder to visualize than edge dislocations

Mixed Dislocation A combination of an edge dislocation and a screw dislocation

Deformation  When a shear force is applied to a material, the dislocations move  Do the “paper clip” experiment  Bend a paper clip back and forth  Just before it breaks, the surface feels rough  It’s the dislocations coming to the surface!!

Slip  When dislocations move slip occurs  Direction of movement – same as the Burgers vector  Slip is easiest on close packed planes  Slip is easiest in the close packed direction

Slip Systems  The combination of a closely packed plane and a close packed direction  The available slip systems depend on the crystal geometry

Common Slip Systems Crystal Structure Slip PlaneSlip Direction Strength FCC Metals {111} Strong and ductile BCC Metals {110} {112} {123} Stronger but less ductile HCP Metals {0001} Very strong but brittle

Some of the FCC Slip Systems Z Y X Notice how the slip systems intersect, which allows for cross-slip

Some of the Body Centered Cubic Slip Systems Cross slip is also possible in body centered cubic cells

Hexagonal Close Packed Slip systems All of these slip systems are parallel, and do not intersect

Slip  Affects  Ductility  Material Strength

What happens when a dislocation runs into a flaw?  Takes more energy to move “over the flaw” – See the video on the CD provided with your book  May stop moving all together  Therefore…..  Introducing flaws into the material, actually strengthens it!!

Dislocation Interactions One type of “flaw”  Dislocation tangles  When dislocations run into each other you get the traffic jam effect  More dislocations actually increase the strength of a material  (Remember – real materials already have a lot of dislocations – just like SLC already has a lot of traffic)  More traffic results in grid lock, not more cars moving

Dislocation Tangles Graphics by Meijie Tang, Rich Cook, Sean Ahern of Lawrence Livermore National Laboratory

Dislocation Tangle

All real materials have some dislocations  Additional dislocations are generated when the materials are deformed  Called a Frank-Read source

Frank Read Source  More dislocations are produced when a moving dislocation encounters an impurity  Applying a force to the material increases the number of dislocations  Traffic jams are more common  Called “strain hardening” or “cold work” and is discussed in Chapter 7

Schmidt’s Law  In order for a dislocation to move in its slip system, a shear force acting in the slip direction must be produced by the applied force.

Schmidt’s Law Slip direction Normal to slip plane  AoAo   F/A o  r  F r / A - Resolved Shear Stress

Schmidt’s Law  F r = F cos(      cos(    cos(  ) cos(    Where:   F r / A = resolved shear stress in the slip direction   = F/A o = unidirectional stress applied to the cylinder

Point Defects  Affect material properties because they affect slip – they make it hard for dislocations to move  All real materials have point defects  More can be added intentionally  Hamper movement of dislocations and MAKE THE MATERIAL STRONGER

Types of Point Defects  Vacancy  Interstitial  Substitutional  Larger  Smaller  Interstitialcy  Frenkel  Schottky You’ll need to know these!!

Vacancies  There are naturally occurring vacancies in all crystals  The number of vacancies goes up as the temperature goes up  You can calculate the number of vacancies N v = N exp(-Q/RT)  Depending on the units for Q, you may use the Boltzmann constant instead of R

# Vacancies goes up with temperature  N v = N exp(-Q/RT)  N is the total number of sites in a sample  N v is the number of vacancies  Q is the activation energy for the formation of a vacancy  R is the gas constant, cal/mole K  N v goes up exponentially with temperature

You can strengthen copper by heating it in boiling water  Additional vacancies are formed  They persist at room temperature – at least for a while

Density  What happens to the predicted density if you have a lot of vacancies?  The material is less dense

 More vacancies equals a stronger material  Vacancies distort the crystal lattice  This makes it harder for dislocations to move

Solid Solution Strengthening  Adding an atom to a crystal matrix  Interstitial  Substitutional

Interstitial atoms  An atom must be fairly tiny to fit into the interstitial holes  Hydrogen and Helium can diffuse fairly rapidly through metals by moving through the interstitial holes  Interstitial Carbon is commonly used to strengthen iron - it distorts the matrix

Substitutional Defects  We’ll talk more about substitutional atoms in later chapters  Substitutional atoms distort the crystal lattice, strengthening the material  Substitutional atoms can be either larger or smaller than the surrounding atoms

Surface and Grain Boundaries  The atoms at the boundary of a grain or on the surface are not surrounded by other atoms – they are not held in place as strongly  Grains don’t line up perfectly where the grain boundaries meet – that’s an imperfection too.  Dislocations can usually not cross grain boundaries

Grain Boundaries Austenitic Steel

Affect of Grain Size on Strength  In a small grain, a dislocation gets to the boundary and stops – slip stops  In a large grain, the dislocation can travel farther  Small grain size equates to more strength

Hall-Petch Equation   y =  0 + K d –1/2   y = yield strength (stress at which the material permanently deforms)  d = average diameter of the grains     constant  K = constant

ASTM Grain Size  N = 2 n-1  N is the number of grains per square inch at a magnification of 100  n is the ASTM grain size

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Amorphous Structures  If you cool a material off too fast it does not have a chance to crystalize  Called a glass  It is relatively easy to make a ceramic glass  It is hard to make a metallic glass  There are no slip planes in a glass!!

Amorphous Metals  Sometimes called liquid metals  We can make it hard for metals to crystallize by alloying with atoms of many different sizes

You can also make an amorphous metal by cooling the molten metal very quickly Amorphous metals are also called metallic glasses

What do you think happens to the strength of a metal if it can’t form regular crystals? It gets stronger and harder!!

Check out this video if you missed the in-class demonstration

Liquid Metal Head on a Racquet – for better bounce

Golf Clubs Liquid Metal Head

Baseball Bats

In Conclusion – How can you Control the Slip Process?  Strain hardening  Forming additional dislocations that run into each other and therefore can’t move  Solid Solution strengthening  Adding impurities which make it hard for dislocations to move  Grain Size strengthening  Controlling the grain size  Smaller crystals are stronger