Physica B 352 (2004) 164–171 Analysis of a P–V–T relationship for MgO Vivek Singh, A.K. Gautam, K.S. Singh à Department of Physics, R.B.S. College, Agra 282002, India Received 27 November 2003; received in revised form 1 July 2004; accepted 10 July 2004 Abstract In the present paper we have studied the pressure–volume–temperature (P–V–T) relationship for MgO under high pressures and at high temperatures. We have used the basic thermodynamic formulation and a numerical method for evaluating the thermal pressure for MgO starting from room temperature (T=300K) up to its melting temperature (TC3000K). The volume–temperature relationships under isobaric conditions have been obtained and compared with the available experimental data based on density measurements. We make use of some important phenomenological forms of the equation of state such as (1) the Birch–Murnaghan EOS, (2) the Rydberg–Vinet EOS and (3) the Shanker EOS. Finally, we have determined the P–V–T relationshipforMgOinthetemperaturerange300–3000Kforpressures upto224GPa.Theresultsobtainedinthepresentstudyareingoodagreementwiththeavailableexperimentaldatafor predicting the pressure–volume relationship along different isotherms at selected temperatures. r 2004 Elsevier B.V. All rights reserved. Keywords: Thermal pressure; P–V–T relationship; MgO; High temperature; High pressure 1. Introduction Thermoelastic and thermodynamic properties such as thermal expansivity, bulk modulus, Gru¨neisen parameter, Anderson–Gru¨neisen para- meter and thermal pressure are of central im- portanceforunderstandingthebehaviourofsolids under high pressures and at high temperatures [1–4].Theinvestigationofthesepropertiesisbased on the Pressure–Volume–Temperature (P–V–T) relationship referred to as an equation of state (EOS) [5]. The importance of the P–V–T relation- ship lies in the fact that pressure and volume at constant temperature determine the isothermal bulk modulus K T [K T =–V (qP/qV) T ] and that volume and temperature at constant pressure determine the thermal expansivity a[a=(1/V) (qV/qT) P ]. MgO is an important geophysical mineral and ceramic material widely studied by theoretical [1–3] as well as experimental workers [4,6–8]. In the present paper we develop a simple method for ARTICLE IN PRESS www.elsevier.com/locate/physb 0921-4526/$-see front matter r 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2004.07.006 à Corresponding author. Tel.: +91-562-2520179; fax:+91- 562-2151288. E-mail address: kshanker1@rediffmail.com (K.S. Singh).