[Wien] Negative strain energy due to isoelectronic substitution

[Oleg Rubel]

Dear Stefaan,

thank you very much for the suggestion. I recalculated GaP taking
Rmt_min*Kmax=7.4 instead of 7.0 [Rmt(P)/Rmt(B)*7.0=7.4]. The new total
energy is Etot(GaP) = -146071.573 Ry, which is less than in case of
Rmt_min*Kmax=7.0, as you expected. Substituting this value in eq. for the
strain energy I obtain Estr = 0.09 Ry. First, it is positive! Second, the
value is close to my expectation (about 0.11 Ry).

Regarding the sigh of the strain energy: I still insist on positive value
of the strain energy. If we could build such an alloy where all bond
lengthes correspond to their equilibrium value for binaries, the total
energy of such a substance would be (1-x)*Etot(GaP) + x*Etot(BP). But in
reality it cannot happen due to the bond stretching. Therefore Etot(GaP:B)
is suspected to be larger than (1-x)*Etot(GaP) + x*Etot(BP).

What about the reference energy, with respect which the total energy is
measured? Am I understand right, it is an average potential? Is it the
same in all cases: GaP:B, GaP, BP? If not, should I take its variation
into account too? Can anyone comment on this issue?

Thank you once again for the valuable suggestions.

Yours,

Oleg Rubel

===========================
Dr. Oleg Rubel
Faculty of Physics
Philipps University Marburg
Renthof 5, 35032 Marburg, Germany
E-mail: Oleg.Rubel at physik.uni-marburg.de

On Mon, 19 Feb 2007, Stefaan Cottenier wrote:

> My first guess would be to suspect your constant RKMax value of 7. Your
> Rmt choices show that for BP it is the B-Rmt that is the smallest one
> (1.75), while for GaP it is the P-Rmt (1.85). If you use
> Rmt_min*Kmax=7.0 for both, your basis set for BP and GaP:B will be
> larger than for GaP. Adapting RKMax for GaP such that a larger basis set
> is used there as well, will lead you to ... an even more negative result.
>
> Anybody comments on the above procedure?
>
> Anyway, this alone isn't going to solve your problem. From the equation
> you give, it is not obvious to me that this should be positive. My naive
> expectation would be that if these two compounds like to mix, this
> equation could lead to a negative value. (?)
>
> Stefaan
>
> >Dear Wien2k users,
> >
> >would you please exchange your experience on calculation of the strain
> >energy (sometimes also called 'formation enthalpy') of an alloy due to
> >isoelectronic substitutional defects.
> >
> >I calculate a 64-atom GaP:B zinc-blend supercell. GaP:B means that one Ga
> >atom is replaced my B atom. I let the supercell keep the equilibrium
> >volume of GaP and relax internal degrees of freedom (atomic positions).
> >Obtained structure I call "relaxed structure". I would like to figure out:
> >What is the strain energy caused by substitutional B atom? For the stain
> >energy I use the following definition [see e.g., Phys. Rev. B 63, 085207
> >(2001)]:
> >
> >Estr = Etot(GaP:B) - (1-x)*Etot(GaP) - x*Etot(BP),
> >
> >where Etot(GaP:B) is the total energy of the relaxed structure, x is the
> >concentration of substitutional atoms (in my case it is 1/32), Etot(GaP)
> >and Etot(BP) are the total energies of 64-atom supercells of binary
> >compounds at their equilibrium lattice constants.
> >
> >At the end I have:
> >Etot(GaP:B) = -142238.0807 Ry
> >Etot(GaP)   = -146071.2169 Ry
> >Etot(BP)    =  -23402.7274 Ry
> >which gives
> >Estr = -0.254 Ry.
> >
> >This result surprises me due to its negative (!) sign. The strain energy
> >should be at least positive. Note: The same approach works fine on PW
> >codes (FHI98md). Maybe the problem is that the reference energy, with
> >respect which the total energy is measured, in Wien2k changes itself from
> >one structure to another? If such, would you please give me a suggestion
> >how to overcome this problem.
> >
> >Thank you in advance.
> >
> >Yours,
> >
> >Oleg Rubel
> >
> >
> >ADDITIONAL INFORMATION: Wien2k version: WIEN2k_06.2 (Release 9/03/2006).
> >Run command ~>min -i 100 -s 10 -j 'run_lapw -p -I -i 40 -fc 1.0 ';
> >minimization method: PORT; LDA; Spin polarization - NO; Rmt(Ga)=1.92 Bohr;
> >Rmt(P)=1.85;  Rmt(B)=1.75; Kmax*Rmt_min = 7; 4x4x4 k-point mesh (shifted);
> >Lmax = 10 (in *.in1c); for the rest parameters I rely on default values.
> >
> >
> >===========================
> >Dr. Oleg Rubel
> >Faculty of Physics
> >Philipps University Marburg
> >Renthof 5, 35032 Marburg, Germany
> >E-mail: Oleg.Rubel at physik.uni-marburg.de
> >
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