Rapid Research Note

On the Activation Volume for Charge Transportin Carbonate SaltsJ. Turner

1) and M. de Souza

Universidade de Sao Paulo, Departamento de Fisica,Instituto de Fisica e Quimica de Sao Carlos, Caixa Postal 369, 13560 Sao Carlos,SP Brasil

(Received February 5, 2002; accepted February 27, 2002)

Subject classification: 66.10.Ed; 66.30.Dn; S11.1

Calcite (CaCO3), magnesite (MgCO3) and dolomite (CaMg(CO3)2) are trigonal carbonate saltsand constitute the calcite group. The activation volumes for electric charge transport in these mate-rials were obtained from conductivity experiments at various pressure values [1–5]. It was sug-gested recently that a systematic trend of the activation volume with the volume of the unit celloccurs [5]. On the other hand, electrical and dielectric measurements have been reported for theentire set of the calcite type crystals previously [6–13]. The conductivity mechanisms were studiedin detail by using the Thermally Stimulated Depolarization Current (TSDC) spectroscopy. Theanalyses of the TSDC signals yielded the activation energy for the conductivity processes. Thescope of the present work is to estimate the activation volumes from the activation energy valuesby means of the cBW model and compare them with the experimental values.Varotsos and Alexopoulos have suggested within the frame of the cBW model [14] that the

activation volume can be calculated from the activation enthalpy hact and the elastic properties ofthe material through the following equation:

uact ffi B�1 dBdP

� 1

� �hact ; ð1Þ

where B denotes the isothermal bulk modulus and dB/dP is its pressure derivative. This modelwas successfully applied to many different materials [14].The transport of charge carriers along the volume of the specimen produces TSDC peaks when

non-ohmic electrodes are used. By analyzing those signals, the activation energies for the conduc-tivity mechanisms can be obtained accurately [8, 10, 11]. However, the activation energy E ob-tained from electrical and dielectric measurements is identical with the activation enthalpy hact

[14]. We can therefore replace the activation energy values and the elastic constants into Eq. (1),so as to calculate the values of the activation volume uactcalc. The results are shown in Table 1,together with the experimentally determined activation volumes (which are simply labeled by uact).We observe that the calculated activation volumes are in good agreement with the experimental

ones. The divergence between the calculated and the experimental values is less than 6%. The

phys. stat. sol. (b) 230, No. 2, R7–R8 (2002)

# WILEY-VCH Verlag Berlin GmbH, 13086 Berlin, 2002 0370-1972/02/23004-00R7 $ 17.50þ.50/0

1Þ Corresponding author; e-mail: jacob.turner@lycos.com

Tab l e 1

Calculation of the activation volumes uactcalc by inserting the activation energies E and theelastc parameters B and dB/dP (Ref. [15]) into Eq. (1). In the last column, the experi-mentally determined activation volumes uact are shown

material E (eV) B (GPa) dB=dP uactcalc (cm3/mol) uact (cm3/mol)

CaCO3 0.65 [10] 32.1 8.1 13.9 13.1 � 0.9 [5]MgCO3 0.751 [11] 27.2 8.4 19.8 21 � 1 [2–4]CaMg(CO3)2 0.70 [8] 23.2 7.5 18.9 19 � 3 [1–4]

activation volumes in carbonates are proportional to the activation energy of the conductivity inregard to the thermodynamic formulation of Eq. (1). Defect volume parameters for carbonatescan well be predicted from TSDC results through the cBW model.

References

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