The Tammann temperature (also spelled Tamman temperature) and the Hüttig temperature of a given 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 an important considerations for catalytic activity, segregation and sintering. The Tammann temperature is important for reactive compounds like explosives and fuel oxiders, such as potassium chlorate (KClO3, TTammann = 42 °C), potassium nitrate (KNO3, TTammann = 31 °C), and sodium nitrate (NaNO3, TTammann = 17 °C), which may unexpectedly react at much lower temperatures than their melting or decomposition temperatures.[1]: 152 [3]: 502 

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.[4]

History

Tammann temperature was pioneered by German astronomer, solid-state chemistry, and physics professor Gustav Tammann in the first half of the 20th century.[1]: 152  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): [1]: 152 

[5]

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):[6][7]

In the solid state the atoms oscillate about their position in the lattice. ... There are always some atoms which happen to be highly energized. Such an atom may become dislodged and switch places with another one (exchange reaction) or it may, for a time, travel about aimlessly. ... the number of diffusing atoms increases with rising temperature, first slowly, and in the higher temperature ranges more rapidly. For every metal there is a definite temperature at which the exchange process is suddenly accelerated. The relationship between this temperature and the melting point in degrees K is constant for all metals. ... On the basis of these elementary processes, sintering is analyzed in relation to the coefficient α which is the fraction of the melting point in degrees K ... When α is between 0.23 and 0.36, activation as a result of the surface diffusion takes place. Loosening or release of adsorbed gasses occurs simultaneously.

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,[4][8] or according to other sources.[9][10][11] 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.[4][8][9][10] 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 example Tammann and Hüttig temperatures calculated from each compound's melting point Tmp according to:

TTammann = 0.5 × Tmp
THüttig = 0.3 × Tmp
Temperatures for metal and semimetal oxides.[8][9]: 26 
Compound Ion type TTammann (K) TTammann (°C) THüttig (K) THüttig (°C)
Ag - 617 344 370 97
Au - 668 395 401 128
Co - 877 604 526 253
Cu - 678 405 407 134
CuO O2− 800 527 480 207
Cu2O O2− 754 481 452 179
CuCl2 Cl1− 447 174 268 −5
Cu2Cl2 Cl1− 352 79 211 −62
Fe - 904 631 542 269
Mo - 1442 1169 865 592
MoO3 O2− 904 631 320 47
MoS2 S2− 729 456 437 164
Ni - 863 590 518 245
NiO O2− 1114 841 668 395
NiCl2 Cl2− 641 368 384 111
Ni(CO)4 O2− 127 −146 76 −197
Rh - 1129 856 677 404
Ru - 1362 1089 817 544
Pd - 914 641 548 275
PdO O2− 512 239 307 34
Pt - 1014 741 608 335
PtO O2− 412 139 247 −26
PtO2 O2− 362 89 217 −56
PtCl2 Cl2− 427 154 256 −17
PtCl4 Cl2− 322 49 193 −80
Zn - 347 74 208 −65
ZnO O2− 1124 851 674 401
Si - 877 604 438 165
SiO2 O2 1032 759 516 243
FeO O2 858 585 426 156
Fe3O4 O2 972 699 486 213

See also

Notes

    References

    1. 1 2 3 4 Conkling, John A. (2019). Chemistry of pyrotechnics : basic principles and theory. Chris Mocella (3 ed.). Boca Raton, FL. ISBN 978-0-429-26213-5. OCLC 1079055294.{{cite book}}: CS1 maint: location missing publisher (link)
    2. ↑ Preparation of solid catalysts. G. Ertl, H. Knözinger, J. Weitkamp. Weinheim: Wiley-VCH. 1999. ISBN 978-3-527-61952-8. OCLC 264615500.{{cite book}}: CS1 maint: others (link)
    3. ↑ Forensic investigation of explosions. Alexander Beveridge (2 ed.). Boca Raton: CRC Press. 2012. ISBN 978-1-4665-0394-6. OCLC 763161398.{{cite book}}: CS1 maint: others (link)
    4. 1 2 3 4 Dai, Yunqian; Lu, Ping; Cao, Zhenming; Campbell, Charles T.; Xia, Younan (2018). "The physical chemistry and materials science behind sinter-resistant catalysts". Chemical Society Reviews. 47 (12): 4314–4331. doi:10.1039/C7CS00650K. ISSN 0306-0012. OSTI 1539900. PMID 29745393.
    5. ↑ Tammann, G. (1924). "Die Temp. d. Beginns innerer Diffusion in Kristallen". Zeitschrift für anorganische und allgemeine Chemie (in German). 157 (1): 321. doi:10.1002/zaac.19261570123.
    6. ↑ Hüttig, G. F. (1948). "Theoretical Principles of Sintering in Metal Powders". Archiv für Metallkunde. 2: 93–99. Retrieved 10 April 2023.
    7. ↑ Michaelson, Herbert B. (1951). The Theories of the Sintering Process: A Guide to the Literature (1931–1951). Oak Ridge, Tennessee: U.S. Atomic Energy Commission, Technical Information Service. p. 34. Retrieved 10 April 2023.
    8. 1 2 3 Argyle, Morris; Bartholomew, Calvin (2015-02-26). "Heterogeneous Catalyst Deactivation and Regeneration: A Review". Catalysts. 5 (1): 145–269. doi:10.3390/catal5010145. ISSN 2073-4344.
    9. 1 2 3 Catalysis. Volume 10 : a review of recent literature. James J. Spivey, Sanjay K. Agarwal. Cambridge, England: Royal Society of Chemistry. 1993. ISBN 978-1-84755-322-5. OCLC 237047448.{{cite book}}: CS1 maint: others (link)
    10. 1 2 Menon, P. G.; Rao, T. S. R. Prasada (1979). "Surface Enrichment in Catalysts". Catalysis Reviews. 20 (1): 97–120. doi:10.1080/03602457908065107. ISSN 0161-4940.
    11. ↑ Spencer, M. S. (1986). "Stable and metastable metal surfaces in heterogeneous catalysis". Nature. 323 (6090): 685–687. Bibcode:1986Natur.323..685S. doi:10.1038/323685a0. ISSN 0028-0836. S2CID 4350909.
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