Lecture 10 Flashcards
how can you write the total differential dU ?
dU = (du/dt)_VdT + /du/dV)_TdV
in the parentheses : partial derivatives
specific heat and enthalpy
specific heat : c_v = (dQ/dT)_V
(dH/dT)_p = c_p
H=U+pV
melting is usually performed at constant p and not volume (volumetric work is performed)
what happens at a phase transition (enthalps and T wise), formula for Tm
At transition, enthalpy is supplied but T does NOT change anymore (melting enthalpy Hm)
dTm/dp = (Vl-Vs)*Tm/Hm
how can the volume difference between liquid and solid state be explaines (2 things) ? an exception ?
1) vibrations of atoms (small increase)
2) exponential increase of vacancy density - main effect (of larger liquids)
BUT : Bi, Sb, In, Ga are smaller in liquid state, because covalent bonds in solid state change to metallic bonds in higher packing fraction in liquid state
are crystallization and melting exothermic or endothermic ?
cryst -> exothermic
melting -> endothermic
how does crystallization start ? what does it depend on ?
nuclei formation !
Nucleus stability depends on the number of bonds (so its size).
- small -> will dissociate
- big -> will keep growing.
There is a critical nucleus size (smallest stable island minus one atom).
how are the solid and liquid state at the crystallization T ? Whan needs to be done to start nuclei growth ?
They are in equilibrium = nuclei have same prob to grow and decay.
-> supersaturation !! (lower T or higher concentration, or higher pressure)
When cooling below Tc, we gain enthalpy that can be used for nuclei formation.
what does deltaG describe ? explain the curves on the graph deltaG-r (radius of nuclei)
deltaG = prob to find a nucleus within a liquid system.
deltaG_V : (negative) we free energy when forming bonds (spontaneous), and it depends on r^3 because entire volume
deltaG_I : energy needed for the atoms that dissociate from the surface of the crystal (scales with r^2)
-> combine the 2 curves : we get the critical nucleus size for this T
explain growth kinetics : where do the atoms deposit first ? what happens at a screw disloc ?
They go where there is the highest bond energy (the most bonds) because that’s the most stable position.
At screw disloc : growth spiral
difference between homogeneous and heterogeneous nucleation
homogenous : requires more energy because interface energy dominates at first, have often large grains
heterogeneous : liquid containing impurities -> growth starts at impurities with moderate supersaturation
explain the graph activation energy VS cluster size
cluster size is the nb of atoms in the island. The activation energy is the energy required to dissociate one atom from the island.
This energy depends on the nb of bonds and on the geometry of the island.
island density VS coverage, what is the ideal case for a monlayer ?
we want a high saturation island density at a small coverage -> when they start combining, the full monolayer is quickly obtained
