What is Schmidt's Rule and its Meaning?

[joelle]

I'd like to know what the meaning of this expression : a crystal obeys schmidt's rule (in fact i don' t know what is the schmidt's rule)
If someone can help me i'll be grateful.
Thx

 

[Gokul43201]

I think this is referring to Goldschmidt's Rule, which is an approximate rule of thumb telling you that substitutions that conserve oxidation state and ionic radius (approximately) introduce least strain in a crystal. This is something of an unwritten philosophy for a synthetic inorganic chemist or materials scientist. Pursuant to Goldschmidt's intuition was the excellent and extensive work done by Shannon and Prewitt on the influence of oxidation state on the ionic radius in a crystal. Shannon-Prewitt tables are a crystal-maker's Bible.

V. M. Goldschmidt was an early geochemist who contributed to the rise of crystallography and crystal chemistry in the mid-1920s.

 

[PerennialII]

... and Schmidt's law is one classical yield rule used in single crystals,

$$\left|s^{(k)}_{i}\sigma_{ij}n^{(k)}_{j}\right| =\tau_{0}$$

where $s^{(k)}_{i}$ are the components of the slip direction in the kth slip system, $n^{(k)}_{j}$is the slip plane normal and $\sigma_{ij}$ the Cauchy stress tensor.

 

[Gokul43201]

Now, I'm kinda sure that (Perennial's post) is what the OP wants. Ignore my previous post. Having had Goldschmidt sit in the back of my head for years made me think of his rule almost reflexively. Guess I should have Googled before posting to make sure there wasn't a Schmidt's Rule (I do not recall having seen it before).