Brigg’s Law

nλ = 2 d sin θ

d = \frac{a}{h ^{2} + k ^{2} + l ^{2}}

Arrhenius’ Law

\frac{N _{V}}{N _{t o t}} = C e^{- \frac{E _{V}}{k T}}

$N_{V}$ is the equilibrium number of vacancies, while $N_{t o t}$ is the total number of atomic sites.

$Δ r < 15%$
Same crystal structure (e.g. FCC, BCC etc.)
Similar electronegativity - $Δ E < 0.4$ for partial solubility and $Δ E < 0.2$ for full solubility.
A metal prefers to dissolve another metal of the same or higher valency
- Same valency means any ratio of two can form, otherwise it will be limited

E = 0.9465 \frac{Γ ν ^{2} L ^{4} ρ}{t ^{2}}

σ_{y} = σ_{0} + \frac{k _{y}}{d}

In plastic field

σ = H ε^{n}

\frac{d ε}{d t} = C σ^{n} e^{- \frac{E _{CR}}{RT}} = A σ^{n}

Around Cracks, stress is higher than the nominal stress $σ_{0}$ .

⟹ K = \frac{σ _{m}}{σ _{0}} = 2 \frac{r _{major}}{r _{minor}} σ_{m} = 2 σ_{0} \frac{r _{major}}{r _{minor}}

σ > σ_{c} ⟹ Crack Propagation

K_{I C} = Y σ_{c} π r_{min or}

σ_{ult} \approx 3.45 \times H B

K_{I C} = 0.016 F_{H} \frac{E}{H V c ^{3}}

Q = k A \frac{Δ T}{Δ x}

σ = E α Δ T = \frac{E _{m} E _{C}}{E _{M} + E _{C}} Δ T (α_{M} - α_{C})

Δ L \approx α L_{0} Δ T

Thermal Shock Resistance \approx \frac{σ _{f} k}{E α}

V = C - f + n

Or in words:

n. of variables = n. of components - n. of phases + n. of physical parameters (p,T)