Tammann and Hüttig temperatures: Difference between revisions
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{{Short description|Chemical properties of materials}} |
{{Short description|Chemical properties of materials}} |
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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 [[Atomic diffusion|diffuse]] readily, and are consequently more [[Reactivity (chemistry)|chemically reactive]] and susceptible to recrystallization, agglomeration or [[sintering]].<ref name="Conkling 2019">{{Cite book |last=Conkling |first=John A. |url=https://www.worldcat.org/oclc/1079055294 |title=Chemistry of pyrotechnics : basic principles and theory |date=2019 |others=Chris Mocella |isbn=978-0-429-26213-5 |edition=3 |location=Boca Raton, FL |oclc=1079055294}}</ref><ref>{{Cite book |url=https://www.worldcat.org/oclc/264615500 |title=Preparation of solid catalysts |date=1999 |publisher=Wiley-VCH |others=G. Ertl, H. Knözinger, J. Weitkamp |isbn=978-3-527-61952-8 |location=Weinheim |oclc=264615500}}</ref> 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]]. |
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 [[Atomic diffusion|diffuse]] readily, and are consequently more [[Reactivity (chemistry)|chemically reactive]] and susceptible to recrystallization, agglomeration or [[sintering]].<ref name="Conkling 2019">{{Cite book |last=Conkling |first=John A. |url=https://www.worldcat.org/oclc/1079055294 |title=Chemistry of pyrotechnics : basic principles and theory |date=2019 |others=Chris Mocella |isbn=978-0-429-26213-5 |edition=3 |location=Boca Raton, FL |oclc=1079055294}}</ref><ref>{{Cite book |url=https://www.worldcat.org/oclc/264615500 |title=Preparation of solid catalysts |date=1999 |publisher=Wiley-VCH |others=G. Ertl, H. Knözinger, J. Weitkamp |isbn=978-3-527-61952-8 |location=Weinheim |oclc=264615500}}</ref> 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]]. |
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Tammann and Hüttig temperatures are |
Tammann and Hüttig temperatures are important for considerations in [[Catalyst|catalytic activity]], [[segregation (materials science)|segregation]] and sintering of solid materials. The Tammann temperature is important for reactive compounds like explosives and [[Oxidizing agent|fuel oxiders]], such as [[potassium chlorate]] ({{chem2|KClO3}}, ''T''<sub>Tammann</sub> = 42 °C), [[potassium nitrate]] ({{chem2|KNO3}}, ''T''<sub>Tammann</sub> = 31 °C), and [[sodium nitrate]] (NaNO<sub>3</sub>, ''T''<sub>Tammann</sub> = 17 °C), which may unexpectedly react at much lower temperatures than their melting or decomposition temperatures.{{r|Conkling 2019|p=152}}<ref name="Beveridge 2012">{{Cite book |url=https://www.worldcat.org/oclc/763161398 |title=Forensic investigation of explosions |date=2012 |publisher=CRC Press |others=Alexander Beveridge |isbn=978-1-4665-0394-6 |edition=2 |location=Boca Raton |oclc=763161398}}</ref>{{Rp|page=502}} |
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The bulk compounds should be contrasted with [[Nanoparticle|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.<ref name="Dai 2018">{{Cite journal |last1=Dai |first1=Yunqian |last2=Lu |first2=Ping |last3=Cao |first3=Zhenming |last4=Campbell |first4=Charles T. |last5=Xia |first5=Younan |date=2018 |title=The physical chemistry and materials science behind sinter-resistant catalysts |url=http://xlink.rsc.org/?DOI=C7CS00650K |journal=Chemical Society Reviews |language=en |volume=47 |issue=12 |pages=4314–4331 |doi=10.1039/C7CS00650K |pmid=29745393 |osti=1539900 |issn=0306-0012}}</ref> For instance, 2 nm [[gold]] nanoparticles melt at only about 327 °C, in contrast to 1065 °C for a bulk gold.<ref name="Dai 2018" /> |
The bulk compounds should be contrasted with [[Nanoparticle|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.<ref name="Dai 2018">{{Cite journal |last1=Dai |first1=Yunqian |last2=Lu |first2=Ping |last3=Cao |first3=Zhenming |last4=Campbell |first4=Charles T. |last5=Xia |first5=Younan |date=2018 |title=The physical chemistry and materials science behind sinter-resistant catalysts |url=http://xlink.rsc.org/?DOI=C7CS00650K |journal=Chemical Society Reviews |language=en |volume=47 |issue=12 |pages=4314–4331 |doi=10.1039/C7CS00650K |pmid=29745393 |osti=1539900 |issn=0306-0012}}</ref> For instance, 2 nm [[gold]] nanoparticles melt at only about 327 °C, in contrast to 1065 °C for a bulk gold.<ref name="Dai 2018" /> |
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== Examples == |
== Examples == |
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The following table gives example Tammann and Hüttig temperatures calculated from each compound's melting point ''T''<sub>mp</sub> according to: |
The following table gives an example Tammann and Hüttig temperatures calculated from each compound's melting point ''T''<sub>mp</sub> according to: |
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:''T''<sub>Tammann</sub> = 0.5 × ''T''<sub>mp</sub> |
:''T''<sub>Tammann</sub> = 0.5 × ''T''<sub>mp</sub> |
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:''T''<sub>Hüttig</sub> = 0.3 × ''T''<sub>mp</sub> |
:''T''<sub>Hüttig</sub> = 0.3 × ''T''<sub>mp</sub> |
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|{{chem2|[[SiO2]]}} |
|{{chem2|[[SiO2]]}} |
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|O<sup> |
|O<sup>2−</sup> |
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|1032 |
|1032 |
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|759 |
|759 |
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|- |
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|{{Chem2|FeO}} |
|{{Chem2|FeO}} |
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|O<sup> |
|O<sup>2−</sup> |
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|858 |
|858 |
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|585 |
|585 |
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|{{Chem2|[[Fe3O4]]}} |
|{{Chem2|[[Fe3O4]]}} |
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|O<sup> |
|O<sup>2−</sup> |
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|972 |
|972 |
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|699 |
|699 |
Latest revision as of 07:06, 20 May 2024
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 (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
[edit]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
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
[edit]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
[edit]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
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
[edit]- Chemical kinetics – Study of the rates of chemical reactions
- Chemical thermodynamics – Study of chemical reactions within the laws of thermodynamics
- Glass transition – Reversible transition in amorphous materials
- Surface melting – Formation of a quasi-liquid film on the surface of a solid
Notes
[edit]References
[edit]- ^ a b c d 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) - ^ 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) - ^ 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) - ^ a b c d 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.
- ^ 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.
- ^ Hüttig, G. F. (1948). "Theoretical Principles of Sintering in Metal Powders". Archiv für Metallkunde. 2: 93–99. Retrieved 10 April 2023.
- ^ 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.
- ^ a b c 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.
- ^ a b c 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) - ^ a b 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.
- ^ 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.