Question
The expanding spheres method of calculating this quantity gives a divergent sum that begins “6, minus 12 over root 2, plus 8 over root 3.” For 10 points each:
[10m] Name this quantity that equals the sum over lattice sites j of “one over p-sub-i-j,” where “p-sub-i-j” is the interatomic distance over nearest-neighbor distance.
ANSWER: Madelung (“MAD-uh-lung”) constant
[10h] Textbooks often introduce the Madelung constant by computing it for this crystal structure that has an fcc lattice. In this crystal structure, which is named for its paradigmatic compound, each ion has a coordination number of 6.
ANSWER: NaCl (“N-A-C-L”) structure [or sodium chloride structure or rock salt structure or halite structure; accept table salt; prompt on salt]
[10e] An fcc lattice is the basis of this material’s namesake crystal structure, which is the crystal structure of silicon and many binary semiconductors. It is the hardest naturally occurring material.
ANSWER: diamond [accept diamond cubic or diamond lattice]
<Physics>
Summary
| 2023 ACF Nationals | 04/22/2023 | Y | 20 | 14.00 | 100% | 30% | 10% |
Data
| Chicago A | Houston A | 10 | 10 | 10 | 30 |
| Chicago B | Virginia A | 10 | 0 | 10 | 20 |
| Stanford A | Claremont A | 0 | 0 | 10 | 10 |
| South Carolina A | Columbia B | 0 | 0 | 10 | 10 |
| Georgia Tech B | Cornell B | 0 | 0 | 10 | 10 |
| Illinois A | MIT A | 0 | 0 | 10 | 10 |
| Florida A | Indiana A | 0 | 0 | 10 | 10 |
| Imperial A | Johns Hopkins A | 0 | 0 | 10 | 10 |
| Vanderbilt A | Maryland A | 0 | 0 | 10 | 10 |
| Minnesota B | Brown A | 0 | 0 | 10 | 10 |
| NYU A | Northwestern A | 0 | 0 | 10 | 10 |
| Harvard A | Penn A | 0 | 0 | 10 | 10 |
| Rutgers B | Columbia A | 0 | 0 | 10 | 10 |
| Purdue A | Toronto A | 0 | 10 | 10 | 20 |
| UC Berkeley A | North Carolina A | 0 | 0 | 10 | 10 |
| Yale A | UC Berkeley B | 10 | 0 | 10 | 20 |
| Texas A | McGill A | 10 | 0 | 10 | 20 |
| Cornell A | Iowa State A | 10 | 0 | 10 | 20 |
| Georgia Tech A | Florida B | 10 | 0 | 10 | 20 |
| Penn State A | Chicago C | 0 | 0 | 10 | 10 |