### Abstract

We have investigated the structural phase stability of crystalline alkali metals under external pressure in terms of their pair potentials, structural free energies, thermomechanical properties viz. the elastic constants and the density-of-sates [DOS] at the Fermi level. The pair potentials are calculated using amenable model potentials, the structural energies and the elastic constants are calculated in terms of the effective pair potentials and the DOS for the systems are calculated by employing the augmented-spherical-waves [ASW] method. The matching between the minima of the pair potentials and the relative positions of the first few lattice vectors of the relevant structures gives a qualitative impression on the relative stability of a crystal phase. Similarly the appearance of a minimum in the energy difference curves between relevant crystal structures manifests a relatively stable structure. On the contrary, a maximum in the bulk modulus indicates a stable structure; these maximum-minimum criteria are controlled by the profile of the effective pair interactions of the constituent atoms. If the relevant lattice vectors are populated in and around the minimum of the respective pair potential the corresponding bulk modulus shows a maximum trend. The same situation gives rise to a minimum in the free energy. Both of these tendencies favor a particular crystalline phase against other relevant structures. Similarly a maximum in the DOS curves gives rise to a minimum in the energy curve manifesting a stable structure. The population of electronic states plays the responsible role here. To treat the two entirely different methods, namely, the perturbative pseudopotential theory and the non-perturbative ASW method on the same footing, we have used the same metallic density in both the methods for the respective element. The calculated results show a qualitative trend in support of the observed structures for these elemental systems.

Original language | English |
---|---|

Pages (from-to) | 4847-4864 |

Number of pages | 18 |

Journal | International Journal of Modern Physics B |

Volume | 16 |

Issue number | 32 |

DOIs | |

Publication status | Published - Dec 20 2002 |

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### ASJC Scopus subject areas

- Electronic, Optical and Magnetic Materials
- Mathematical Physics
- Physics and Astronomy (miscellaneous)
- Condensed Matter Physics
- Statistical and Nonlinear Physics

### Cite this

*International Journal of Modern Physics B*,

*16*(32), 4847-4864. https://doi.org/10.1142/S0217979202015017

**Phase stability of alkali metals under pressure : Perturbative and non-perturbative treatments.** / Mujibur Rahman, S. M.; Ali, Issam; Bhuiyan, G. M.; Ziauddin Ahmed, A. Z.

Research output: Contribution to journal › Article

*International Journal of Modern Physics B*, vol. 16, no. 32, pp. 4847-4864. https://doi.org/10.1142/S0217979202015017

}

TY - JOUR

T1 - Phase stability of alkali metals under pressure

T2 - Perturbative and non-perturbative treatments

AU - Mujibur Rahman, S. M.

AU - Ali, Issam

AU - Bhuiyan, G. M.

AU - Ziauddin Ahmed, A. Z.

PY - 2002/12/20

Y1 - 2002/12/20

N2 - We have investigated the structural phase stability of crystalline alkali metals under external pressure in terms of their pair potentials, structural free energies, thermomechanical properties viz. the elastic constants and the density-of-sates [DOS] at the Fermi level. The pair potentials are calculated using amenable model potentials, the structural energies and the elastic constants are calculated in terms of the effective pair potentials and the DOS for the systems are calculated by employing the augmented-spherical-waves [ASW] method. The matching between the minima of the pair potentials and the relative positions of the first few lattice vectors of the relevant structures gives a qualitative impression on the relative stability of a crystal phase. Similarly the appearance of a minimum in the energy difference curves between relevant crystal structures manifests a relatively stable structure. On the contrary, a maximum in the bulk modulus indicates a stable structure; these maximum-minimum criteria are controlled by the profile of the effective pair interactions of the constituent atoms. If the relevant lattice vectors are populated in and around the minimum of the respective pair potential the corresponding bulk modulus shows a maximum trend. The same situation gives rise to a minimum in the free energy. Both of these tendencies favor a particular crystalline phase against other relevant structures. Similarly a maximum in the DOS curves gives rise to a minimum in the energy curve manifesting a stable structure. The population of electronic states plays the responsible role here. To treat the two entirely different methods, namely, the perturbative pseudopotential theory and the non-perturbative ASW method on the same footing, we have used the same metallic density in both the methods for the respective element. The calculated results show a qualitative trend in support of the observed structures for these elemental systems.

AB - We have investigated the structural phase stability of crystalline alkali metals under external pressure in terms of their pair potentials, structural free energies, thermomechanical properties viz. the elastic constants and the density-of-sates [DOS] at the Fermi level. The pair potentials are calculated using amenable model potentials, the structural energies and the elastic constants are calculated in terms of the effective pair potentials and the DOS for the systems are calculated by employing the augmented-spherical-waves [ASW] method. The matching between the minima of the pair potentials and the relative positions of the first few lattice vectors of the relevant structures gives a qualitative impression on the relative stability of a crystal phase. Similarly the appearance of a minimum in the energy difference curves between relevant crystal structures manifests a relatively stable structure. On the contrary, a maximum in the bulk modulus indicates a stable structure; these maximum-minimum criteria are controlled by the profile of the effective pair interactions of the constituent atoms. If the relevant lattice vectors are populated in and around the minimum of the respective pair potential the corresponding bulk modulus shows a maximum trend. The same situation gives rise to a minimum in the free energy. Both of these tendencies favor a particular crystalline phase against other relevant structures. Similarly a maximum in the DOS curves gives rise to a minimum in the energy curve manifesting a stable structure. The population of electronic states plays the responsible role here. To treat the two entirely different methods, namely, the perturbative pseudopotential theory and the non-perturbative ASW method on the same footing, we have used the same metallic density in both the methods for the respective element. The calculated results show a qualitative trend in support of the observed structures for these elemental systems.

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U2 - 10.1142/S0217979202015017

DO - 10.1142/S0217979202015017

M3 - Article

VL - 16

SP - 4847

EP - 4864

JO - International Journal of Modern Physics B

JF - International Journal of Modern Physics B

SN - 0217-9792

IS - 32

ER -