Lecture 2
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Characteristics of gases and liquids
Gases : density 10^19 cm^-3, free mean path large compared to size Liquid: density 10^22 cm^-3, stronger interactions, mean free path comparable to size
Differences between amorphous and crystalline solid
Amorphous: short range order, microscopically stable Crytsalline: 10^23 cm^-3, most sable (lowest energy), gain of energy by crystal formation
Do perfect crystals exist ?
No -> defects (type, density, distribution)
How can we visualize crystalline solids ?
Direct : scanning tunneling microscopy or TEM. Indirect : x-ray diffraction
Some general features of TEM
strong interactions bewteen probe and condensed matter -> very thin samples and vacuum conditions -> very expensive
features of STM, what is it sensitive to ?
Works under ambient conditions, sample and tip need to be conductive for current to pass, current depends exponentially (negative) on distance. Sensitive to local electronic structure of the sample
Why do we have a specific lattice constant ?
equilibrium of repulsive and attractive forces (LOOK AT GRAPHS ON SLIDE 9)
Describe the crystalline structure (components)
basis (building block) + lattice (mathematical points) Translation vectors. Unit cell volume : a*bxc
What are primitive lattice vectors?
map any lattice point to all other points
2 conditions for the choice of lattice
• primitive lattice should ba as small as possible, angles of 90 or 120 • system of 3 axes should be right-handed
What are P, I, F and C unit cells ?
primitve, bcc, fcc, one side fc
How many crystal systems and lattice types do we have in 3d ? Why do we use those bravais lattices ?
7 systems and 14 lattices (SLIDE 13) We use them because not always advantageous to take the primitive unit cell.
What is the formula for packing fraction ?
Voccupied/Vcell
How many lattices in 2D?
5 (SEE SLIDE 15)
What planes form the crystal’s surface ?
The one with small indices, because it means high point densities = minimal surface tension
Why is the surface important to consider ?
Because it exhibits a different arrangement of atoms than the bulk
In what order (mm, micro, nano, ..) does the surface dominate ?
nano range
What does texture describe ?
orientation distribution of crystals within a polycrystalline aggregate (describes the non-random distribution of crystallographic orientations within a polycrystalline material or single crystal. In other words, it characterizes how the crystal lattice planes or axes are oriented with respect to a particular direction or surface within the material.)