Thank you for this great tutorial! I am not sure if you will read this or answer it but as and when you do, I hope it will help more people. I was wondering if you could recommend a textbook that explains that same concept for low order symmetry crystal systems. I am currently looking at TEM images of nanomaterials that have a tetragonal crystal symmetry: a=b not = c alpha=beta=gamma = 90 degrees a) Is it correct to write: {a0c} for (a0c), (0bc), (-a0c), (0b-c) as these are equivalent crystallographically... and would the same be true of directions? i.e. for [00a] and [00-a]? b) Is there a minimum number of directions that constitute a family of planes or directions? On question a), can I write {-a0c} to represent them all, or should I stick to the positive variant of it? Thank you in advance
Howdy! First comment - it is best to avoid mixing your hkl's (which are used to index planes and directions), with your abc's (which are the lengths of your principal lattice vectors) a) for your question here. For a tetragonal structure, it is true that {h0l} family of planes includes the following: (h0l), (0hl), (-h0l), (0-hl). (Replace h and l with any integers and try it!). It is also true that the "family" could be named after any member (e.g., could be {0-hl}). Finally, because a plane doesn't generally have a sign, multiplying all your indices by -1 results in an equivalent (parallel) plane (for example, you could replace (-h0l) with (h0-l). These represent the same plane, just shifted relative to the origin of the lattice. b) I suppose the "minimum" number of unique planes or directions in a family would be 2, simply because you wouldn't refer to a "family" that consisted of just 1 member.
This is my biggest bucket of fortune regarding cristallography! Thanks a lot!
“The symmetry of properties follows the symmetry of that lattice”
👍🏼😍
Very well explained!!
Thank you
Thank you for this great tutorial! I am not sure if you will read this or answer it but as and when you do, I hope it will help more people. I was wondering if you could recommend a textbook that explains that same concept for low order symmetry crystal systems. I am currently looking at TEM images of nanomaterials that have a tetragonal crystal symmetry:
a=b not = c
alpha=beta=gamma = 90 degrees
a) Is it correct to write: {a0c} for (a0c), (0bc), (-a0c), (0b-c) as these are equivalent crystallographically... and would the same be true of directions?
i.e. for [00a] and [00-a]?
b) Is there a minimum number of directions that constitute a family of planes or directions?
On question a), can I write {-a0c} to represent them all, or should I stick to the positive variant of it?
Thank you in advance
Howdy!
First comment - it is best to avoid mixing your hkl's (which are used to index planes and directions), with your abc's (which are the lengths of your principal lattice vectors)
a) for your question here. For a tetragonal structure, it is true that {h0l} family of planes includes the following: (h0l), (0hl), (-h0l), (0-hl). (Replace h and l with any integers and try it!). It is also true that the "family" could be named after any member (e.g., could be {0-hl}). Finally, because a plane doesn't generally have a sign, multiplying all your indices by -1 results in an equivalent (parallel) plane (for example, you could replace (-h0l) with (h0-l). These represent the same plane, just shifted relative to the origin of the lattice.
b) I suppose the "minimum" number of unique planes or directions in a family would be 2, simply because you wouldn't refer to a "family" that consisted of just 1 member.
could we write the family of direction in the example instead of ?
Surely. (as long as [0 1] and [1 0] are both members of the same family).
great video
Thank you!
wow! thank you very much
my mats prof is shit, why did I just find this two days before my final?
same here.