Nucleation-kinetics Flashcards
Boltzmann distribution equation
N = Noexp(-E’/kT)
N/No is
probability that an atom in the system has energy >= E’
exp(-E’/kT) is
the probability function of thermally activated macroscale properties
Processes with energy barriers around kT are ____ to occur because:
likely; most atoms have enough thermal energy to overcome the barrier
How does the Boltzmann distribution function change with temperature?
higher probability of finding atoms with higher energy at higher temperatures
Critical undercooling temp
a temperature above which no practical amounts of nucleation can occur
Between Tm and Tc, you can metastably undercool the liquid and __ __ solidification
not get
What’s the difference between solid state heterogeneous and solid state homogeneous nucleation?
SS heterogeneous contains the -ΔGd term, defect energy
What is the difference between solidification and SS precipitation?
SS precipitation contains the ΔGs term, strain energy term (+) limits nucleation
Why does ΔG defect energy lower the energy of the system?
when a nucleus forms on a defect, the defect is “consumed” and removed from the system, lowering the system’s eneryg
What is Boltzmann distribution function used for?
It is used to describe the probability of atoms to arrange themselves into a nucleus with critical size r*
C*/Co =
exp(-ΔG/kT) or = exp(-A/ΔT^n) because ΔG = preexp(1/(Tm-T’)^2)
C* =
of atoms in atomic cluster with size >= r*
Co =
atoms/vol parent phase
