Tammann and Hüttig temperatures. 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. 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.

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. For instance, 2 nm gold nanoparticles melt at only about 327 °C, in contrast to 1065 °C for a bulk gold.

History 
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): 

  

where  is a constant dimensionless number.

The threshold temperature for activation and diffusion of atoms at surfaces was studied by :de:Gustav Franz Hüttig, physical chemist on the faculty of Graz University of Technology, who wrote in 1948 (translated from German):

Description 

The Hüttig temperature for a given material is
  
where  is the absolute temperature of the material's bulk melting point (usually specified in Kelvin units) and  is a unitless constant that is independent of the material, having the value  according to some sources, or  according to other sources. It is an approximation to the temperature necessary for a metal or metal oxide surfaces to show significant atomic diffusion along the surface, sintering, and surface recrystallization. Desorption of adsorbed gasses and chemical reactivity of the surface often increase markedly as the temperature is increases above the Hüttig temperature.

The Tammann temperature for a given material is
  
where  is a unitless constant usually taken to be , regardless of the material. It is an approximation to the temperature necessary for mobility and diffusion of atoms, ions, and defects within a bulk crystal. Bulk chemical reactivity often increase markedly as the temperature is increased above the Tammann temperature.

Examples 
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

See also

Notes

References 

Heat_transfer
Thermodynamic properties