The Tammann temperature (also spelled Tamman temperature) and the Hüttig temperature of a given solid material are approximations to the absolute temperatures at which atoms in a bulk crystal lattice (Tammann) or on the surface (Hüttig) of the solid material become sufficiently mobile to diffuse readily, and are consequently more chemically reactive and susceptible to recrystallization, agglomeration or sintering.[1] [2] These temperatures are equal to one-half (Tammann) or one-third (Hüttig) of the absolute temperature of the compound's melting point. The absolute temperatures are usually measured in Kelvin.
Tammann and Hüttig temperatures are important for considerations in catalytic activity, segregation and sintering of solid materials. The Tammann temperature is important for reactive compounds like explosives and fuel oxiders, such as potassium chlorate (TTammann = 42 °C), potassium nitrate (TTammann = 31 °C), and sodium nitrate (NaNO3, TTammann = 17 °C), which may unexpectedly react at much lower temperatures than their melting or decomposition temperatures.[3]
The bulk compounds should be contrasted with nanoparticles which exhibit melting-point depression, meaning that they have significantly lower melting points than the bulk material, and correspondingly lower Tammann and Hüttig temperatures.[4] For instance, 2 nm gold nanoparticles melt at only about 327 °C, in contrast to 1065 °C for a bulk gold.
Tammann temperature was pioneered by German astronomer, solid-state chemistry, and physics professor Gustav Tammann in the first half of the 20th century. He had considered a lattice motion very important for the reactivity of matter and quantified his theory by calculating a ratio of the given material temperatures at solid-liquid phases at absolute temperatures. The division of a solid's temperature by a melting point would yield a Tammann temperature. The value is usually measured in Kelvins (K):
TTammann={\beta}{ x }Tmeltingpoint(inK)
where
{\beta}
The threshold temperature for activation and diffusion of atoms at surfaces was studied by, physical chemist on the faculty of Graz University of Technology, who wrote in 1948 (translated from German):[6] [7]
The Hüttig temperature for a given material is
THüttig=\alpha x Tmp
Tmp
\alpha
\alpha=0.3
\alpha=1/3
The Tammann temperature for a given material is
TTammann=\beta x Tmp
\beta
0.5
The following table gives an example Tammann and Hüttig temperatures calculated from each compound's melting point Tmp according to:
TTammann = 0.5 × Tmp
THüttig = 0.3 × Tmp
| - | 617 | 344 | 370 | 97 | ||
| - | 668 | 395 | 401 | 128 | ||
| - | 877 | 604 | 526 | 253 | ||
| - | 678 | 405 | 407 | 134 | ||
| O2− | 800 | 527 | 480 | 207 | ||
| O2− | 754 | 481 | 452 | 179 | ||
| Cl1− | 447 | 174 | 268 | −5 | ||
| Cl1− | 352 | 79 | 211 | −62 | ||
| - | 904 | 631 | 542 | 269 | ||
| - | 1442 | 1169 | 865 | 592 | ||
| O2− | 904 | 631 | 320 | 47 | ||
| S2− | 729 | 456 | 437 | 164 | ||
| - | 863 | 590 | 518 | 245 | ||
| O2− | 1114 | 841 | 668 | 395 | ||
| Cl2− | 641 | 368 | 384 | 111 | ||
| O2− | 127 | −146 | 76 | −197 | ||
| - | 1129 | 856 | 677 | 404 | ||
| - | 1362 | 1089 | 817 | 544 | ||
| - | 914 | 641 | 548 | 275 | ||
| O2− | 512 | 239 | 307 | 34 | ||
| - | 1014 | 741 | 608 | 335 | ||
| O2− | 412 | 139 | 247 | −26 | ||
| O2− | 362 | 89 | 217 | −56 | ||
| Cl2− | 427 | 154 | 256 | −17 | ||
| Cl2− | 322 | 49 | 193 | −80 | ||
| - | 347 | 74 | 208 | −65 | ||
| O2− | 1124 | 851 | 674 | 401 | ||
| - | 877 | 604 | 438 | 165 | ||
| O2− | 1032 | 759 | 516 | 243 | ||
| O2− | 858 | 585 | 426 | 156 | ||
| O2− | 972 | 699 | 486 | 213 |