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{{Short description|Chemical properties of materials}}
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]]. 

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&nbsp;°C), [[potassium nitrate]] ({{chem2|KNO3}}, ''T''<sub>Tammann</sub> = 31&nbsp;°C), and [[sodium nitrate]] (NaNO<sub>3</sub>, ''T''<sub>Tammann</sub> = 17&nbsp;°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}}

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&nbsp;nm [[gold]] nanoparticles melt at only about 327&nbsp;°C, in contrast to 1065&nbsp;°C for a bulk gold.<ref name="Dai 2018" />

== History ==
Tammann temperature was pioneered by German astronomer, [[solid-state chemistry]], and [[Solid-state physics|physics]] professor [[Gustav Heinrich Johann Apollon Tammann|Gustav Tammann]] in the first half of the 20th century.{{r|Conkling 2019|p=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): {{r|Conkling 2019|p=152}}

: <math>T_{\text{Tammann}}  ={\beta} {\times} T_{\text{melting point}} (\text{in K})</math> <ref name="Tammann 2924">{{Cite journal |last1=Tammann |first1=G. |date=1924 |title=Die Temp. d. Beginns innerer Diffusion in Kristallen |journal=Zeitschrift für anorganische und allgemeine Chemie |language=de |volume=157 |issue=1 |pages=321|doi=10.1002/zaac.19261570123 }} </ref>

where <math>{\beta}</math> 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):<ref name="Huttig 1948">{{cite journal |last1=Hüttig |first1=G. F. |title=Theoretical Principles of Sintering in Metal Powders |journal=Archiv für Metallkunde |date=1948 |volume=2 |pages=93–99 |url=https://books.google.com/books?id=Eo01iNFSvhsC |access-date=10 April 2023}}</ref><ref name="Michaelson 1951">{{cite book |last1=Michaelson |first1=Herbert B. |title=The Theories of the Sintering Process: A Guide to the Literature (1931–1951) |date=1951 |publisher=U.S. Atomic Energy Commission, Technical Information Service |location=Oak Ridge, Tennessee |page=34 |url=https://books.google.com/books?id=Eo01iNFSvhsC |access-date=10 April 2023}}</ref>
{{blockquote|text=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
: <math>T_{\mathrm{\text{Hüttig}}} = \alpha \times T_{\mathrm{mp}}</math> 
where <math>T_{\text{mp}}</math> is the [[absolute temperature]] of the material's bulk melting point (usually specified in [[Kelvin]] units) and <math>\alpha</math> is a unitless constant that is independent of the material, having the value <math>\alpha=0.3</math> according to some sources,<ref name="Dai 2018" /><ref name="Argyle 2015" /> or <math>\alpha=1/3</math> according to other sources.<ref name="Spivey 1993" /><ref name="Menon 1979">{{cite journal | last1=Menon | first1=P. G. | last2=Rao | first2=T. S. R. Prasada | title=Surface Enrichment in Catalysts | journal=Catalysis Reviews | volume=20 | issue=1 | year=1979 | issn=0161-4940 | doi=10.1080/03602457908065107 | pages=97–120}}</ref><ref name="Spencer 1986">{{cite journal | last=Spencer | first=M. S. | title=Stable and metastable metal surfaces in heterogeneous catalysis | journal=Nature | volume=323 | issue=6090 | year=1986 | issn=0028-0836 | doi=10.1038/323685a0 | pages=685–687| bibcode=1986Natur.323..685S | s2cid=4350909 }}</ref> 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. [[wikt:Desorption|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
: <math>T_{\mathrm{Tammann}} = \beta \times T_{\mathrm{mp}}</math> 
where <math>\beta</math> is a unitless constant usually taken to be <math>0.5</math>, regardless of the material.<ref name="Dai 2018" /><ref name="Argyle 2015" /><ref name="Spivey 1993" /><ref name="Menon 1979" /> 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 ''T''<sub>mp</sub> according to:
:''T''<sub>Tammann</sub> = 0.5 × ''T''<sub>mp</sub> 
:''T''<sub>Hüttig</sub> = 0.3 × ''T''<sub>mp</sub> 

{| class="wikitable sortable" style="text-align: center; width: 100%"
|+Temperatures for metal and [[semimetal]] oxides.<ref name="Argyle 2015">{{Cite journal |last1=Argyle |first1=Morris |last2=Bartholomew |first2=Calvin |date=2015-02-26 |title=Heterogeneous Catalyst Deactivation and Regeneration: A Review |journal=Catalysts |language=en |volume=5 |issue=1 |pages=145–269 |doi=10.3390/catal5010145 |issn=2073-4344|doi-access=free }}</ref><ref name="Spivey 1993">{{Cite book |url=https://www.worldcat.org/oclc/237047448 |title=Catalysis. Volume 10 : a review of recent literature |date=1993 |publisher=Royal Society of Chemistry |others=James J. Spivey, Sanjay K. Agarwal |isbn=978-1-84755-322-5 |location=Cambridge, England |oclc=237047448}}</ref>{{Rp|page=26}}
!Compound
!Ion type
!''T''<sub>Tammann</sub> (K)
!''T''<sub>Tammann</sub> (°C)
!''T''<sub>Hüttig</sub> (K)
!''T''<sub>Hüttig</sub> (°C)
|-
|{{chem2|[[Ag]]}}
| -
|617
|344
|370
|97
|-
|{{chem2|[[Au]]}}
| -
|668
|395
|401
|128
|-
|{{chem2|[[Co]]}}
| -
|877
|604
|526
|253
|-
|{{chem2|[[Cu]]}}
| -
|678
|405
|407
|134
|-
|{{chem2|[[CuO]]}}
|O<sup>2−</sup>
|800
|527
|480
|207
|-
|{{chem2|[[Cu2O]]}}
|O<sup>2−</sup>
|754
|481
|452
|179
|-
|{{chem2|[[CuCl2]]}}
|Cl<sup>1−</sup>
|447
|174
|268
| −5
|-
|{{chem2|[[Cu2Cl2]]}}
|Cl<sup>1−</sup>
|352
|79
|211
| −62
|-
|{{chem2|[[Fe]]}}
| -
|904
|631
|542
|269
|-
|{{chem2|[[Mo]]}}
| -
|1442
|1169
|865
|592
|-
|{{chem2|[[MoO3]]}}
|O<sup>2−</sup>
|904
|631
|320
|47
|-
|{{chem2|[[MoS2]]}}
|S<sup>2−</sup>
|729
|456
|437
|164
|-
|{{chem2|[[Ni]]}}
| -
|863
|590
|518
|245
|-
|{{chem2|[[NiO]]}}
|O<sup>2−</sup>
|1114
|841
|668
|395
|-
|{{chem2|[[NiCl2]]}}
|Cl<sup>2−</sup>
|641
|368
|384
|111
|-
|{{chem2|[[Ni(CO)4]]}}
| O<sup>2−</sup>
|127
| −146
|76
| −197
|-
|{{chem2|[[Rh]]}}
| -
|1129
|856
|677
|404
|-
|{{chem2|[[Ru]]}}
| -
|1362
|1089
|817
|544
|-
|{{chem2|[[Pd]]}}
| -
|914
|641
|548
|275
|-
|{{chem2|[[Palladium(II) oxide|PdO]]}}
|O<sup>2−</sup>
|512
|239
|307
|34
|-
|{{chem2|[[Pt]]}}
| -
|1014
|741
|608
|335
|-
|{{chem2|[[PtO]]}}
|O<sup>2−</sup>
|412
|139
|247
|−26
|-
|{{chem2|[[PtO2]]}}
|O<sup>2−</sup>
|362
| 89
|217
|−56
|-
|{{chem2|[[PtCl2]]}}
|Cl<sup>2−</sup>
|427
|154
|256
|−17
|-
|{{chem2|[[PtCl4]]}}
|Cl<sup>2−</sup>
|322
| 49
|193
|−80
|-
|{{chem2|[[Zn]]}}
| -
|347
| 74
|208
|−65
|-
|{{chem2|[[ZnO]]}}
|O<sup>2−</sup>
|1124
|851
|674
|401
|-
|{{chem2|[[Si]]}}
| -
|877
|604
|438
|165
|-
|{{chem2|[[SiO2]]}}
|O<sup>2−</sup>
|1032
|759
|516
|243
|-
|{{Chem2|FeO}}
|O<sup>2−</sup>
|858
|585
|426
|156
|-
|{{Chem2|[[Fe3O4]]}}
|O<sup>2−</sup>
|972
|699
|486
|213
|}

== See also ==
* {{Annotated link|Chemical kinetics}}
* {{Annotated link|Chemical thermodynamics}}
* {{Annotated link|Glass transition}}
* {{Annotated link|Surface melting}}

== Notes ==
{{Notelist}}

== References ==
<references />

[[Category:Heat_transfer]]
[[Category:Thermodynamic properties]]