**8. References**

540 Thermodynamics – Interaction Studies – Solids, Liquids and Gases

defined by the macroscopic parameter of adsorption density (mol/m2), can be inevitably ambiguous, because the chemical potential of mixed microscopic MEA states cannot be unambiguously described by the macroscopic parameter of adsorption density. Failure in recognizing this theoretical gap has greatly hindered our understanding on many adsorption related issues especially in applied science and technology fields where the use

**HO/AsO4 Adsorption reaction equations ΔG K Bidentate binuclear complexes** 



Monodentate mononuclear complexes


H-bond complexes


[Ti2(OH)4(H2O)6AsO2(OH)2]3+ + OH-( H2O)11

[Ti2(OH)4(H2O)6AsO2(OH)2]3+ + 2OH-(H2O)10

Table 2. Calculated Δ*G*ads (kJ/mol) and equilibrium adsorption constant *K* at 25 °C of

Metastable-equilibrium adsorption (MEA) theory pointed out that adsorbate would exist on solid surfaces in different forms (i.e. MEA states) and recognized the influence of adsorption reaction kinetics and reactant concentrations on the final MEA states (various outer-sphere and inner-sphere complexes) that construct real adsorption equilibrium state. Therefore, traditional thermodynamic adsorption theories need to be further developed by taking metastable-equilibrium adsorption into account in order to accurately describe real

[Ti2(OH)4(H2O)4AsO2(OH)2]3+(H2O)2 + OH-( H2O)11

[Ti2(OH)4(H2O)5AsO2(OH)2]3+ H2O + OH-( H2O)11

[Ti2(OH)4(H2O)4AsO2(OH)2]3+(H2O)2 + 2OH-

<sup>2</sup>H2AsO4- ( H2O)12+ [Ti2(OH)6(H2O)4]2+ <sup>→</sup>

<sup>0</sup>H2AsO4- ( H2O)12+ [Ti2(OH)4(H2O)6]4+<sup>→</sup>

1-1 H2AsO4- ( H2O)12+ [Ti2(OH)5(H2O)5]3+<sup>→</sup>

<sup>2</sup>H2AsO4- ( H2O)12+ [Ti2(OH)6(H2O)4]2+<sup>→</sup>

<sup>1</sup>H2AsO4- ( H2O)12+ [Ti2(OH)5(H2O)5]3+ <sup>→</sup>

<sup>2</sup>H2AsO4- ( H2O)12+ [Ti2(OH)6(H2O)4]2+ <sup>→</sup>

arsenate on various protonated Ti-(hydr)oxide surfaces.

equilibrium properties of surface adsorption.

[Ti2(OH)5(H2O)4AsO2(OH)2]2+ H2O + OH-

[Ti2(OH)4(H2O)4AsO2(OH)2]3+(H2O)2+ 12H2O -244.5 6.80×1042

[Ti2(OH)4(H2O)5AsO2(OH)2]3+ H2O + 12H2O -225.4 3.13×1039

[Ti2(OH)5(H2O)4AsO2(OH)2]2+ H2O + 12H2O -135.6 5.72×1023

[Ti2(OH)4(H2O)6AsO2(OH)2]3+ + 12H2O -203.1 3.91×1035

(H2O)10

( H2O)11

13.1 5.15×10-3

211.5 8.72×10-38

32.1 2.37×10-6

27.5 1.54×10-5

54.4 2.96×10-10

252.9 5.01×10-45

of surface concentration (mol/m2) is common or inevitable.

<sup>0</sup>H2AsO4

<sup>1</sup>H2AsO4

1-2 H2AsO4

<sup>0</sup>H2AsO4


**0**

**21**

In Gee Kim

*Republic of Korea*

*Graduate Institute of Ferrous Technology,*

*Pohang University of Science and Technology, Pohang*

*G* = *E* + *PV* − *TS*, (1)

**Towards the Authentic** *Ab Intio* **Thermodynamics**

A phase diagram is considered as a starting point to design new materials. Let us quote the

A phase diagram is a map that presents the domains of stability of phases and their combiations. A point in this space, which represents a state of the system that is of

In practice, for example to calculate the lattice stability, the construction of the phase diagram is to find the phase equilibria based on the comparison of the Gibbs free energies among the possible phases. Hence, the most important factor is the accuracy and precesion of the given Gibbs free energy values, which are usually acquired by the experimental assessments. Once the required thermodynamic data are obtained, the phase diagram construction becomes rather straightforward with modern computation techniques, so called CALPHAD (CALculation of PHAse Diagrams) (Spencer, 2007). Hence, the required information for constructing a phase diagram is the reliable Gibbs free energy information. The Gibbs free

where *E* is the internal energy, *P* is the pressure, *V* is the volume of the system, *T* is the temperature and *S* is the entropy. The state which provides the minimum of the free energy under given external conditions at constant *P* and *T* is the equilibrium state. However, there is a critical issue to apply the conventional CALPHAD method in general materials design. Most thermodynamic information is relied on the experimental assessments, which do not available occasionally to be obtained, but necessary. For example, the direct thermodynamic information of silicon solubility in cementite had not been available for long time (Ghosh & Olson, 2002; Kozeschnik & Bhadeshia, 2008), because the extremely low silicon solubility which requires the information at very high temperature over the melting point of cementite. The direct thermodynamic information was available recently by an *ab initio* method (Jang et al., 2009). However, the current technology of *ab initio* approaches is usually limited to zero temperature, due to the theoretical foundation; the density functional theory (Hohenberg & Kohn, 1964) guarrentees the unique total energy of the ground states only. The example demonstrates the necessity of a systematic assessment method from first principles. In order to obtain the Gibbs free energy from first principles, it is convenient to use the equilibrium statistical mechanics for grand canonical ensemble by introducing the *grand*

interest in a particular application, lies within a specific domain on the map.

**1. Introduction**

statements by DeHoff (1993):

energy *G* is defined by

[31] He, G. Z.; Pan, G.; Zhang, M. Y.; Wu, Z. Y., *J. Phys. Chem. C* 2009, 113 (39), 17076-17081. [32] Zhang, M. Y.; He, G. Z.; Pan, G., *J. Colloid Interface Sci.* 2009, 338 (1), 284-286.
