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Falling into a smallish Black Hole will result in enormous tidal forces trying to pull the diamond apart as it approaches the event horizon. Its tensile strength we can guess at around 100GPa. So if we assume a cross section of 1 sq cm as soon as the tidal forces approach 10 MN the diamond will be ripped apart. That's like hanging a 1000 tonne weight from ...

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Suppose you have a cubic lattice, but the motif is asymmetric. If you reflect and twin in the plane {100} you'd get something like: Now suppose you reflect in the {100} place but twin in the {101} plane then you'd get: This is perhaps a somewhat contrived example, but it shows how the two planes need not be identical. I don't think you could get this ...

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I have the feeling that there may not be a rigourous proof of the type you describe in your question. I remember a couple of years ago there was a proof that the close packed structures (ccp / hcp) gave the best 'space filling' characteristics. This proof by Hales was confirmed in August of 2014 The proof relies in part on computer checking that other ...

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There are two separate issues here. Firstly the smallest possible unit cell for a crystal is called the primitive unit cell. However in many cases this is an awkward shape and it's easier to use a bigger unit cell that contains more than one primitive unit cell. The FCC unit cell is one of these non-primitive (I'm not sure what the actual term is) unit ...

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To tear something apart outright by magnetostriction is, as far as I know, impossible for the following reason: all magnetic materials saturate, i.e. their domains become fully aligned as the magnetic field increases. Further increase of the magnetic field cannot align the domains any better than they are, so no further increase in magnetostrictive strain ...

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Count: the central blue dot is shared by eight unit lattices.

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When a plane is parallel to two vectors, the dot product between its normal and that of the vectors is zero (they are perpendicular). So you are looking for a vector that is perpendicular to both $3\vec a + \vec c$ and $\vec b$. The answer, by inspection, is the vector $-\vec a + 0 \vec b + 3 \vec c$, from which the Miller indices are (if I remember this ...

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In answer to your first question: yes, as that figure shows. As for your second question, consider this: what would happen if you keep the diatomic basis but set the masses of the two atoms to be equal. The answer is that it'd look like the above figure but without a bandgap; it's the monoatomic case with the ends of the dispersion relation folded over to ...

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The simple answer to find the average number of atoms/molecules per unit volume is.... N/V (average atoms or molecules/$m^3$ ) = density ($kg/m^3$) * 1000 / atomic(or molecular) mass * $N_a$ where $N_a$ is Avogadro's number (~$6 \times 10^{23}$) In general in solid or liquid the distance between the nuclei of atoms is approximately 1 Angstrom = $10^{-10}$ ...

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The number of atoms (or molecules) in a body is given by Avogadro's constant, or $6.022 \times 10^{23}$ per mole. A mole is the amount of material, in grams, equal to the atomic or molecular mass of the substance in question. For example, for water ($H_2O$), 1 mole equals 18 grams. To get this number, remember that hydrogen ($H$) has an atomic mass of ...

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