Kumari-Dass equation of state: Difference between revisions
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'''Kumari and Dass'''<ref>[http://dx.doi.org/10.1088/0953-8984/2/14/006 M. Kumari and N. Dass "An equation of state applied to sodium chloride and caesium chloride at high pressures and high temperatures", Journal of Physics: Condensed Matter '''2''' pp. 3219-3229 (1009)]</ref><ref>[http://dx.doi.org/10.1088/0953-8984/2/39/003 M. Kumari and N. Dass "An equation of state applied to 50 solids. II", Journal of Physics: Condensed Matter '''2''' pp. 7891-7895 (1990)]</ref> presented a model based on a linear [[Compressibility |bulk modulus]] equation, in the spirit of the [[Murnaghan equation of state]]. The equation of state does not correctly model the bulk modulus as the [[pressure]], <math>p</math>, tends towards infinity, as it remains bounded. This is apparent in the equation relating the bulk modulus to pressure: | |||
:<math>B=B_0+\frac{B_0'}{\lambda}\left(1-e^{-\lambda | :<math>B=B_0+\frac{B_0'}{\lambda}\left(1-e^{-\lambda p}\right)</math> | ||
where <math>B_0</math> is the isothermal bulk modulus, <math>B_0'</math> is the pressure derivative of the bulk modulus and <math>\lambda</math> is a softening parameter for the bulk modulus. This leads to a equation for pressure dependent on these parameters of the form: | where <math>B_0</math> is the isothermal bulk modulus, <math>B_0'</math> is the pressure derivative of the bulk modulus and <math>\lambda</math> is a softening parameter for the bulk modulus. This leads to a equation for pressure dependent on these parameters of the form: | ||
:<math> | :<math>p=\frac{1}{\lambda}\left[\frac{\lambda B_0 \left(V/V_0\right)^{-\lambda B_0 + B_0'}+B_0'}{\lambda B_0 + B_0'}\right]</math> | ||
Latest revision as of 14:00, 14 November 2011
Kumari and Dass[1][2] presented a model based on a linear bulk modulus equation, in the spirit of the Murnaghan equation of state. The equation of state does not correctly model the bulk modulus as the pressure, , tends towards infinity, as it remains bounded. This is apparent in the equation relating the bulk modulus to pressure:
where is the isothermal bulk modulus, is the pressure derivative of the bulk modulus and is a softening parameter for the bulk modulus. This leads to a equation for pressure dependent on these parameters of the form:
![{\displaystyle p={\frac {1}{\lambda }}\left[{\frac {\lambda B_{0}\left(V/V_{0}\right)^{-\lambda B_{0}+B_{0}'}+B_{0}'}{\lambda B_{0}+B_{0}'}}\right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4abbff65eb9ad837c6db8a229dfc3842a39ee491)
References[edit]
- ↑ M. Kumari and N. Dass "An equation of state applied to sodium chloride and caesium chloride at high pressures and high temperatures", Journal of Physics: Condensed Matter 2 pp. 3219-3229 (1009)
- ↑ M. Kumari and N. Dass "An equation of state applied to 50 solids. II", Journal of Physics: Condensed Matter 2 pp. 7891-7895 (1990)