What is a Unit Cell?

What is a unit cell? And what are cell parameters or Miller indices? In this video, we make sense of the confusing jumble of information about unit cells and learn why they’re so useful for understanding crystals and surfaces.
Chapters:
0:00 Introduction
01:12 Unit Tiles for 2D Patterns
04:31 Unit Cells for 3D Patterns
10:30 Interpenetrating Unit Cells
11:53 Bravais Lattices
15:02 Planes and Miller Indices
21:24 Crystal Surfaces
23:44 Macroscale Crystals
25:42 Further reading/watching
Frank Hoffman’s lecture series on unit cells: • Unit 1.1 - Crystal and...
Wilson Bentley’s snowflake photographs courtesy of the Natural History Museum, London: tinyurl.com/yxkeabwb
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Three Twentysix Project Leader: Dr Andrew Robertson
Assistant Editor: Purple Saptari
3D Animations: Es Hiranpakorn
Graphic Design contributor: Maria Sucianto
This video was produced at Kyushu University and supported by JSPS KAKENHI Grant Number JP21K02904. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of Kyushu University, JSPS or MEXT.

[@harshit3971]

Never understood unit cells like this before. Thanks for your efforts!

[@ThreeTwentysix]

Thanks for watching.

[@abcde_fz]

Your getting an award (conceptually speaking) for BEST CINEMATOGRAPHY in Special Subject videos. Very comfortable lighting, blocking, and depth of field. Like your sitting across a table in a well-lit room, speaking only to me.

[@helpicantgetoffofyoutube]

Did you work with cinema before? This might be the best, most clear, most beautifully made video about the subject Ive ever seen

[@rebanelson607]

Wish this had been available when I was taking a chemistry class back in the early '90s.

[@m74w]

I really love your very informative videos. Please go on with them !!! Your work helps a lot in understanding crystallography.

[@Ganpatthealth]

Wow, your videos are incredible! Thank you so much for your amazing teaching....truly grateful sir

[@mrogelj]

Your channel is awesome and continues to be so helpful! Thanks for breaking these complicated topics down in a really palatable and accessible way, to say nothing of the great cinematography of your videos!

[@abdelz1617]

Great video!

[@broli123]

This is absolutely fascinating! You won a new subscriber. I stumbled upon this after reading a fascinating theory on how the universe galactic clusters have a cubic crystal structure. I believe our universe IS a bigger fractal of a crystal lattice that might or might not be "living". How amazing is it to think that we are the individual sub atomic particles of that universe holding everything together. Being driven by the thermal heat of the proton aka our sun. Insane. We dont need to build larger atomic colliders we ARE the sub atomic particles on a different scale.

[@Darthvanger]

RIP textbooks :) No sane person is going to choose a textbook over this awesome step by step explanation with animations. Well, if you really want to understand, rather than just turn off your brain and memorise to pass the exam :) It's not just textbooks though, but lectures and even video lessons may be as dry and confusing. KZbin makes wonders :) This format of presentation is so comfy and beyond awesome. No university comes even close :) Thank you, the best chemistry teacher so far!

[@th0har]

Never had this subject explained quite so simply and elequently before. Someone buy that homeless man a cup of tea!

[@ThreeTwentysix]

That started so nicely...

[@maxvanmon8322]

This is the best chemistry channel on youtube, change my mind

[@Dr.Kraig_Ren]

I can't. 😅

[@Dr.Kraig_Ren]

9k Views on this video hurts me. Keep making videos. You'll soon get thousands of loyal viewers.

[@JK-0423]

Omg this video is so cute and it’s everything !!

[@WAMTAT]

If videos like this existed when I was studying I might have stuck with Chemistry.

[@ScienceLearning-hr2oo]

Good work

[@ikhbayarerdenebat5195]

great content, keep it up!

[@ThreeTwentysix]

Thanks!

[@gentrelane]

Thanks for all the mineralogy flashbacks

[@modernscience3495]

Thanks ❤

[@raisulislam7689]

Thank you for the video. This was very helpful. Can you make a video on reciprocal lattice and Brillouin zone? 🙏🏾

[@ThreeTwentysix]

Thanks for the suggestion but, to be honest, that one's going to be a little further down the pipeline!

[@INV.EngineerTlais]

I don't know how to thank this great man!

[@ThreeTwentysix]

Thank you. A subscribe and a share would be great.

[@lexscarlet]

Is there an analog concept for time crystal lattices?

[@HaileISela]

hey there! could you speak to Buckminster Fuller's Synergetics in relation to this? as it is an experientially derived kind of geometry that has everything to do with closest drawn spheres and the generalized principles at play as spacetime is structured, there are several ways in which it comes to surprising insights, particularly in comprehending the so called fcc pattern with the 'tetrahedral' (i'd call that foureyes) cell as the volumetric unit on one quantum, rendering the 'octahedral' (or eighteyes) gaps between them as four quanta. a 'cubic' shape where one keeps the triangulation in mind, so at minimum one inscribed foureyes ('tetrahedron') is present, has a quantum volume of three. in this frame of reference, the 'cube's' edges are no longer normalized as units, but rather the square's root becomes a unit of one. that's as in one diameter of the spheres involved, or one interval between the centers of two spheres connected by this vector. one radius from one sphere's center to the kissing point and a second radius into the other center. this also then recognizes the triangle between three spheres as the unit for area. this triangle is in fact dynamically structured, defines a plane and can be accounted for by the same operation of second powering as the 'square', except in polyformity as the triangle's unfolding, as all of spacetime, is complementary in nature. i have much material and models over on my channel, presenting aspects of synergetics in my own words if you were interested. otherwise the book "A Fuller Explanation" by Amy Edmondson offers a superb overview of the framework and some of its deeper waters and of course Bucky himself left many artifacts, the two volumes of "Synergetics - The Geometry Of Thinking" which can be accessed at www.synergetics.info and countless hours of lectures and presentations. and there is much more to be found in the wider cosmos of the bfi, Buckminster Fuller Institute, the ongoing series by @52livingideas on Bucky, the work of Kirby Urner, @scientificgenius, Daniel Ari Friedman, the Synergetics collaborative, Synergetics-University, and so many more. if you were so kind as to consider this corner of Universe, it might be of great interest to you, revealing further connections and comprehensiveness between seemingly disparate fields of science. it certainly has changed my whole life and being and i sincerely feel like it holds the keys to a paradigmshift unlike any others before, offering practical patterns of creating in compendence of synergy rather than dependence on energy, realizations on the nature of structure and the spectrum of shapes of spacetime and their qualities. if more people knew of this frame of mind, earthquakes and rising sea levels, increasing temperatures and violence of atmospheric systems, waste production and innumerable other crises and catastrophes could be handled in very different ways, thereby addressing everyone's needs in regenerative ways, no longer in conflict with the rest of Universe. peace Struppi

[@abeljones7900]

Bro. Yes. That was the first thing that came to mind when i saw the thumbnail and title. Thank you for commenting. I’ll check the channel out!!

[@HaileISela]

@@abeljones7900 what a rare pleasure to find others who have this come to mind on this matter. i really hope we will collectively lift synergetics from its current place of obscurity and bring it to everyone's attention. there's too many good reasons not to ignore it, and scientists in particular would likely benefit tremendously from reassessing their ongoing subscription to the abstract geometries of ancient mystics. at the very least, they should consider the alternative option of an experiential geometry, one based on the scientific principles of observation, modeling and experiment. i do not think most people are actually aware of the cognitive dissonance at play when the application of the scientific method in their practice never even reaches the non-scientific, axiomatic foundation of their trade, never truly reconsidering the underlying axiom that geometry "naturally" needs complete abstraction. no wonder there's endless paradoxa budding on a scientific tree rooted in such unchecked ignorance of, well, facts. i mean, to those reading this my statement may appear outlandish, maybe even ridiculous, but it is actually based on evidence which cannot be said of the 'platonic' geometry and its offspring. so before one dismissed my points, please at least take the time to consider the evidence i present, among other places, in the following video: m.kzbin.info/www/bejne/mWjTqmappr6AadU peace struppi

[@matthewbartsh9167]

Great vid, as usual, but you said "minerologist". It's "mineralogist". Just before 16:01.

[@matthewbartsh9167]

At 9:40 the video says that different crystals of the one substance have different densities, and that iron can form three different crystals. I think the vid should have said something about the densities of these three different crystals. Are they very different? The idea is a bit surprising. The density of iron is normally stated to be 7.8 g per cc. There's no mention of which crystal of iron that refers to.

[@ThreeTwentysix]

These are allotropes of iron, body-centred cubic, face-centred cubic and hexagonal close packed (the first two at least are in the video). The density of iron depends on which crystal form you have, and that depends on temperature and pressure (and it's formation history too, in some cases). Listed densities are for the most common structure, which I can't remember off the top of my head but I'll put my money on BCC.

[@matthewbartsh9167]

@@ThreeTwentysix I've seen some other KZbinrs add a printed note to a video to fix it. I'm guessing that it doesn't affect the view and like tally. If so, how about adding a note listing the densities of the three allotropes of iron? As it is, the video seems to go off on a tangent, forgetting the point being made was about density, and talking instead about the desires of metallurgists and how they can be met via knowledge of crystals.

[@matthewbartsh9167]

That bleep shortly before 22:04 was way too loud. It hurt my ears.

[@lyubomirmilanov3710]

DO you think that they may have built the pyramids using unit cells

[@alllove1754]

I compare it to what Jesus wanted for us to be like.

[@Freekniggers]

*the story of jesus

[@Freekniggers]

It is ridiculous and promotes insanity to believe what many Christians say he was. They he was God and that is not true, they also say he is the only way to forgiveness, that is also untrue as forgiveness isn't needed for you to become nothing again just as before you were born you shall return. We are noore than snowmen in a very very short season. I do believe that so of the stories have helped many people while they were alive but there is no need for a demigod. There is only the value that God gave us and our value is to God. We should not beg to go to heaven we should not beg until it is unavoidable for us to live without doing so. I love God souch but there is no way demigod is replacing God, not merely my God but, the creator of the most highest of all creators the father of good and evil death and life. I love that 1 to the point there is no need for heaven, although it would be awesome if one were made after I post this, there is only the desire to be loved by God and to share the infinite supply of love that God provides to us to share and enjoy while here.

[@canadiangemstones7636]

@@FreekniggersGod says if you do not love me, I will set you on fire. Why worship a psychopath? 😂

[@moodystatusking7918]

If they are imaginary then what is there use in real sense

[@rickyardo2944]

WOW! you are so clear and cool! well done and please keep it coming, thank you.

[@ThreeTwentysix]

Thank you! Will do!

[@ghostedyoutuber263]

Dood, comb your hair... and wash it as well. I am not being cheeky or anti-social... just observant. To PROOVE that I am not being cheeky, I extend to you the olive branch salutation of wishing you that "May all your double bonds be conjugated!"