No, the thermal conductivity and hardness of a material are completely independent properties. You can understand this very well with examples:
There is a relationship between elasticity (velocity of sound) and thermal conductivity. But elasticity and hardness are not identical terms.
With Regard
R. Mitdank
That's not always true either. For example, tungsten's modulus of elasticity is 406 GPa and its thermal conductivity is 180 W/mK. The modulus of elasticity of copper is only 130 GPa, but the thermal conductivity of copper (400 W/mK) is much higher than that of tungsten.
There is no solid relationship between these features (not for all the materials). For instance, consider high thermal conductivity of DLC coating with excellent friction behavior. On the other hand , consider thermally sprayed WC-containing coatings with superior wear resistant and relatively insignificant conductivity. Can you relate?
To Vadim:
You are right but let me discuss the relationship more precisely : The thermal conductivity is proportional to the mean free path of phonons, the specific heat and the velocity of sound (for isolators - for metals you must add an electronic part). The velocity of sound correlates with the module of elasticity.
That means the relations are more complex. Nevertheless, a relationship with hardness cannot be suggested.
With Regard
R. Mitdank
Thermal conductivity for solids can be due to the phonons, there is also electronic thermal conductivity, but the one that can affect the hardness is probably the thermal expansion of a solid. They are different.
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