The Hume-Rothery Rules describe how two elements can come together to form an alloy. The more of these rules that are met, the more likely the alloy will be one phase.
1. Size factor: less than 15% difference in atomic radius
2. Same crystal structure (i.e. BCC to BCC; FCC to FCC)
3. Low electronegativity: the higher the electronegatitivity, the higher the chance of forming a compound
4. Same valence number
1. Au + Ag: All rules satisfied, a complete alloy
2. Cu + Zn (Brasses): Two rules satisfied, partial solution
3. Ag + K: No rules satisfied, will not mix