『Abstract
　With previous two-dimensional (2D) simulations based on surface-specific feldspar dissolution succeeding in relating the macroscopic feldspar kinetics to the molecular-scale surface reactions of Si and Al atoms (Zhang and Luttge（uの頭に¨）, 2008, 2009), we extended our modeling effort to three-dimensional (3D) feldspar particle dissolution simulations. Bearing on the same theoretical basis, the 3D feldspar particle dissolution simulations have verified the anisotropic surface kinetics observed in the 2D surface-specific simulations. The combined effect of saturation state, pH, and temperature on the surface kinetics anisotropy has been subsequently evaluated, found offering diverse options for morphological evolution of dissolving feldspar nanoparticles with varying grain sizes and starting shapes. Among the three primary faces on the simulated feldspar surface, the (100) face has the biggest dissolution rate across an extensively wide saturation state range and thus acquires a higher percentage of the surface area upon dissolution. The slowest dissolution occurs to either (001) or (010) faces depending on the bond energies of Si-(O)-Si (ΦSi-O-Si/kT) and Al-(O)-Si (ΦAl-O-Si/kT). When the ratio of ΦSi-O-Si/kT to ΦAl-O-Si/kT changes from 6:3 to 7:5, the dissolution rates of three primary faces change from the trend of (100)＞(010)＞(001) to the rend of (100)＞(001)＞(010). The rate difference between faces becomes more distinct and accordingly edge rounding becomes more significant. Feldspar nanoparticles also experience an increasing degree of edge rounding from far-from-equilibrium to close-to-equilibrium. Furthermore, we assessed the connection between the continuous morphological modification and the variation in the bulk dissolution rate during the dissolution of a single feldspar particle. Different normalization treatments equivalent to the commonly used mass, cube assumption, sphere assumption, geometric surface area, and reactive surface area normalizations have been used to normalize the bulk dissolution rate. For each of the treatments, time consistence and grain size dependence of the normalized dissolution rate have been evaluated and the results revealed significant dependences on the magnitude of surface kinetic anisotropy under differing environmental conditions. In general, the normalized dissolution rates are strongly dependent on grain size. Time-consistent normalization treatment varies with the investigated condition. The modeling results suggest that the sphere-, cube-, and BET-normalized dissolution rates are appropriate under the far-from-equilibrium conditions at low pH where these normalizations are time-consistent and are slightly dependent on grain size.』

1. Introduction
2. Kinetic model
　2.1. 2D surface-specific kinetic anisotropies
　2.2. 3D feldspar particle dissolution
3. Results and discussion
　3.1. Anisotropic surface kinetics and processes
　　3.1.1. Anisotropic surface kinetics
　　3.1.2. ΦSi-O-Si vs. ΦAl-O-Si
　　3.1.3. Anisotropic surface processes
　　3.1.4. The bulk dissolution rate
　3.2. 3D simulations associated with feldspar particle dissolution
　　3.2.1. Morphological evolution of feldspar particles
　　3.2.2. Layer-retreat velocities of specific faces
　　3.2.3. Saturation state dependence
　　3.2.4. Size dependence of morphological evolution
　3.3. Dissolution rate normalization
4. Conclusions
Acknowledgments
Reference