Question
A class of materials named in analogy to this substance, which include Pr2Zr2O7 (“P-R-two-Z-R-two-O-seven”), have spins that obey the two-in, two-out rule. For 10 points each:
[10e] Name this material that is the most common example of a solid that is [emphasize] less dense than its liquid counterpart.
ANSWER: ice [or water ice; accept spin ices; prompt on frozen water or H2O]
[10h] Pr2Zr2O7’s spin ice structure partly arises from “doublets” named for not satisfying an assumption of this theorem. The surface states of topological insulators can form “pairs” named for this theorem.
ANSWER: Kramers’s degeneracy theorem [accept Kramers pairs; accept non-Kramers doublets]
[10m] At low temperatures, Pr2Zr2O7’s value for this quantity suddenly peaks in an example of the Schottky anomaly. As temperature approaches zero, this quantity also approaches zero, as shown by a model based on independent quantum harmonic oscillators.
ANSWER: heat capacity [or thermal capacity; or specific heat capacity; or molar heat capacity] (The model is the Einstein model.)
<Physics>
Summary
| 2024 ACF Nationals | 2024-04-21 | Y | 20 | 15.00 | 100% | 50% | 0% |
Data
| Berkeley A | Chicago D | 10 | 0 | 10 | 20 |
| Chicago A | Georgia Tech | 10 | 0 | 10 | 20 |
| Chicago C | McGill | 10 | 0 | 0 | 10 |
| Claremont Colleges | Brown | 10 | 0 | 0 | 10 |
| Florida | Virginia | 10 | 0 | 0 | 10 |
| Berkeley B | Indiana | 10 | 0 | 10 | 20 |
| Toronto A | Iowa State | 10 | 0 | 10 | 20 |
| Minnesota A | Illinois | 10 | 0 | 0 | 10 |
| NYU | Minnesota B | 10 | 0 | 0 | 10 |
| Cornell A | North Carolina B | 10 | 0 | 10 | 20 |
| Columbia A | Ottawa | 10 | 0 | 10 | 20 |
| Purdue | Penn | 10 | 0 | 0 | 10 |
| Rutgers | Chicago B | 10 | 0 | 10 | 20 |
| South Carolina | WUSTL B | 10 | 0 | 0 | 10 |
| Stanford | Maryland | 10 | 0 | 10 | 20 |
| Arizona State | Texas | 10 | 0 | 10 | 20 |
| Toronto B | Columbia B | 10 | 0 | 0 | 10 |
| Vanderbilt | Truman State | 10 | 0 | 0 | 10 |
| WUSTL A | Duke | 10 | 0 | 0 | 10 |
| Waterloo | Michigan | 10 | 0 | 10 | 20 |