1.4 Classification of latices

[@introductiontomaterialsscience]

I have made two mistakes in this video 😞: 1. I have considered Trigonal and Rhombohedral as synonyms for the same crystal system. However, as per the International Tables of Crystallography Vol A it.iucr.org/A/ the two terms are NOT synonymous. Crystal System should only be called Trigonal and not Rhombohedral. 2. I have shown only one Bravais lattice in the trigonal crystal system. But in reality there are two Bravais lattices in the trigonal system: hexagonal prinmitive (hP) and hexagonal rhombohedral (hR). And so there is no trigonal P Bravais lattice as shown in the table in this video. I plan to make a video to clarify this. Wil share the link once I do it. You can check en.wikipedia.org/wiki/Crystal_system.

[@one.darkstar]

Thank you, sir. We will note that. You are awesome.

[@Summer69384]

Hats off to his dedication ❤

[@andersonalvarado7278]

espectacular, estoy muy agradecido por esa información compartida. Mucho respeto y agradecimiento para el profesor Rajesh Prasad e igualmente para el Instituto de tecnología Delhi y el NPTEL. Gracias :)

[@melvindavis3629]

I wish i could have a professor like you when i was doing B.E

[@rifqihammami3935]

I like with his explanation. Everything is easy to understand. Keep it up, Sir and don't be bored to share knowledge. May God bless you always. Aamiin ...

[@unmeshlondhe2497]

Sir you are simply great... The way you are teaching is amazing... Thanks for your vedio lectures..

[@swastikdeshmukh406]

Stunning teaching art sir thanks a lot

[@preetishsajwan4502]

By far the best explanation of this topic on this platform.

[@jaswanthkumar8157]

Even at end of lectures your making it so interesting sir

[@makhmulshaikh8670]

Sir I am enjoying this sessions..nd feeling like in college lecture... Thank you very much

[@ThePabler6]

Me too

[@akashdeep5088]

Describing you in a word " Legends"

[@sirbaggy]

Really interesting and well presented series of lectures.

[@a.kanagavalliponvetrivel2271]

excellent explanation sir. thank you sir

[@bg7363]

Its pleasuring to learn with your video...

[@natashawhite712]

i respect you so much professor.

[@sci-fi1998]

Sir,Thank you for your nice lecturure.. And i am requesting you to make a video for crystallization magma..unicompoments, bicomponent and ternary.. How to calculate those percentages of component

[@sameerkhan-fw2lq]

Excellent explanation 👌

[@KajalKumari-nk3wl]

Good explanation

[@truescienceknowledge]

Sir please explain what is 1) cubic 2) tetragonal 3) orthorhombic 4) hexagonal 5)trigonal or rhombohedrical 6) monoclinic 7) triclinic

[@jaswanthkumar8157]

Thank you sir, the finest lectures I heard on MMS subject. Sir,could you please suggest me the reference books of your lecture.

[@blzKrg]

Try Charles kittel or Physics of materials by Prathap Haridoss.

[@jaswanthkumar8157]

Thank you sir for your suggestion

[@sayanjitb]

Ashcroft mermin ... You can try it

[@jaswanthkumar8157]

@@sayanjitb 🙏thank you sir

[@paulboro5278]

Sir, some books also consider unit cells which do not have lattice points on the corners, which is very confusing to me.

[@introductiontomaterialsscience]

It is possible to choose unit cell where corners are not lattice points. All that is required is that the corners should be translationally equivalent points. Thus if you begin with a unit cell with corners at the lattice point and shift it parallel to itself by a non-lattice translation then you will get a unit cell whose corners are not lattice points. I avoided this complication in my video as it is simpler to choose a unit cell with corners at the lattice point. I would like to see the specific example which you came across in the book you studied.

[@blzKrg]

Urgent question! What exactly does it mean to say "crystal system?" Are we classifying crystals or unit cells? Some books say there are 7 types of unit cells and some others say there are 7 types of crystal systems and i can't figure out the difference.

[@rajeshprasadlectures]

We are classifying crystals based on whether they possess certain characteristic rotational and reflection symmetry. Thus if the crystal has four three-fold axes it will be said to belong to the cubic crystal system. If the crystal has this symmetry it is also possible to select a conventional unit cell in the shape of a cube. The definition of the crystal system should be based on symmetry and not unit cell shape. There are two reasons for this: 1. If the crystal has cubic symmetry, then as stated above, a conventional unit cell in the shape of a cube can always be selected. One can also select a different unit cell that is not cubic. Even if we select a non cubic unit cell the crystal system remains cubic because of it symmetry. We are concerned with the symmetry of the entire crystal and not a particular unit cell. An interesting example is a selection of a primitive rhombohedral unit cell in an FCC lattice: kzbin.info/www/bejne/aZDHqmucrMR0rZY 2. Reverse is also possible. Sometimes, accidentally one may select a unit cell that is cubic in shape but the crystal does not have the cubic symmetry. An example is provided by a base-centered (or end-centered cubic) lattice. Despite the cubic unit cell the lattice produced does not have cubic symmetry. So the crystal system is not cubic but tetragonal.kzbin.info/www/bejne/h6ubgpWIismCbtU Thus in summary, 7 crystal systems are classification of crystals on the basis of symmetry and not unit cell shapes.

[@blzKrg]

@@rajeshprasadlectures thank you so much professor! I've been confused about this topic for really long.

[@sayantanbhattacharya8794]

Sir,I am searching for an answer that why are there only 7 crystal systems ?

[@rajeshprasad101]

A difficult question to answer.

[@pranitudanshive5121]

Mathematically, in 3-D ,we cannot have any other periodic arrangement of atoms or molecules different than these 7 crystal systems.

[@alijutt3675]

Amazing way of teaching. Well, I have a question, crystal system is basically a method of classifying a crystalline substance on the basis of its unit cell. so when we say we have 7 crystal systems, does it mean we have only 7 types of unit cell periodicity? and in the previous video, you told that we may have infinity unit cells.

[@rajeshprasad101]

7 crystal systems are not seven kind of unit cells, although that is how it is usually presented. It seven different types of rotational/reflection symmetry which a lattice can have.

[@blzKrg]

Yes, we can have infinite unit cells in a lattice, however in this video he uses the word "conventional" unit cell as in the unit cell that is most appropriate.

[@akshayzade3153]

At 19:00 in lecture, rather than considering all edge centered in Simple cubic, if we consider only 1 set of parallel faces as edge centered then is that lattice structure possible ? Also as its possible that length of unit cell can vary in all three directions a,b,c. We can say, Its not compulsory to get another lattice point by traveling same distance like you did in lecture at 19:00, please explain..

[@rajeshprasad101]

Is it possible for you to draw a figure?

[@aashrithyellambhatla6331]

Sir, in proving that an edge centered lattice is not possible ,the reason which you have given is not quite convincing for me because if I take a bcc lattice then according to your explanation the corner lattice points and the center lattice point are not equivalent even though we are saying this lattice is possible. Can you please explain it for me sir?

[@introductiontomaterialsscience]

In BCC the lattice point is at the centre of the cube. This is allowed. What is not allowed are lattice points at the centre of the edges of the cube.

[@blzKrg]

All points in the corner are at the same distance from the body center point so it doesn't violate the definition of a lattice.

[@Upgradezz]

The real issue is why only 7 crystal system and why only 14 bravais lattices

[@BC-yr6eg]

👍🏻👍🏻👍🏻👍🏻👍🏻👍🏻

[@amanbhati8465]

Rajesh sir moj kaar de

[@sahilgajbhiye0656]

ty very much sir

[@saritasatua3267]

Thanku sir

[@muzammilhussain9805]

Ty sir

[@serialscindy]

What steps are required to mathematically prove that there are only 7 crystal systems?

[@rajeshprasad101]

You have asked a hard question. This is something I have not yet figured out!

[@Upgradezz]

@@rajeshprasad101 really?

[@introductiontomaterialsscience]

@@VijendraSingh-hc5ky I think what you say has some truth in it in the sense that classification into 7 system is not totally mathematical but there is an element of convention in it. There are 32 point groups of crystals. This is a purely mathematical result. But the classification of these point groups into crystal systems involves some arbitrary convention.

[@cokedupnormies2651]

Can a unit cell be triangular?

[@rajeshprasad101]

In our definition of unit cell it should be a region which can tile the space by translations. Triangle cannot do it by translations. So we cannot select a triangle as a unit cell.

[@staycalmandgetsuccess8743]

@@rajeshprasad101 sir please explain simply . I am not getting the answer. I think triangular lattice is possible but triangular crystal is not possible.correct me if i am wrong

[@staycalmandgetsuccess8743]

@@rajeshprasad101 is this 7 systems are derived or we have found that practically?

[@blzKrg]

@@staycalmandgetsuccess8743 triangular lattice might be possible but triangular unit cell isn't possible because a unit cell has to tile all of space by only "translations" but we need to rotate a triangle to make a lattice. Try it at home by making a simple lattice and trying to cover all of it by just translating a triangle.

[@saikalyan9184]

Watching in 1.25x speed, saves the time

[@adarshshrivastav7552]

i m doing so in 2x ....lol

[@amanrajput574]

2x...saves more😅