@TaylorSparks please, does it matter if I do AB x AC VERSUS AC x AB? The direction of the cross product would be opposite each other for those 2 cases, I don't know if that means significant difference in miller indices of planes for example i did this but many times i got the opposite answer as my professor who does origin shifting. for example, he might get (hkl) = (1 -2 2) and i would get (-1 2 -2) using the cross product method. Are both correct? If orientation does matter, how do I select the correct orientation/order to multiply when doing cross product method?
@@irisce2799 Good question. If you reverse the order of the cross product you will just get the opposite normal. One is normal up and one is normal down so to speak. I would need to work it out both ways, but I'm guessing they are equivalent planes. To be certain. You can do the right hand rule cross product and pick the one that is pointing normal (up) to the plane as it is drawn
@@TaylorSparks oh wow I was totally not expecting a response so fast! Yes I was reading and also came across using the right hand rule to select the most "upward" pointing orientation. Thank you professor! I have another question. At 5:27, you said the vector cross product only works for cubic systems and not other crystal systems. Why wouldn't it work for hexagonal unit cells? I was doing a problem with a hexagonal unit cell, and I used the same vector cross product method to get (hkl), then i = -(h+k) to convert to the Miller-Bravais (hkil) format. The weird thing is that in the problem the professor drew the unit cell as a rectangular prism so it looked like the xyz cubic system, but they denoted the angle between 2 axes to be 120 degrees and then stated that it was a hexagonal unit cell. Honestly, I have no idea how to solve that kind of problem by shifting the origin and stuff, so I just used the cross product method and converted it. Would I be correct to solve it this way?
Can you help for this question, sir In orthorombic crystal Intercepts 2,4,2 and corresponding primitive vectors are 3,6,4 amstrong. Find out Miller indices Plz help me
Hey man thanks for the video. How about this... The three points are (1, 0, 0), (1/2, 1/2, 1) and (0, 1, 1/2). Cross multiplication gives the miller indices (-3, -3, 0) but that doesn't feel right to me.
yup, I get (3,3,0) www.symbolab.com/solver/vector-cross-product-calculator/%5Cbegin%7Bpmatrix%7D%5Cfrac%7B1%7D%7B2%7D%26-%5Cfrac%7B1%7D%7B2%7D%26-1%5Cend%7Bpmatrix%7D%5Ctimes%5Cbegin%7Bpmatrix%7D-%5Cfrac%7B1%7D%7B2%7D%26%5Cfrac%7B1%7D%7B2%7D%26-%5Cfrac%7B1%7D%7B2%7D%5Cend%7Bpmatrix%7D you can plot that plane to see if it intersects the points
When I draw (-1:-6:4) plane from Miller indice I draw a different plane, could you explain why is that happening? How do we draw -1 -6 4 plane? I mean how can you do the reverse?
These type of questions are almost always resolved by considering what it would look like if you started from another lattice point. Remember, you can choose to draw the plane from any corner of the unit cell. What you will find is that by drawing it from a different corner of the unit cell you end up with the same thing or a parallel plane
Hi can u help to solve this problem.. they give 3 point which is ( 1/2,0,0) , (0,0,1/2), and ( 1/2, 1/2,0) .. and it ask me to find the miller indices through this point
sure. let's follow the steps in the video. First thing we do is draw points on a lattice and then connect these points to form a plane. This plane intersects only w of our axes (x & z because it runs parallel to y). It intersects x axis at 1/2, z at 1/2, and y at infinity (parallel). To turn this into miller indices we invert these numbers to get (202) because 1 over infinity is zero.
Sure. Looking at it and drawing it on unit cell I set my origin at the standard back left lower corner. I see that the plane would intersect the y-axis at 1.5 (it drops from z=1 to 1=/2 in one half a unit cell, in another unit cell plus the half unit cell it started from or y=1.5 it will intersect y-axis). It will never intersect the x-axis because it runs parallel to it. . The z-axis will intersect at 1.5 for the same reasons. Therefore the intersections are (infinity, 1.5, 1.5) so inverting we get (0 2/3 2/3). Multiplying by 3 we get (0 2 2) reducing to lowest integer we get (0 1 1). So, unless I made an error somewhere I would expect that to be the family. You could test by plugging it into VESTA and double-checking it crosses those points. EDIT: I messed up x the first time. We fixed it in comment thread below.
@@erincolleen2647 when you plot the 111 plane or when you plot those three points and connect them with a plane? when I connect the three points they don't cross the x-axis either. You have to extend the plane out of the unit cell as we do in the video
@@TaylorSparks I extended the plane out of the unit cell, and because the second two points form a line segment parallel to the x axis it doesnt show it crossing. I appreciate your help btw!
Going from point B to point C it goes from 3/4 the way up a unit cell in the Z direction down to 1/2. If it continues at this same rate then one more unit cell over it will reach 1/4 and one more it will reach 0 and intersect the x axis. Since you have to go back 3 unit cells to intersect the x axis, x=-3
Well spoken, quick and to the point. Thank you!
The most straightforward explanation
thank you very much for answering this question. you are well experienced in teaching material science
Thank you for breaking down Miller Indices!
Hi, good day. please I don't understand how X ended up as -3
Im still confused how you got -3 for the x
it went from 3/4*z to 1/2*z in a single unit cell. It will take two more unit cells (3 total) to reach the x intercept.
@@TaylorSparks so you did 3/4-1/2 to to find out you need to go down by 1/4 each time till you get to the x-axis?
@@alanzoMC correct
@TaylorSparks please, does it matter if I do AB x AC VERSUS AC x AB? The direction of the cross product would be opposite each other for those 2 cases, I don't know if that means significant difference in miller indices of planes
for example i did this but many times i got the opposite answer as my professor who does origin shifting.
for example, he might get (hkl) = (1 -2 2) and i would get (-1 2 -2) using the cross product method. Are both correct?
If orientation does matter, how do I select the correct orientation/order to multiply when doing cross product method?
@@irisce2799 Good question. If you reverse the order of the cross product you will just get the opposite normal. One is normal up and one is normal down so to speak. I would need to work it out both ways, but I'm guessing they are equivalent planes. To be certain. You can do the right hand rule cross product and pick the one that is pointing normal (up) to the plane as it is drawn
@@TaylorSparks oh wow I was totally not expecting a response so fast! Yes I was reading and also came across using the right hand rule to select the most "upward" pointing orientation. Thank you professor!
I have another question. At 5:27, you said the vector cross product only works for cubic systems and not other crystal systems.
Why wouldn't it work for hexagonal unit cells? I was doing a problem with a hexagonal unit cell, and I used the same vector cross product method to get (hkl), then i = -(h+k) to convert to the Miller-Bravais (hkil) format.
The weird thing is that in the problem the professor drew the unit cell as a rectangular prism so it looked like the xyz cubic system, but they denoted the angle between 2 axes to be 120 degrees and then stated that it was a hexagonal unit cell.
Honestly, I have no idea how to solve that kind of problem by shifting the origin and stuff, so I just used the cross product method and converted it.
Would I be correct to solve it this way?
Pls have you done a video about the basics of this crystallographic direction am so confused as to how u could get the points on the plane
How to write these point on cubic crystal 1/2 , 3/4...please reply??
Can you help for this question, sir
In orthorombic crystal
Intercepts 2,4,2 and corresponding primitive vectors are 3,6,4 amstrong. Find out Miller indices
Plz help me
Hello plz help to solve the problem having 3 points at A(1/2, 1, 1/2) B(0, 1, 1) and C(1/2, 1/2, 1/2)... miller indices for the plane
at 7:30, the direction of AB x AC should be pointing downwards, not upwards.
Hey man thanks for the video. How about this... The three points are (1, 0, 0), (1/2, 1/2, 1) and (0, 1, 1/2). Cross multiplication gives the miller indices (-3, -3, 0) but that doesn't feel right to me.
yup, I get (3,3,0) www.symbolab.com/solver/vector-cross-product-calculator/%5Cbegin%7Bpmatrix%7D%5Cfrac%7B1%7D%7B2%7D%26-%5Cfrac%7B1%7D%7B2%7D%26-1%5Cend%7Bpmatrix%7D%5Ctimes%5Cbegin%7Bpmatrix%7D-%5Cfrac%7B1%7D%7B2%7D%26%5Cfrac%7B1%7D%7B2%7D%26-%5Cfrac%7B1%7D%7B2%7D%5Cend%7Bpmatrix%7D you can plot that plane to see if it intersects the points
When I draw (-1:-6:4) plane from Miller indice I draw a different plane, could you explain why is that happening? How do we draw -1 -6 4 plane? I mean how can you do the reverse?
These type of questions are almost always resolved by considering what it would look like if you started from another lattice point. Remember, you can choose to draw the plane from any corner of the unit cell. What you will find is that by drawing it from a different corner of the unit cell you end up with the same thing or a parallel plane
I failed the exam question soooo hard dude feels so bad
Hi can u help to solve this problem.. they give 3 point which is ( 1/2,0,0) , (0,0,1/2), and ( 1/2, 1/2,0) .. and it ask me to find the miller indices through this point
sure. let's follow the steps in the video. First thing we do is draw points on a lattice and then connect these points to form a plane. This plane intersects only w of our axes (x & z because it runs parallel to y). It intersects x axis at 1/2, z at 1/2, and y at infinity (parallel). To turn this into miller indices we invert these numbers to get (202) because 1 over infinity is zero.
Can you help with (110),(011),(001)?
Thank you
;)
HI! Can you help with this one... (1/2,1/2,1) (0,1,1/2) & (1,1,1/2) Thanks!!
Sure. Looking at it and drawing it on unit cell I set my origin at the standard back left lower corner. I see that the plane would intersect the y-axis at 1.5 (it drops from z=1 to 1=/2 in one half a unit cell, in another unit cell plus the half unit cell it started from or y=1.5 it will intersect y-axis). It will never intersect the x-axis because it runs parallel to it. . The z-axis will intersect at 1.5 for the same reasons. Therefore the intersections are (infinity, 1.5, 1.5) so inverting we get (0 2/3 2/3). Multiplying by 3 we get (0 2 2) reducing to lowest integer we get (0 1 1). So, unless I made an error somewhere I would expect that to be the family. You could test by plugging it into VESTA and double-checking it crosses those points.
EDIT: I messed up x the first time. We fixed it in comment thread below.
@@TaylorSparks Thanks for your response! when I plot it, it shows that it doesnt cross the x axis at all, this is where im confused
@@erincolleen2647 when you plot the 111 plane or when you plot those three points and connect them with a plane? when I connect the three points they don't cross the x-axis either. You have to extend the plane out of the unit cell as we do in the video
@@TaylorSparks I extended the plane out of the unit cell, and because the second two points form a line segment parallel to the x axis it doesnt show it crossing. I appreciate your help btw!
@@erincolleen2647 oh geez. You are completely correct. I messed up on x! You are correct. Therefore it would be (0 1 1). Sorry!
In a silicon crystal, if a plane has intercepted at 10.86 A, 16.29 A, and 21.72 8, along the three Cartesian, find the Miller indices of the plane.
please give me the solution.
why are you going down a quarter 3 times for? whats the purpose of going down ? oh wait are you trying to get back down to the new origin?
can someone explain me why x=-3??
Going from point B to point C it goes from 3/4 the way up a unit cell in the Z direction down to 1/2. If it continues at this same rate then one more unit cell over it will reach 1/4 and one more it will reach 0 and intersect the x axis. Since you have to go back 3 unit cells to intersect the x axis, x=-3
@@TaylorSparks thank you👌
bad expression , bad explanation ,
🤪 thanks random internet person!
MAAAANNNNNN!!!!! The points on the unit cell (cubic crystal system) are wrong.....
Oh?
Thank you