Symmetry Operations, Types of Twinning, & Miller Indices of Crystal Planes- Mineralogy | GEO GIRL

[@larsfredriksson3108]

For the upper orange one, move the origin to the front down right corner of the cube. For the upper middle one, move the origin to either of the down right corners. Upper right: Move origin to either of the down back corners. One is always free to move the origin so that the indices can be found. The reason for this being possible is that these planes repeat themselves over and over again; they are fixed in the individual unit cell but not fixed between the unit cells. Alternatively and equivalently, one may hence move the plane itself but keep the origin constant.

[@GEOGIRL]

Wow thanks for this comment! I am going to pin it to the top so people can find it since you explain better than I did haha ;)

[@KerriEverlasting]

I have absolutely zero clue what this comment means. Goal for the day right there. 😂💖

[@zhoujie19800907]

@GEOGIRL Since this notation only about direction, move the plane parallelly won't change the direction. Moving the plane out of the origin could easily find the answer, and using this way could further prove (-1, 0, 1) = (1, 0, -1).

[@WhatDuhDogDoin]

Thankyou so much, the position of the origin there made it look like complete nonsense

[@green_tuber]

At 22:54 so genuine to say "we don't know" 😆😆. That is really great. At least we know that we have something to figure out ourselves. Instead of just believing whatever we have told.

[@GEOGIRL]

Hahaha Well I am so worried about giving wrong information that I would rather tell you guys when I don't know something than tell you something that is wrong, so I am glad you appreciate my honesty😅

[@lawrencekosinski-jackson613]

I’ve been stumbling over learning this section in my Gem Identification Course and your video just came over my recommended and I can honestly say I’m so grateful and found a new song I can listen to that helps me learn what’s needed to pass my courses… I wish my grandfather was still here so I could have shown him this. Thank you 🙏 ❤

[@GEOGIRL]

Thank you so much for the kind words! I am so happy you have found my videos to be helpful! :)

[@binhaowang283]

Great video! A minor comment for better understanding the indices for some of the "weird" cases. The Miller indices show the normal vector (pole) of the plane and are scaled so that each component is an integer. Calculating the reciprocals of the intercepts is just one specific way to get the normal vector of a plane. Hope this helps!

[@lethargogpeterson4083]

I would like to second this comment. Basically I think you are just specifying the plane's alignment in 3 dimensional space by specifying a single vector perpendicular to that plane. If you try it on the peach colored (-1, 1, 0) one, you can see that it works. If you draw a line segment from the diagram's origin to point -1, 1, 0, you can see that it is perpendicular to the peach plane.

[@HappyFlowerDE]

21:30 Why (-1,1,0)? Hi @ all or GEO GIRL TL;DR: The Miller indices represent the smallest integer intercepts of a family of parallel planes in a coordinate system. They can also be viewed as normal vectors of these planes. Explicit: The index (-1,1,0) describes planes that are parallel to the a3 axis and have inclinations towards a1 and a2. Inclinations are represented by negative values (counterclockwise) and positive values (clockwise). The index (-1,1,0) means that the plane is rotated counterclockwise from a1 and clockwise from a2. The angle can be determined using the tangent: |a2|/|a1|. In this example, the plane is at -45° to a1 and +45° to a2. Since this Miller index describes a family of planes, it refers to infinitely many parallel planes with the same inclination. It is important to note that this index represents a plane with distinct intercepts with the axes. If we shift the displayed plane (which passes through the origin) along a2, we obtain a new plane that intersects at -a1 and +a2, thereby resulting in the Miller index (-1,1,0) for this family of planes. Fun Fact: Each plane has two normal vectors, which means that the Miller index can be inverted. Sometimes it may be desirable to keep the first component of the Miller index positive, making inversion of the index sensible. Greets Léna

[@williamnajera1173]

I watched the full video and laughed at the end when you said you were explaining the fundamentals of Miller indices without really understanding it, and I guess my understanding is that the light of a crystal or jewel diffracts these indices onto each other; I have a jewel tray that I like to put on the windowsill so the sunlight will shine celestial light beams onto the ceiling and the light signatures seem to mix together more than they would shine greater amounts of speckles; I also noticed that sunlight grows a stronger current in a limited spectrum like when it's shining through the window shutter blinds and this seems like it could be measured with the intensity of the light refracting or in this case diffracting off of a jewel. Thank you for making this video!

[@babyblossom1179]

Hey geo girl! I love love watching you videos to learn geology. you make it so easy to grasp the concepts which i used to find so hard, with your fun and entertaining videos. now these topics dont feel like a chore to me .for that you are a blessing indeed. I am really waiting for you to cover braggs law and some more indepth mineralogy videos.... Thank you soo much and much love to you

[@GEOGIRL]

Thanks so much for the kind words, I am so happy that my videos have helped you find these topics more understandable and even entertaining! ;D That makes my day!!

[@emmah794]

You are single handedly helping my mineralogy grade so much

[@GEOGIRL]

I am so glad you have found the minerology videos helpful! Good luck in your course ;D

[@yvonnejansen9645]

Bless your heart! Super helpful! I was super confused in my geology class. I appreciate it

[@GEOGIRL]

So glad you found it helpful! Thanks for the comment, and best of luck in your class ;)

[@fxzq]

at 22:40 you can figure out the indices by shifting the origin. for example for (-1 1 0) if you shift the origin to be at the tip of \vec{a_{1}} you can see why the intercept would be at -1 I hope this helps.

[@JoesFirewoodVideos]

YAY! I get to learn about crystals tonight from my favorite geologist I ❤️ GEO GIRL!

[@GEOGIRL]

Hope you enjoy! ;D

[@toughenupfluffy7294]

20:46. The issue I see with the bar 110 is that the origin is set at the forward face of the cube, with the a2 axis going into the paper; whereas the normal placement that I've ever seen has the origin at the rear face, with the a2 axis coming out of the paper. This orientation, I think, is why the a1 is negative instead of positive. All other resources I've ever seen regarding Miller indices use the second orientation, giving this plane a 110 without the negative (bar 1).

[@Anonymous-vn8ik]

For the negative values for the indices, I think of it as shifting the plane being observed along the axes till it forms a polygon with the origin being the polygon's one vertex not touching the plane.

[@maleehakhan3902]

Thank you sooo much for posting this! It’s is SO helpful for my biophysics class!

[@GEOGIRL]

Oh wow, I never even imagined it'd be helpful for a biophysics class, but I am so glad it was! Thanks for letting me know :)

[@HappyFlowerDE]

21:30 Warum (-1,1,0)? Hi an alle oder GEO GIRL: TL;DR: Die Millerschen Indizes zeigen die kleinsten ganzen Schnitte einer Ebenenschar von parallelen Ebenen in einem Koordinatensystem an. Sie können auch als Normalenvektoren dieser Ebenen betrachtet werden. Explicit: Der Index (-1,1,0) beschreibt Ebenen, die parallel zur Achse a3 sind und Neigungen zu a1 sowie a2 aufweisen. Neigungen werden durch negative Werte (gegen den Urzeigersinn) und positive Werte (mit dem Urzeigersinn) dargestellt. Der Index (-1,1,0) bedeutet, dass die Ebene gegen den Urzeigersinn von a1 und mit dem Urzeigersinn von a2 gedreht ist. Der Winkel kann durch den Tangens ermittelt werden: |a2|/|a1|. In diesem Beispiel liegt die Ebene bei -45° zu a1 und +45° zu a2. Da dieser Millersche Index eine Ebenenschar beschreibt, bezieht er sich auf unendlich viele parallele Ebenen mit gleicher Neigung. Wichtig ist, dass dieser Index eine Ebene mit eindeutigen Schnittpunkten mit den Achsen repräsentiert. Wenn wir die angezeigte Ebene (die durch den Ursprung verläuft) um a2 verschieben, erhalten wir eine neue Ebene, die bei -a1 und +a2 schneidet, wodurch der Millersche Index (-1,1,0) für diese Ebenenschar entsteht. Fun Fact: Jede Ebene hat zwei Normalenvektoren, sodass der Millersche Index invertiert werden kann. Manchmal kann es gewünscht sein, die erste Komponente des Millerschen Index positiv zu halten, was eine Inversion des Index sinnvoll macht. Grüße Léna

[@ruatfelahrahsel9536]

your videos are so good,i can understand them easily

[@GEOGIRL]

I am so glad to hear that :D Thanks for the comment!

[@abhilashsundaram2432]

You’ve a very delightful personality and the content is great as well. A little bit of work on the animation bit will thrust your channel into the elite league. Ps: I’ve been watching your videos for a geology exam that i’d be writing. I had no clue since I majored in physics, but your videos have been super helpful. Thanks!

[@GEOGIRL]

Thank you so much ! :D So glad my videos have been helpful for you!

[@m74w]

21:58 As the mineral structure repeats itself in layers, the next layer (Not indicated in the box) will cross the a1 axis in -1. Therefor (-1,1,0) . But couldn't it as well be (1,-1,0) ? Would be equivalent, no ?

[@williamphillips7980]

Bragg's Law OMG!!!! not many youtube videos on this!

[@GEOGIRL]

OMG!!!! YASS hahaha Thanks for the comment, Billy, I don't know what I would do without your input ;)

[@SpottedWeasel]

You make learning very enjoyable! Thanks for that, keep it up :)

[@anthonyjnr.alakpa2135]

Will we have the same answers if our origin is at onother plane? I tried it, and my answers are different. 20:39

[@burninsmoke3150]

Thank you so much I really appreciate your hard work

[@GEOGIRL]

Thank you! So glad you enjoyed the video :)

[@Abbyisradd9]

Your video is helping me a lot! Question, I am writing a paper about an introduction to this topic and was wondering if you have any good scholarly sources you can pass my way.

[@Geologywonders.311]

Great explained. thank you so much.

[@hukaihurren1885]

Really beneficial, thank you.

[@GEOGIRL]

No problem, glad I could help :D

[@vasanth7141]

Hey sis, hope you're doing well Subject : Doubt on Monoclinic system forms Actually I have this doubt for a while, my professor couldn't explain it properly on that time. It was about Clino dome in Monoclinic system. He showed us a Gypsum crystal model and said it has Pyramid on top and bottom. He also said it meets all three axes. I was really confused with that. Because its side is clinopinacoid, that means its edge with top face also parallel to clino axis, right? Also clino axis angle is same as inclined plane. So that top and bottom faces are seems to be parallel to clino axis. If so, it would be clino dome and crystal might have two set of clino domes(4 faces). But yeah it would surely Pyramid I think, because I don't think it was wrongly categorised for years, it is popular crystal gypsum after all lol So what I wanna learn is how actually it is Pyramid? and why not clinodome? Does they meet all 3 axes? (cuz in tetragonal system 2nd order pyramid only meet 1 horizontal axis, but sources says it meet all the axes) And how? (This was that crystal in case you want reference: images.app.goo.gl/1pwMW5pMtBxfe7qR8) Explain if you'll have time, thank youu!! :)

[@GEOGIRL]

Hi there, thanks for the comment! Unfortunately, I don't think I will be able to help you very much, I am no expert in the crystal systems. However, I did look up clinodome and it says that is characteristic of monoclinic crystals, I couldn't find anything about pyramids related to monoclinic crystals so I am not sure what he means... Sorry I couldn't be of more help. Best of luck! :)

[@vasanth7141]

@@GEOGIRL Ohh thanks for your effort and that's true there is not much sources, hope I'll understand it one day. Thank youu!! :)

[@conorhaynes-mannering5094]

In a tetrahedral would the corner we're looking through in a 2D diagram actually count as a rotational axis? I can see that if you were to rotate it 109.5 degrees down along an edge you would get the same image but I wasn't sure if that was what was meant by rotational axis (axis normally differentiating among x, y, z, etc.).

[@GEOGIRL]

Yep, tetahedral molecules/structures have multiple rotational axes actually through both their corners (C3 axes, a 120 degree rotation) and their edges (C2 axes, a 180 degree rotation). The reason it is 120 instead of 109.5 for the corner rotation is because you aren't rotating each atom into the spot of the next atom on the most direct path, you are rotating it so that the atoms move at a slightly indirect path to the placement of the next atom (it's really hard to explain, so see my suggestion below...) If you want to visualize the symmetry of a tetrahedron and its rotation axes better, I suggest going to this website: symotter.org/gallery, where you can scroll down to tetrahedral on the left side of the screen and click the down arrow, then click methane (Td), and then click the C3 rotation on the right side of the screen, you can then press the play button to see the actual rotation of the molecule around that axis and you can check the box on the right to show the axis on the molecule. It's a very helpful website, has gotten me through many symmetry chemistry exams ;)

[@conorhaynes-mannering5094]

@@GEOGIRL woww, this resource is insane! I can see the difference between the angles but now you've just opened a whole new amazing rabbit hole for me :P hahaa

[@GEOGIRL]

@@conorhaynes-mannering5094 Yes! I love that website so much, so glad to hear you are finding it helpful as well ;) Have fun! ;D

[@jaredmeeks4491]

GR8 job??? Does a spectrometer yield the results D to the crystals atomic value?

[@GabrielMercier-ue9gs]

If we are free to chosse the origin, 1 -1 0 and -1 1 0 are the same thing, so are 111 and -1-1 -1. I guess we are free to choose the orientation too, so 100 and 001 are the same thing too. There are probably rules about that, but if you have a perfect cube of halite in you hand, there no way you can tell 100 apart from 010.

[@Enkaptaton]

Did you know that you have to rotate an electron 720 degrees before it looks the same again? I think the example for when you need to do Miller Indices is needed in the beginning of the video. You need every bit of motivation if you want to get through this stuff Hahaha Very very cool channel btw. I study medicine, but I am interested in stones sice i was a child. Now learning the basics feels great, thank you for this :)

[@GEOGIRL]

Thanks for the comment and information! Best of luck with your medical degree, and thank you for your interest in my channel. I do share some geobiology, but it tends to be more about microorganisms rather than humans haha, so not sure how relevant it will be, but as long as you enjoy it ;D

[@BorisNVM]

Apparently the miller indices show components of the vector normal/perpendicular to the plane. I think it's a basic concept to get, I'd argue it is enough to learn what it is a vector and its components and what is a normal vector to a plane. It could confuse at first because (111) and (222) would represent the same thing.

[@mayankmishra4357]

Support from India ❤

[@George-yn8po]

You are a genius, aren't you??

[@GEOGIRL]

HAHA! I wish! ;)

[@briancurtis6022]

So, every shape has an R1 rotation axis, as a trivial case? And is there an example of a faceted shape that *doesn't* have a center of symmetry?

[@GEOGIRL]

Yes everything has a 360 rotational axis, but many people omit this when labeling symmetry elements since everything has that. And yes, there are many shapes that don't have centers of symmetry, it's kind of hard to explain in words though, so I will just send you here so you can take a look at a few yourself (the ones that say 'none'): geometrydictionaryt.weebly.com/uploads/5/3/9/1/53910381/870227406.gif But there are also many examples of lacking this symmetry element in the world of molecules & chemistry where symmetry is very useful. Hope that helps ;)

[@tuathaigh-aa]

I can't believe I didn't find your channel earlier; please improve your audio quality as the echo is really frustrating - otherwise so helpful, don't stop please!

[@GEOGIRL]

Thanks for the support and encouragement! I did make this video a long time ago and have since improved the audio, sorry about that! ;)

[@vikramraj6852]

Thank you so much Ma'am

[@vivianloney8826]

I was wondering if you could do a video on stereo diagrams?

[@GEOGIRL]

Like for structural geology? I plan to in the future, but just haven't quite gotten to those yet, but I will try and get to them asap ;)

[@taladiv3415]

27:51 cute moment of confession. 😊

[@parazitmaly]

little bit confused i was, but in the end, i think i understand it, probably

[@GEOGIRL]

Lol, I feel the same way don't worry! ;)

[@nthumara6288]

what are those dots are they represent atoms

[@nthumara6288]

apaat from the nathural crystals can humans also buid those stucthurs using atomes

[@nthumara6288]

using those units cells when we try to buid a cyrstal one atom will get divided

[@metilarancia]

you actually saved me thx

[@GEOGIRL]

Thanks! I am glad I could help ;)

[@AalaaMady-x5l]

so useful thaaaank u

[@Diamond-qz7jp]

Thank you so much

[@davidhand9721]

Seems like this field needs geometric algebra. Maybe projective geometric algebra if you need to talk about distances between planes. All of the symmetries you're going over are very elegantly expressed in GA; all transformations (translations in PGA only) are composed from reflections. All the math is independent of dimension and coordinate system. I can't believe we still do any mathematical geometry without it.

[@ty92470]

Thank you.

[@anasallala]

thx girl

[@MarkMoore-l4g]

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