Classification of lattices on the basis of symmetry

[@Upgradezz]

Mr Dr Rajesh is a nice man. He is humble and honest.

[@arduinotalk8544]

Sir please use some animation to explain.. So that it is easier to understand..

[@jayprakashmaurya281]

Thank you sir for teaching. Nice video

[@blzKrg]

Urgent question again! Why are there 7 point groups? And why do some books show 32 point groups?! Isn't a point group a collection of all point symmetries, so shouldn't there be only 1 point group? How come we have 7 of them and 14 space groups?!!

[@sheen7862]

Sir you clear my concepts thank you .. Ap Genius 😎

[@gilthunder1737]

it was 3 yrs. But still very helpful 💕🤞

[@amritjena3210]

great effort sir ... Clarity of your teaching is amazing ...Sir I have a doubt ....why 4- three fold axis why not 3-four fold or other axis of symmetry for cube... There is no justification in the lecture

[@amritjena3210]

how charcter define symmetry is decided for crystal system ,when it satisfy multiple rotational axis of symmetry

[@introductiontomaterialsscience]

Please see my answer to naga saibabu.

[@amritjena3210]

@@introductiontomaterialsscience thank you sir

[@AnuvabAhmedApurno]

Would have been better if you had explained the 3-fold symmetry with models.

[@SandeepKumar-qv2fd]

Thank you very much sir to help me

[@nagasaibabu4709]

sir ,how you took 4-3 fold symmetry as characteristic symmetry in cubic ?? is there any reason??

[@introductiontomaterialsscience]

There are crystals which have three four-fold axes. These also have four three-fold axes. But there are crystal which have four three-fold axes but do not possess three four-fold axes. Crystallographers wish to classify both these types as cubic. So the common symmetry which is four three-fold axes is taken as the characteristic symmetry for cubic crystals.

[@unfiltered836]

@@introductiontomaterialsscience Respected Sir Can you please elaborate the above answer with some examples? Sir, in case of SC BCC and FCC of cubic crystals all other axes of symmetry are equally applicable then why only four 3-fold axes chooses as characteristic symmetry?

[@rajeshprasadlectures]

@@unfiltered836 You are right. Monatomic SC, BCC and FCC crystals all have complete cubic symmetry. However, as I indicated in my previous answer, there are cubic crystals which lack four-fold axes or mirror planes. In fact, there are five different kinds of cubic symmetry, call five cubic crystal classes or five cubic point groups. Although I have mentioned point groups when classifying lattices intro crystal systems, I haven't gone into these details. These five groups have symbols 23, m3, bar43m, 432 and m3m. All these five groups have four three-fold axes along the body diagonals of the cube. But 23 and m3 do not have four-fold axes. Similarly, 23 and 432 do not have mirror planes. The mineral ullmanite (en.wikipedia.org/wiki/Ullmannite ) has the point group 23. Thus it is cubic but does not possess four-fold symmetry.

[@AnupKumar-wd1ln]

@@rajeshprasadlectures Sir, you mentioned that there are 5 point groups present in cubic lattice but, i have some doubts in the concepts of symmetry in crystallography as i was looking for more details. 1. Does all these 5 point groups are present simultaneously in cubic lattice ( or cubic unit cell). 2. Again ullmannite has point group ‘23’ which belongs to cubic lattice. It means ullmannite is made up of cubic unit cell. So how it is possible that the ullmannite which is made up of cubic unit cell having 5 point groups ( simultaneously if the answer of Q1. is yes) developed into a crystal that has only one point group. Also it is found in nature in the form of cubic, octahedral, or pyritohedral forms. So we see that the same crystal (ulmannite) found in different forms (cubic, octahedral, or pyritohedral) in nature, have single point group ‘23’ out of 5 (as mentioned in cubic lattice), made up of the periodic arrangement of same crystal system( cubic), how it is possible? Or, what determine the point group or crystal class of the particular crystal? Or, how can we know that ulmannite has point group ‘23’ or it belongs to ‘23’ crystal class? 3. Is it possible that same crystal can have more than one point groups( out of 32 point groups which are possible in 3d)?

[@introductiontomaterialsscience]

@@AnupKumar-wd1ln Answers to both 1 and are NO. A given crystal can have only one of the 32 point groups and a given cubic crystal can have only one of the 5 point groups. A given conventional unit cell shape can belong to more than one point groups. This set of point groups is called a crystal system. Thus all the five point groups have the same unit cell shape and are said to belong to the cubic crystal system. 'Cubic, octahedral and pyritohedra'l are names of external shapes the crystal can acquire. This does depend on the point group of the crystal, but not uniquely. A crystal can have different external shapes depending upon the growth conditions etc. Hope this clarifies.

[@yogeskumar8001]

Sir, point symmetry have only rotational and reflection symmetry.. (Except translational symmetry) Moreover, 7 Crystal system comes under the point groups So my question was -;Is this 7 crystal system have translation symmetry or not??

[@introductiontomaterialsscience]

Crystal system is classification of crystals (or space groups) based on point groups (rotational or rotoinversion symmetry). So it does not consider translational syymetry.

[@BC-yr6eg]

👍🏻👍🏻👍🏻👍🏻👍🏻

[@manojn6645]

SIr, what about the other 7 translational symmetries that you have mentioned in the space group?

[@rajeshprasad101]

Please explain your question in a bit more detail.

[@manojn6645]

Sir, @4:48, you mentioned that when all the 7 distinct point symmetries were clubbed with their translational symmetries form the 14 bravias lattices. I couldn't understand, how can a simple cubic lattice translate to form a bcc/fcc cubic lattice.

[@rajeshprasad101]

@@manojn6645 Simple cubic (SC), BCC and FCC all have the same rotational and reflection symmetry. Therefore they belong to the same crystal system. But their translational symmetries are different. In BCC the translation from corner to the centre of the cube is a symmetry translation. This is not so for SC or FCC. Similarly for FCC corner to the centre of a face of the cube is a symmetry translation. This is not so for SC or BCC. Thus translationally they are all different. So they form three different Bravais lattices in the same crystal system.

[@adityapatil2790]

@@rajeshprasad101 Sir, In your next lecture "ssymetry base approach to bravis lattice" At 7.32 min. analysis of 2 fold assymetry axis passing through centre of faces not done for Cubic C?

[@adityapatil2790]

@@rajeshprasad101 Sir, In your next lecture "ssymetry base approach to bravis lattice" At 7.32 min. analysis of 2 fold assymetry axis passing through centre of faces not done for Cubic C?

[@anonymousreviewer3816]

Is inversion symmetry included in the Point group?

[@anonymousreviewer3816]

@Introduction to Materials Science and Engineering

[@rajeshprasadlectures]

Yes.

[@clearheartboy777]

Sir why you didn’t consider inversion symmetry in cubic system or all 7 crystal system. You described the crystal sytem on the basis of just rotational and mirror symmetry

[@introductiontomaterialsscience]

In the discussion of lattice, invasion symmetry is trivial, as all lattices have this symmetry. Thus it cannot be used as a basis for classification.

[@nipunfernando6689]

Thanks ♡♡♡♡♡

[@shubhiagarwal2487]

slow ki bhi had ho gyi ...really iit m esa pdate h

[@introductiontomaterialsscience]

Thanks for your comments. The idea was to keep it slow for clarity. But as you have remarked, I also feel that I have overdone it.

[@alijutt3675]

@@introductiontomaterialsscience sir you are great. pace does not matter. if a person learns it matters. many students are really thankful for you. thanks

[@lakhanlalwelding]

@@introductiontomaterialsscience Ur lectures are just awesome.never learnt this subject with such clear explanations...Thank you.___/\____

[@riteshsingh6757]

tbhi aap jaiso ko iit nhi milta :P

[@franciscol3304]

If you wanna speed up you can easily change the speed on youtube. No big deal