KIMERA: A Kinetic Montecarlo Code for Mineral Dissolution
Abstract
:1. Introduction
2. The Reversible Kinetic Monte Carlo Model for Mineral Dissolution
3. The KIMERA Code
3.1. Operation
3.1.1. System Definition
- The mineral structure. The program can either read it from a standard ‘.xyz’ file, or can be defined by commands, or a combination of both. The ‘.xyz’ file [43] is easily obtained by tools such as VESTA [44] from downloadable ‘.cif’ files in mineralogical databases [45]. In principle KIMERA is thought to construct mineral surfaces replicating a small unit cell. Nevertheless, it is also possible to define a complex system within a ‘.xyz’ file and threat it as the whole system box. Coarse grained systems can be also simulated.
- The system dimensions. The program replicates the unit cell in the three spatial directions. Studies of different planes are possible by unit cell transformations with external programs such as VESTA [46]. KIMERA can apply periodic boundary conditions (PBC) in the three spatial directions.
- System shape. The program has commands to create different crystalline shapes of the system into complex surfaces or particles. For the moment the available geometries are cubic, spherical, parallelepiped, ellipsoidal, tick planes, or a combination of them.
- Topographic defects can be defined in the system, such as insoluble regions, dislocations, impurities and vacancies. There are two ways of defining impurities; it is possible to define them in the unit cell indicating their occupancy, or introducing them ex post once the system has been defined.
- Event definition. The KMC algorithm simulates the time evolution of a system as a set of possible events. These events take place at a rate that follows an Arrhenius equation (Equation (1)). A recent study demonstrates that the net dissolution of a mineral can be characterized using decoupled reactions of dissolution and precipitation [29]. Hence, we use that KMC scheme, so the fundamental frequency of the Arrhenius equation, f, splits into or , and into or depending if considering a dissolution or a precipitation event respectively. The energy barrier is characteristic of each chemical reaction and its neighbourhood, and can be obtained from the bibliography and/or ab initio calculations [22,23]. Supposing n neighbours of an atom, KIMERA can set and as a linear (Equation (6)) or a specific (Equation (7)) function of each neighbour j [23,47] (see Figure 2):Note that Equation (6) is a specific case of Equation (7). Moreover, since the contribution to the energy barrier can be determined for several types of neighbours, k represents each set of contributors with the same characteristics and and its contribution for dissolution and precipitation energy barrier respectively.With these two ways of defining the energy barrier, two different approaches can be considered to describe the dissolution events:
- 1
- A bond by bond description: Each linking bond breaks sequentially so that when an atom has no bonds left, it is released from the mineral.
- 2
- A site by site description: All bonds reactions are unified in only one event, and each site dissolves with joint probability.
As an additional element, KIMERA supports conditional event definition. Furthermore, it is possible to define the events based on ghost positions in the unit cell without physical meaning and to make a differentiation between atoms of the same type, for example it is possible to split the atoms of silica into Si1, Si2, etc. in the unit cell and then define events for each sub-element. - Target time (s). Predicting the time scale beforehand in a complex system can be tough. There are two options for the simulation to finish. The simplest option is to indicate the number of simulation steps, that is, the number of events to accomplish. The other option is to specify the target time (s) until the simulation is going to run. The user can request the program to do an estimation of it by considering the initial possible events. Given s initial sorted groups of rates corresponding to atom removals with different coordination , the program approximates the total time for the system to dissolve as if all atoms had the same rate value; the previous to the middle one.
- Optional parameters related with the output files. As we will see, output files contain information of the system time evolution like snapshots for visualization or the quantity of dissolved atoms.
3.1.2. System Preparation
3.1.3. Simulation Process
- Initial KIMERA file of the system in its own format (‘.initialkimerabox’). It is designed to save time in calculating neighbourhood, linked and affected atoms. A later simulation which reads this file will not need to do the preparation step.
- Final KIMERA file of the system (‘.finalkimerabox’). When the simulation has finished, or has encountered an error, the system is printed in KIMERA format.
- File with system snapshots (‘.box’) in LAMMPS format [33] for visualization. As this file can contain a lot of data, it may be better to handle the surface file unless for checking reasons.
- File with surface snapshots (‘.surface’) in LAMMPS format. Instead of the whole system, only the atoms on the surface are printed in this file.
- Data file with the time evolution of the following parameters (‘.data’): The total number of atoms dissolved of each type, its fraction, the surface dispersion, the gyradius (in no PBC systems) as well as all their derivatives.
- Coordination file with the mean coordination to each type of atom along the dissolution process (‘.meandiscoord’). This data is key to calculate correctly value as explained below.
- Layer atom files with the amount of atoms in each layer and each spatial direction (‘.alayer’, ‘.blayer’, ‘.clayer’). For example, the ‘.clayer’ file contains the total number of atoms of the cells in plane ab, layer by layer in c direction.
3.2. Parallelization Level
4. Gibbs Free Energy Difference,
5. Examples of KIMERA Capabilities
5.1. Model A-B Kossel Crystals
- The system dimensions are indicated; 60 × 60 × 15 unit cells.
- The unit cell parameters. We used Å and . Inside the cell, we define the 8 positions of the atoms in the unit cell that later on is repeated along the system. The positions are: (0,0,0), (2.5,0,0), (0,0,2.5), (2.5,0,2.5), (0,2.5,0), (2.5,2.5,0), (0,2.5,2.5) and (2.5,2.5,2.5) Å. All the positions are initially define as A atoms, and we later will redefine half of them as B type. Note that although the unit cell has Å the distance between atoms is Å, which is a typical distance reported for minerals [54].In ‘configuration 1’, the positions are the same, but half of them are of type B. Specifically, atoms in (0,0,0), (0,0,2.5), (2.5,2.5,0) and (2.5,2.5,2.5) are B type. Since the alternating disposition of the atoms is already taken into account with this definition, no additional commands to modify the system are needed.
- We set periodic boundary conditions along x and y axes.
- Physical parameters for the simulation. The target time s and the local units, which ensures far from equilibrium conditions. In ‘configuration 1’ the time scale is different due to its faster dissolution and s.
- Event definition. We have chosen for this example an energy barrier for A-A atoms of units, for B-B units, which are respectively the higher and lower limit value for most minerals [27]. For the AB interaction the energy barrier is obtained from the Lorentz–Berthelot rule [55], units. The precipitation energy barrier for all the cases is units.For the frequency s−1 s which lies in the range of values for atomic vibration in a mineral (– s−1 at 300 K) [56].Lastly, KIMERA requires the number of neighbours that a bulk atom has to later define the initial reactive surface. For both for A and B atoms, a bulk atom has 3 A type neighbours and 3 B type neighbours. In ‘configuration 1’ the event definition is similar, but the number which defines a bulk atom changes. A bulk A atom has 2 A and 4 B neighbours. A bulk B atom has 4 A and 2 B neighbours.
- Topographic defects. We define the last plane as insoluble and we include one partial dislocation in the center with one third of the system depth. Since there are atoms within the dislocation that have a lower coordination than a bulk atom, the program recognised them as initial reactive surface. Therefore, we remove such condition because it is physically meaningless.
5.2. Quartz Model I: Dissolution of an Ellipsoidal Grain
- System dimensions. A box in which we will define the ellipsoid is created with 50 × 40 × 30 unit cells.
- The unit cell parameters. For -quartz , , and . Inside the cell, we load a ‘.xyz’ file containing the positions, which has been converted from a ‘.cif’ file downloaded from The American Mineralogist crystal structure database [45]. Oxygen atoms can be removed for performance purposes since they are not explicitly taken into account for the quartz dissolution reaction in this case. The dissolution of a SiO2 is considered in a single step with a joint probability (Equation (6)). This can be interpreted as a coarse grain of a SiO2 unit in each Si site.
- Physical parameters. The target time s and the local units.
- Topographic defects. An ellipsoid with radius in the three axes, Å, Å and Å is defined as the simulation system. A dislocation along the x axis is placed in the middle.
- Event definition. The energy barrier with first neighboring silicon atom is units and with second . Precipitation energies of and are used. All the four first silicon neighbours are at 3.09832 Å. If an atom is surrounded by the four first neighbours, it is considered to be in bulk. 12 second silicon neighbours are at 5.01 Å. Finally, the fundamental frequencies values are s−1 [57].
5.3. Quartz Model II: Dissolution of a Wulff Shape Particle
- System dimensions. A box in which the wulff shape fit in is created with 16 × 16 × 47 units cells
- Same unit cell parameters as the previous example. , , and . The ‘.xyz’ file is also called, but this time the oxygen atoms do play an important role and they cannot be removed.
- This time instead of target time, we define a target step = 62,700 steps, which is approximately the total amount of silicon and oxygen atoms forming the particle.
- Topographic defects. The wulff shape is sculpted from the system by defining planes in which the atoms are removed. The equations of these planes are taken from GEODEBRA3D tool [60] which was used to visualise the system beforehand. Besides, two dislocations are defined and inner atoms removed from the initial surface. One dislocation is placed transversally in the center of the {100} plane, and another one perpendicular to the previous and longitudinally to the wulff shape
- Event definition. The and for the linking oxygen bond is directly related with the number of oxygen atoms within Å. 6 surrounding oxygen atoms indicates that the considered one is in a bulk position and therefore it is not reactive. Besides, the silicon atom must be automatically released if all of its four surrounding oxygen atoms have reacted. Finally, the fundamental frequency values s−1 are indicated [61]. The value sets very far from equilibrium conditions.
6. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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A-A | A-B | B-B | B-A | ||
---|---|---|---|---|---|
Configuration 1 | 1.0 | 1.33 | 1.0 | 2.66 | |
Configuration 2 | 1.5 | 0.423 | 1.5 | 2.576 |
Si-Si-3.09832 | Si-Si-5.0100 | Si-Si-5.66774 | Si-Si-4.42416 | |
---|---|---|---|---|
1.95 | 1.92 | 1.92 | 1.95 |
Bond | Surrounding Oxygen Atoms | ||
---|---|---|---|
Q1-Q1 | - | - | 0 |
Q1-Q2 | 75 | 60 | 1 |
Q1-Q3 | 85 | 70 | 2 |
Q1-Q4 | 95 | 80 | 3 |
Q2-Q2 | 85 | 70 | 2 |
Q2-Q3 | 95 | 80 | 3 |
Q2-Q4 | 105 | 105 | 4 |
Q3-Q3 | 105 | 105 | 4 |
Q3-Q4 | 135 | 135 | 5 |
Q4-Q4 | - | - | 6 |
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Martin, P.; Gaitero, J.J.; Dolado, J.S.; Manzano, H. KIMERA: A Kinetic Montecarlo Code for Mineral Dissolution. Minerals 2020, 10, 825. https://doi.org/10.3390/min10090825
Martin P, Gaitero JJ, Dolado JS, Manzano H. KIMERA: A Kinetic Montecarlo Code for Mineral Dissolution. Minerals. 2020; 10(9):825. https://doi.org/10.3390/min10090825
Chicago/Turabian StyleMartin, Pablo, Juan J. Gaitero, Jorge S. Dolado, and Hegoi Manzano. 2020. "KIMERA: A Kinetic Montecarlo Code for Mineral Dissolution" Minerals 10, no. 9: 825. https://doi.org/10.3390/min10090825
APA StyleMartin, P., Gaitero, J. J., Dolado, J. S., & Manzano, H. (2020). KIMERA: A Kinetic Montecarlo Code for Mineral Dissolution. Minerals, 10(9), 825. https://doi.org/10.3390/min10090825