Physics:Tamman and Hüttig temperature

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Tamman and Hüttig Temperature is an approximation of the absolute temperature at which atoms in the crystal lattice or on the surface (Hüttig) of a bulk solid[lower-alpha 1] material become "loosened" and therefore more reactive or susceptible to a diffusion by other molecules.[2][3][2]:507 It's approximately equal to a half (Tamman) and a third (Hüttig) of a compound's absolute melting point. A crystalline lattice of a solid compound maintains constant vibrational motion at normal room temperature. As the temperature increases, the amplitude of motion of the ions in the lattice also increases until the melting point is reached and the material transitions to a liquid phase.[2]:152 At this temperature approximately 70% of ions (atoms) in the lattice have the same freedom of motion that they have at the melting point, therefore allowing for diffusion of other particles, increasing the chances of a chemical reaction.[2]:152

Tamman and Hüttig temperatures are an important factor for some compounds like explosives and fuel oxiders, e.g., potassium chlorate (KClO3) potassium nitrate (KNO3, Tt=31 °C (88 °F)), sodium nitrate (NaNO3, Tt 17 °C (63 °F)) that may react at surprisingly lower temperatures than one would expect.[2]:152[4](p502)

The bulk compounds should be contrasted with nanoparticles that exhibit melting-point depression effect, and therefore significantly lower melting points (as well as lower Tammann and Hüttig temperatures) due to smaller molecular radii.[5] For instance, 2nm Au nanoparticles melt only about 327 °C (621 °F) contrasting to 1,065 °C (1,949 °F) for a bulk Au.[5] This notion is important in regards to sintering process.[5]

History

Tamman Temperature was pioneered by German astronomer, solid-state chemistry, and physics professor Gustav Tammann in the first half of the 20th century.[2]:152 He considered a lattice motion 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 Tamman temperature. The value is usually measured in Kelvins (K): [2]:152

[math]\displaystyle{ T_{\mathit{\text{Tamman}}} ={\beta} {\times} T_{\text{melting point}} (\text{in K}) }[/math] [6]

where [math]\displaystyle{ {\beta} }[/math] is a constant dimensionless number.

Definition

Hüttig temperature is[7]
[math]\displaystyle{ T_{\mathit{\text{Hüttig}}} \text{(K)} =0.26 T_f }[/math] — A temperature necessary for metal or metal oxide surface recrystallization.
Tamman temperature is[7]
[math]\displaystyle{ T_{\mathit{Tammann}} \text{(K)} =0.52 T_f }[/math] — A temperature necessary for metal or metal oxide lattice (bulk) recrystallization.

where:

  • [math]\displaystyle{ T_f }[/math] — An absolute melting temperature for a given compound expressed in Kelvin (K) units.

Examples

Below are examples of some compounds' pre-calculated approximations of Tamman and Hüttig temperatures.

Temperatures for metal and semimetal oxides.[8][9](p26)
Metal Type ~TTamman/K ~TTamman/℃ ~THüttig/K ~THüttig/℃
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
Cu
2O 		O2- 754 481 452 179
CuCl
2 		Cl1- 447 174 268 -5
Cu
2Cl
2 		Cl1- 352 79 211 -62
Fe - 904 631 542 269
Mo - 1442 1169 865 592
MoO
3 		O2- 904 631 320 47
MoS
2 		S2- 729 456 437 164
Ni - 863 590 518 245
NiO O2- 1114 841 668 395
NiCl
2 		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
PtO
2 		O2- 362 89 217 -56
PtCl
2 		Cl2- 427 154 256 -17
PtCl
4 		Cl2- 322 49 193 -80
Zn - 347 74 208 -65
ZnO O2- 1124 851 674 401
Si - 877 604 438 165
SiO
2 		O2 1032 759 516 243
FeO O2 858 585 426 156
Fe
3O
4 		O2 972 699 486 213

See also

Notes

  1. ↑ The bulk compounds should be contrasted with Nanoparticles which exhibit significantly lower melting temperatures due to smaller radii and therefore - lower Tammann and Hüttig rates.[1]

References

  1. ↑ Dai, Yunqian; Lu, Ping; Cao, Zhenming; Campbell, Charles T.; Xia, Younan (2018). "The physical chemistry and materials science behind sinter-resistant catalysts" (in en). Chemical Society Reviews 47 (12): 4314–4331. doi:10.1039/C7CS00650K. ISSN 0306-0012. PMID 29745393. http://xlink.rsc.org/?DOI=C7CS00650K. 
  2. ↑ 2.0 2.1 2.2 2.3 2.4 2.5 2.6 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. https://www.worldcat.org/oclc/1079055294. 
  3. ↑ Preparation of solid catalysts. G. Ertl, H. Knözinger, J. Weitkamp. Weinheim: Wiley-VCH. 1999. ISBN 978-3-527-61952-8. OCLC 264615500. https://www.worldcat.org/oclc/264615500. 
  4. ↑ Forensic investigation of explosions. Alexander Beveridge (2 ed.). Boca Raton: CRC Press. 2012. ISBN 978-1-4665-0394-6. OCLC 763161398. https://www.worldcat.org/oclc/763161398. 
  5. ↑ 5.0 5.1 5.2 Dai, Yunqian; Lu, Ping; Cao, Zhenming; Campbell, Charles T.; Xia, Younan (2018). "The physical chemistry and materials science behind sinter-resistant catalysts" (in en). Chemical Society Reviews 47 (12): 4314–4331. doi:10.1039/C7CS00650K. ISSN 0306-0012. PMID 29745393. http://xlink.rsc.org/?DOI=C7CS00650K. 
  6. ↑ Tammann, G. (1924). "Die Temp. d. Beginns innerer Diffusion in Kristallen" (in de). Zeitschrift für anorganische und allgemeine Chemie 157 (1): 321. 
  7. ↑ 7.0 7.1 C. Jentoft, Friederike (October 31, 2003), Thermal Treatment of Catalysts; Modern Methods in Heterogeneous Catalysis Research, http://www.fhi-berlin.mpg.de/acnew/department/pages/teaching/pages/teaching__wintersemester__2003_2004/jentoft_calcination_311003.pdf 
  8. ↑ Argyle, Morris; Bartholomew, Calvin (2015-02-26). "Heterogeneous Catalyst Deactivation and Regeneration: A Review" (in en). Catalysts 5 (1): 145–269. doi:10.3390/catal5010145. ISSN 2073-4344. 
  9. ↑ 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. https://www.worldcat.org/oclc/237047448. 




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