[Pw_forum] About F_QHA.x

Tue May 25 15:29:55 CEST 2010

Dear Prof. Eyvaz Isaev

Thank your explanations!

On Tue, 25 May 2010 04:26:33 +0530  wrote
>Hi,
> One can see there is excellent agreement with the experimental data. >So, the conversion prescribed in F_QHA.f90 is correct. Please check >again experimental data for Si (may be it is in cal/mol/K?).

> You can note that 4.6966*1.985=9.32 cal/mol/K, not too far from >experimental data you provided C_v(300K)=9.789. Besides, may be >experimental value is C_p, but not C_v.

I would like to correct a mistake in last post, for Si,  C (298 K) = 19.789 J.mol^{-1}.K^{-1} (and not 9.789 J.mol^{-1}.K^{-1} ) (Sorry for it.)

For Si, C_p - C_v < 0.004 (Ref.:Flubacher et.al, Phil Mag, 4: 39, 273 — 294)

Also, from PRB, 50, 14587, C_v {~300} ~ 20 J.mol^{-1}.K^{-1}

Regards
Amit N. Harode

Well, let me add that I have found experimental C_v for Al (Phys. Rev. 162, 549). From Table II CV(300K)=22.91(J/mol/K) and C_v(500K)=24.23(J/mol/K)

>From phonon calculations: C_v(300K)=2.7491(R)� and C_v(500K)=2.9065 (R)

>From F_QHA.f90: from R to J/(mol K) multiply C_v by 8.314

Doing this, one gets (from calculated):

C_v(300K)=2.7491*8.314=22.856 J/mol/K, C_v(500K)=24.164 J/mol/K

By the way, you have mistaken. 3N in F_QHA.f90 refers to the total number of phonon modes and has no commons with "mol" unit. 

Bests,

Eyvaz.

P.S. In Kittel's textbook provided C_p is about 4.7 cal/mol/K (most likely per atom) Introduction to solid state physics (1996); Fig.5.8

-------------------------------------------------------------------

Prof. Eyvaz Isaev, 

Department of Physics, Chemistry, and Biology (IFM), Linkoping University, Sweden 

Theoretical Physics Department, Moscow State Institute of Steel & Alloys, Russia, 

isaev at ifm.liu.se, eyvaz_isaev at yahoo.com

--- On Mon, 5/24/10, Yamit  wrote:

From: Yamit 

Subject: Re: [Pw_forum] About F_QHA.x

To: pw_forum at pwscf.org

Date: Monday, May 24, 2010, 6:28 PM

Dear Prof Nicola Marzari

Thank you for your reply! The phonon values from this work are in good agreement (with error of ~1-2 %) with the values reported in Giannozzi, PRB 43-7231-1991.

=====================================================

Table :(Frequency in cm^{-1},)

- & Current work & PRB 43-7231-1991 

Gamma_{TO/LO} & 525.350461 & 517 

L_{TA} & 109 & 111 

L_{LA} & 379 & 378 

=========================================================

As the output of "F_QHA.x", I have obtained the following results, (in QHA.out file)

############################################################################################################

# T in K, F_vib in Ry/cell, C_v in R (the universal gas constant by 3N modes), S in k_B

############################################################################################################

# T E_internal F_vibration Specific heat (C_v) Entropy

############################################################################################################

:

:

295.00 0.0139740852 0.0055747646 4.6621714979 4.4956255367

300.00 0.0141222695 0.0054311560 4.6966380876 4.5742737931

305.00 0.0142715257 0.0052850687 4.7298757363 4.6521815403

310.00 0.0144218157 0.0051365259 4.7619351485 4.7293532915

:

:

:

############################################################################################################

>From the above results, at 300 K:

4.6966380876 * 8.314 = 39.048

(where, Gas constant, R = 8.314 J/(mol K) ) and for Silicon N = 2, so 3N=6 modes

So, Specific heat, C_v= 38.761 / 3N = 6.5080 J/(mol K)

Experimentally the Specific heat, C_v of Si at 25 °C (~298) is found equal to 9.789 J·mol−1·K−1.

Can anybody could explain the reason behind this huge error in the calculation of specific heat ?

Regards

Amit N.Harode

CR Labs INDIA

> Try to compare your calculated phonons and phonon DOS for Si first - > do they

> come out as obtained e.g. by Giannozzi/De Gironcoli/Pavone/Baroni > PRB 1991 ?

> nicola

On Mon, 24 May 2010 18:38:31 +0530� wrote

>Dear All

>

>

I have attempted to calculate the specific heat of Si using "F_QHA.x", and the calculated Silicon phonon dos� as an input.

>

(The calculated Si phonon frequencies are in excellent agreement with available experimental data. )

>

>

As the output of "F_QHA.x", I have obtained the following results, (in QHA.out file)

>

>

############################################################################################################

>

>

# T in K, F_vib in Ry/cell, C_v in R (the universal gas constant by 3N modes), S in k_B

>

############################################################################################################

>

#� �� T� � � � �� E_internal� � � � F_vibration� � � � � Specific heat (C_v)� � � �� Entropy

>

############################################################################################################

>

:

>

:

>

� 295.00� � � 0.0139740852� � � 0.0055747646� � � � � �� 4.6621714979� � � � � 4.4956255367

>

 300.00� � � 0.0141222695� � � 0.0054311560� � � � � �� 4.6966380876� � � � � 4.5742737931

>

 305.00� � � 0.0142715257� � � 0.0052850687� � � � � �� 4.7298757363� � � � � 4.6521815403

>

 310.00� � � 0.0144218157� � � 0.0051365259� � � � � �� 4.7619351485� � � � � 4.7293532915

>

:

>

:

>

:

>

############################################################################################################

>

>

>From the above results, at 300 K:

>

>

4.6966380876� * 8.314 = 39.048

>

(where, Gas constant, R = 8.314 J/(mol K) ) and for Silicon N = 2, so 3N=6 modes

>

>

So, Specific heat, C_v= 38.761 / 3N = 6.5080� J/(mol K)

>

>

Experimentally the Specific heat, C_v of Si at 25 °C (~298) is found equal to 9.789 J·mol−1·K−1. 

>

>

Can anybody could explain the reason behind this huge error in the calculation of specific heat ?

>

>

Warm Regards

>

Amit N. Harode

>

C R Labs INDIA

>

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