[Pw_forum] About F_QHA.x

[Yamit]

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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