### Re: [SIESTA-L] [*] Re: [SIESTA-L] [*] Re: [SIESTA-L] question about elastic constant

bipul, you are absolutely right...to get 3 elastic constants you have to do 3 calculations for 3 different strainsas you have written. s.auluck > Respected Sir, > Sorry for so many queries. > > In the paper of S Q Wang et al. J Phys. Cond. Matter 15 (2003) 5307, > He uses three types of strains > > 1. Tri-axial shear strain to calculate C44 > 2. volume conservative orthorombic strain to calculate shear modulus C` > and > 3. Hydrostatic pressure to calculate Bulk modulus. > > In my calculations, on applying the 3rd strain, I am getting different > volumes (Volume non-conserve) and 1st & 2nd type volume remain conserve. > > > Because in order to calculate 3 elastic constants (C11, C12 and C44) we > require 3 equations, so do I have to use the above three equations, both > type (volume conservative and non-conservative) to calculate a single set > of elastic constants? > > > > > > Bipul Rakshit > > PhD in Physics > > Computational Research Lab. > > Barkatullah University, > > Bhopal 462 026, India > > Mob.: +919713445650 > > --- On Wed, 15/7/09, Sushil Auluck wrote: > > From: Sushil Auluck > Subject: Re: [*] Re: [SIESTA-L] question about elastic constant > To: "bipul rakshit" > Date: Wednesday, 15 July, 2009, 8:56 PM > > bipul, > you can have 2 kinds of strains...volume conserving > and volume non conserving...each gives different > elastic constants. > s.auluck > >> Dear Sir, >> I have one more doubt, that, if I calculate the set of lattice vector, >> applying the following strains >> ÃÂ ÃÂ e = (ÃÂ´, ÃÂ´, (1 + ÃÂ´)^ (Ã¢Ëâ2)ÃÂ Ã¢Ëâ 1, 0, 0, 0) >> >> as given in the paper attached with this mail, >> >> then the cell volume was not remain constant for all the lattice >> vectors. >> Means for different lattice vectors, the cell volume changes. >> >> But for other two set of strains >> e = (0, 0, 0, ÃÂ´, ÃÂ´, ÃÂ´) >> and e =(ÃÂ´, ÃÂ´, ÃÂ´, 0, 0, 0) >> the cell volume doesnt change for all the lattice vector. >> >> So is it the correct method I am applying? Or there should be no change >> of >> cell volume? >> >> ÃÂ delta E/VÃÂ = 6*C*ÃÂ´^2 + O(ÃÂ´^3 >> ).ÃÂ ÃÂ ÃÂ ÃÂ ÃÂ ÃÂ ÃÂ ÃÂ ÃÂ ÃÂ ÃÂ ÃÂ ÃÂ ÃÂ ÃÂ ÃÂ ÃÂ ÃÂ ÃÂ ÃÂ ÃÂ ÃÂ ÃÂ ÃÂ >> (7) >> V >> >> >> Bipul Rakshit >> >> PhD in Physics >> >> Computational Research Lab. >> >> Barkatullah University, >> >> Bhopal 462 026, India >> >> Mob.: +919713445650 >> >> --- On Wed, 15/7/09, Sushil Auluck wrote: >> >> From: Sushil Auluck >> Subject: Re: [*]Â Re: [SIESTA-L] question about elastic constant >> To: bipu...@yahoo.co.in >> Date: Wednesday, 15 July, 2009, 7:01 PM >> >> bipul, >> if you look at the derivation you will find terms like (1+d)**(1/2) >> or (1+d)**(1/3)d is delta.so when you expand using binomial >> theorem you will terms linear in d, quadratic in d, and cubic in d... >> in this context the series is terminated after the quadratic and so >> the remaining terms ( these are niglected) are order d**3. >> s.auluck >> >>> Respected Sushil Auluck, >>> Thanks for your kind reply. As you said that the term means of order >>> delta >>> cube. >>> But I just want to know the equation of that term. Means how that order >>> delta cube, mathematically looks like. I asked this because, using that >>> equation, I have to find the elastic constants. >>> regards >>> >>> Bipul Rakshit >>> >>> PhD in Physics >>> >>> Computational Research Lab. >>> >>> Barkatullah University, >>> >>> Bhopal 462 026, India >>> >>> Mob.: +919713445650 >>> >>> --- On Mon, 13/7/09, Sushil Auluck wrote: >>> >>> From: Sushil Auluck >>> Subject: Re: [SIESTA-L] question about elastic constant >>> To: SIESTA-L@listserv.uam.es >>> Date: Monday, 13 July, 2009, 9:48 PM >>> >>> hi, >>> that means terms of order delta cubed (delta**3).. >>> s.auluck >>> >>>> DearÃâÃÂ Siesta Users, >>>> I have read the paper >>>> "S. Q. Wang, H. Q. Ye, J. Phys.: Condens. Matter 15 (2003) p. 5307." >>>> ÃâÃÂ >>>> Most of the thing is clear to me, except in Equation (7) what is >>>> "O(ÃÅ½ÃÂ´^3)" >>>> ? What does 'O' here. >>>> >>>> >>>>

### Re: [SIESTA-L] [*] Re: [SIESTA-L] question about elastic constant

Respected Sir, Sorry for so many queries. In the paper of S Q Wang et al. J Phys. Cond. Matter 15 (2003) 5307, He uses three types of strains 1. Tri-axial shear strain to calculate C44 2. volume conservative orthorombic strain to calculate shear modulus C` and 3. Hydrostatic pressure to calculate Bulk modulus. In my calculations, on applying the 3rd strain, I am getting different volumes (Volume non-conserve) and 1st & 2nd type volume remain conserve. Because in order to calculate 3 elastic constants (C11, C12 and C44) we require 3 equations, so do I have to use the above three equations, both type (volume conservative and non-conservative) to calculate a single set of elastic constants? Bipul Rakshit PhD in Physics Computational Research Lab. Barkatullah University, Bhopal 462 026, India Mob.: +919713445650 --- On Wed, 15/7/09, Sushil Auluck wrote: From: Sushil Auluck Subject: Re: [*] Re: [SIESTA-L] question about elastic constant To: "bipul rakshit" Date: Wednesday, 15 July, 2009, 8:56 PM bipul, you can have 2 kinds of strains...volume conserving and volume non conserving...each gives different elastic constants. s.auluck > Dear Sir, > I have one more doubt, that, if I calculate the set of lattice vector, > applying the following strains > Â Â e = (Î´, Î´, (1 + Î´)^ (âˆ’2)Â âˆ’ 1, 0, 0, 0) > > as given in the paper attached with this mail, > > then the cell volume was not remain constant for all the lattice vectors. > Means for different lattice vectors, the cell volume changes. > > But for other two set of strains > e = (0, 0, 0, Î´, Î´, Î´) > and e =(Î´, Î´, Î´, 0, 0, 0) > the cell volume doesnt change for all the lattice vector. > > So is it the correct method I am applying? Or there should be no change of > cell volume? > > Â delta E/VÂ = 6*C*Î´^2 + O(Î´^3 > ).Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â (7) > V > > > Bipul Rakshit > > PhD in Physics > > Computational Research Lab. > > Barkatullah University, > > Bhopal 462 026, India > > Mob.: +919713445650 > > --- On Wed, 15/7/09, Sushil Auluck wrote: > > From: Sushil Auluck > Subject: Re: [*] Re: [SIESTA-L] question about elastic constant > To: bipu...@yahoo.co.in > Date: Wednesday, 15 July, 2009, 7:01 PM > > bipul, > if you look at the derivation you will find terms like (1+d)**(1/2) > or (1+d)**(1/3)d is delta.so when you expand using binomial > theorem you will terms linear in d, quadratic in d, and cubic in d... > in this context the series is terminated after the quadratic and so > the remaining terms ( these are niglected) are order d**3. > s.auluck > >> Respected Sushil Auluck, >> Thanks for your kind reply. As you said that the term means of order >> delta >> cube. >> But I just want to know the equation of that term. Means how that order >> delta cube, mathematically looks like. I asked this because, using that >> equation, I have to find the elastic constants. >> regards >> >> Bipul Rakshit >> >> PhD in Physics >> >> Computational Research Lab. >> >> Barkatullah University, >> >> Bhopal 462 026, India >> >> Mob.: +919713445650 >> >> --- On Mon, 13/7/09, Sushil Auluck wrote: >> >> From: Sushil Auluck >> Subject: Re: [SIESTA-L] question about elastic constant >> To: SIESTA-L@listserv.uam.es >> Date: Monday, 13 July, 2009, 9:48 PM >> >> hi, >> that means terms of order delta cubed (delta**3).. >> s.auluck >> >>> DearÃ‚Â Siesta Users, >>> I have read the paper >>> "S. Q. Wang, H. Q. Ye, J. Phys.: Condens. Matter 15 (2003) p. 5307." >>> Ã‚Â >>> Most of the thing is clear to me, except in Equation (7) what is >>> "O(ÃŽÂ´^3)" >>> ? What does 'O' here. >>> >>> >>> Please guide me for the same. >>> >>> >>> Bipul Rakshit >>> >>> PhD in Physics >>> >>> Computational Research Lab. >>> >>> Barkatullah University, >>> >>> Bhopal 462 026, India >>> >>> Mob.: +919713445650 >>> >>> >>>Â Â Â Â Â See the Web's breaking stories, chosen by people like you.. >>> Check >>> out Yahoo! Buzz. http://in.buzz.yahoo.com/ >> >> >> >> Prof. Sushil AuluckÂ Â Â Â Â Â Â Â Â Â Â >> Phone:+91-512-6797092/6148 >> Department of PhysicsÂ Â Â Â Â Â Â Â Â Â Â Â Â >

### Re: [SIESTA-L] question about elastic constant

I did not read the paper, but O(delta^3) term should be the omitted term in series expansion, and it looks like Const delta^3. To recover the value of the constant, one should repeat the derivation of equation and keep the next order term. Valentin. bipul rakshit wrote: > Respected Sushil Auluck, > Thanks for your kind reply. As you said that the term means of order delta cube. > But I just want to know the equation of that term. Means how that order delta cube, mathematically looks like. I asked this because, using that equation, I have to find the elastic constants. > regards > > Bipul Rakshit > PhD in Physics > Computational Research Lab. > Barkatullah University, > Bhopal 462 026, India > Mob.: +919713445650 > > --- On Mon, 13/7/09, Sushil Auluck wrote: > > > From: Sushil Auluck > Subject: Re: [SIESTA-L] question about elastic constant > To: SIESTA-L@listserv.uam.es > Date: Monday, 13 July, 2009, 9:48 PM > > hi, > that means terms of order delta cubed (delta**3).. > s.auluck > > > Dear Siesta Users, > > I have read the paper > > "S. Q. Wang, H. Q. Ye, J. Phys.: Condens. Matter 15 (2003) p. 5307." > > > > Most of the thing is clear to me, except in Equation (7) what is "O(^3)" > > ? What does 'O' here. > > > > > > Please guide me for the same. > > > > > > Bipul Rakshit > > > > PhD in Physics > > > > Computational Research Lab. > > > > Barkatullah University, > > > > Bhopal 462 026, India > > > > Mob.: +919713445650 > > > > > > See the Web's breaking stories, chosen by people like you. Check > > out Yahoo! Buzz. http://in.buzz.yahoo.com/ > > > > Prof. Sushil Auluck Phone:+91-512-6797092/6148 > Department of Physics +91-512-6798177(Home) > Indian Institute of Technology Cell :+91-9305548667 > Kanpur 208016 (UP) Fax :+91-512-6790914 > IndiaE-mail:saul...@iitk.ac.in > ...:saul...@gmail.com > http://www.iitk.ac.in/phy/People/phy_facvis.html > http://www.iitk.ac.in/phy/New01/profile_SA.html > ... > ~ > > > See the Web's breaking stories, chosen by people like you. Check out Yahoo! Buzz. -- Valentin V. Karassev __ University of Florida Quantum Theory Project 2300 NPB #92 P.O. Box 118435 Gainesville, FL, 32611-8435 tel: (352)870-2453 fax: (352)392-8722 __ C. Quimica, IVIC tel/fax: 58(212)504-1356 web: http://www.ivic.ve/quimica/fqteorica/

### Re: [SIESTA-L] question about elastic constant

In mathematical notation, this implies that "Terms O(d^3) will always be small compared to terms O(d^2) and O(d) for sufficiently small d". What's "sufficiently small" has to be determined on a case to case basis, but once you have checked that, it means "we know that there are more terms, but we can neglect them because they are O(d^3) and d is small". Herbert bipul rakshit wrote: Respected Sushil Auluck, Thanks for your kind reply. As you said that the term means of order delta cube. But I just want to know the equation of that term. Means how that order delta cube, mathematically looks like. I asked this because, using that equation, I have to find the elastic constants. regards Bipul Rakshit PhD in Physics Computational Research Lab. Barkatullah University, Bhopal 462 026, India Mob.: +919713445650 --- On *Mon, 13/7/09, Sushil Auluck //* wrote: From: Sushil Auluck Subject: Re: [SIESTA-L] question about elastic constant To: SIESTA-L@listserv.uam.es Date: Monday, 13 July, 2009, 9:48 PM hi, that means terms of order delta cubed (delta**3).. s.auluck > DearÂ Siesta Users, > I have read the paper > "S. Q. Wang, H. Q. Ye, J. Phys.: Condens. Matter 15 (2003) p. 5307." > Â > Most of the thing is clear to me, except in Equation (7) what is "O(Î´^3)" > ? What does 'O' here. > > > Please guide me for the same. > > > Bipul Rakshit > > PhD in Physics > > Computational Research Lab. > > Barkatullah University, > > Bhopal 462 026, India > > Mob.: +919713445650 > > > See the Web's breaking stories, chosen by people like you. Check > out Yahoo! Buzz. http://in.buzz.yahoo.com/ Prof. Sushil Auluck Phone:+91-512-6797092/6148 Department of Physics +91-512-6798177(Home) Indian Institute of Technology Cell :+91-9305548667 Kanpur 208016 (UP) Fax :+91-512-6790914 IndiaE-mail:saul...@iitk.ac.in ...:saul...@gmail.com http://www.iitk.ac.in/phy/People/phy_facvis.html http://www.iitk.ac.in/phy/New01/profile_SA.html ... ~ See the Web's breaking stories, chosen by people like you. Check out Yahoo! Buzz <http://in.rd.yahoo.com/tagline_buzz_1/*http://in.buzz.yahoo.com/>. -- Herbert Fruchtl Senior Scientific Computing Officer School of Chemistry, School of Mathematics and Statistics University of St Andrews -- The University of St Andrews is a charity registered in Scotland: No SC013532

### Re: [SIESTA-L] question about elastic constant

Respected Sushil Auluck, Thanks for your kind reply. As you said that the term means of order delta cube. But I just want to know the equation of that term. Means how that order delta cube, mathematically looks like. I asked this because, using that equation, I have to find the elastic constants. regards Bipul Rakshit PhD in Physics Computational Research Lab. Barkatullah University, Bhopal 462 026, India Mob.: +919713445650 --- On Mon, 13/7/09, Sushil Auluck wrote: From: Sushil Auluck Subject: Re: [SIESTA-L] question about elastic constant To: SIESTA-L@listserv.uam.es Date: Monday, 13 July, 2009, 9:48 PM hi, that means terms of order delta cubed (delta**3).. s.auluck > DearÂ Siesta Users, > I have read the paper > "S. Q. Wang, H. Q. Ye, J. Phys.: Condens. Matter 15 (2003) p. 5307." > Â > Most of the thing is clear to me, except in Equation (7) what is "O(Î´^3)" > ? What does 'O' here. > > > Please guide me for the same. > > > Bipul Rakshit > > PhD in Physics > > Computational Research Lab. > > Barkatullah University, > > Bhopal 462 026, India > > Mob.: +919713445650 > > > See the Web's breaking stories, chosen by people like you.. Check > out Yahoo! Buzz. http://in.buzz.yahoo.com/ Prof. Sushil Auluck Phone:+91-512-6797092/6148 Department of Physics +91-512-6798177(Home) Indian Institute of Technology Cell :+91-9305548667 Kanpur 208016 (UP) Fax :+91-512-6790914 India E-mail:saul...@iitk.ac.in ...:saul...@gmail.com http://www.iitk.ac.in/phy/People/phy_facvis.html http://www.iitk.ac.in/phy/New01/profile_SA.html ~ See the Web's breaking stories, chosen by people like you. Check out Yahoo! Buzz. http://in.buzz.yahoo.com/

### Re: [SIESTA-L] question about elastic constant

The simbol is "big O" notation. Shortly it means that the term O(x) has the same order as "x", in the case below, the same ordrer as \delta^3. Valentin. P.S. see also: http://en.wikipedia.org/wiki/Big_O_notation bipul rakshit wrote: > > Dear Siesta Users, > > I have read the paper > "S. Q. Wang, H. Q. Ye, J. Phys.: Condens. Matter 15 (2003) p. 5307." > > > > Most of the thing is clear to me, except in Equation (7) what is "O(^3)" ? What does 'O' here. > > > Please guide me for the same. > > > Bipul Rakshit > PhD in Physics > Computational Research Lab. > Barkatullah University, > Bhopal 462 026, India > Mob..: +919713445650 > > Yahoo! recommends that you upgrade to the new and safer Internet Explorer 8.

### Re: [SIESTA-L] question about elastic constant

hi, that means terms of order delta cubed (delta**3).. s.auluck > DearÂ Siesta Users, > I have read the paper > "S. Q. Wang, H. Q. Ye, J. Phys.: Condens. Matter 15 (2003) p. 5307." > Â > Most of the thing is clear to me, except in Equation (7) what is "O(Î´^3)" > ? What does 'O' here. > > > Please guide me for the same. > > > Bipul Rakshit > > PhD in Physics > > Computational Research Lab. > > Barkatullah University, > > Bhopal 462 026, India > > Mob.: +919713445650 > > > See the Web's breaking stories, chosen by people like you. Check > out Yahoo! Buzz. http://in.buzz.yahoo.com/ ... Prof. Sushil Auluck Phone:+91-512-6797092/6148 Department of Physics +91-512-6798177(Home) Indian Institute of Technology Cell :+91-9305548667 Kanpur 208016 (UP) Fax :+91-512-6790914 IndiaE-mail:saul...@iitk.ac.in ...:saul...@gmail.com http://www.iitk.ac.in/phy/People/phy_facvis.html http://www.iitk.ac.in/phy/New01/profile_SA.html ... ~