Tammann and Hüttig temperatures

Template:Short description 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 (Template:Chem2, T_Tammann = 42 °C), potassium nitrate (Template:Chem2, T_Tammann = 31 °C), and sodium nitrate (NaNO₃, T_Tammann = 17 °C), which may unexpectedly react at much lower temperatures than their melting or decomposition temperatures.Template:RTemplate:Rp

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.Template:R 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): Template:R

$T_{\text{Tammann}}=\beta \times T_{\text{melting point}}(\text{in K})$

where $\beta$ 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): Template:Blockquote

Description

The Hüttig temperature for a given material is

$T_{\text{Hüttig}}=\alpha \times T_{\mathrm{m}\mathrm{p}}$

where $T_{\text{mp}}$ is the absolute temperature of the material's bulk melting point (usually specified in Kelvin units) and $\alpha$ is a unitless constant that is independent of the material, having the value $\alpha =0.3$ according to some sources, or $\alpha =1/3$ 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

$T_{\mathrm{T}\mathrm{a}\mathrm{m}\mathrm{m}\mathrm{a}\mathrm{n}\mathrm{n}}=\beta \times T_{\mathrm{m}\mathrm{p}}$

where $\beta$ is a unitless constant usually taken to be $0.5$, 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 T_mp according to:

T_Tammann = 0.5 × T_mp

T_Hüttig = 0.3 × T_mp

Temperatures for metal and semimetal oxides.Template:Rp

Compound	Ion type	TTammann (K)	TTammann (°C)	THüttig (K)	THüttig (°C)
Template:Chem2	-	617	344	370	97
Template:Chem2	-	668	395	401	128
Template:Chem2	-	877	604	526	253
Template:Chem2	-	678	405	407	134
Template:Chem2	O2−	800	527	480	207
Template:Chem2	O2−	754	481	452	179
Template:Chem2	Cl1−	447	174	268	−5
Template:Chem2	Cl1−	352	79	211	−62
Template:Chem2	-	904	631	542	269
Template:Chem2	-	1442	1169	865	592
Template:Chem2	O2−	904	631	320	47
Template:Chem2	S2−	729	456	437	164
Template:Chem2	-	863	590	518	245
Template:Chem2	O2−	1114	841	668	395
Template:Chem2	Cl2−	641	368	384	111
Template:Chem2	O2−	127	−146	76	−197
Template:Chem2	-	1129	856	677	404
Template:Chem2	-	1362	1089	817	544
Template:Chem2	-	914	641	548	275
Template:Chem2	O2−	512	239	307	34
Template:Chem2	-	1014	741	608	335
Template:Chem2	O2−	412	139	247	−26
Template:Chem2	O2−	362	89	217	−56
Template:Chem2	Cl2−	427	154	256	−17
Template:Chem2	Cl2−	322	49	193	−80
Template:Chem2	-	347	74	208	−65
Template:Chem2	O2−	1124	851	674	401
Template:Chem2	-	877	604	438	165
Template:Chem2	O2−	1032	759	516	243
Template:Chem2	O2−	858	585	426	156
Template:Chem2	O2−	972	699	486	213

See also

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