Advanced Materials Simulation Project Guidelines
Explore advanced materials simulation project guidelines for PHYS4061 Project A Part II. Learn to calculate reciprocal lattice vectors, implement periodic boundary conditions, and generate neighbor lists for various crystal structures. Understand the concepts of simulation boxes and periodic boundary in 2D lattice. Enhance your coding skills by creating modular and reusable code for efficient simulations.
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PHYS4061 Project A part II
Reminder about lab1 Finish part I. you will need it for part II You may need to modify your part I so you can use it in part II (modular and reusable code) Later in other labs, you will use the position arrays of atoms you generate in part I as input. For example, you can use the following 1D arrays to save the coordinates of N atoms: x[N] , y[N], z[N] You can also use class or struct, but be aware of the overhead in computing Lattice Constant should be a float, some student used int instead. Count your number of atoms and periodicity, incorrect code generate fewer / more atoms than specified.
Project A Part II 1. Write a function that calculate the reciprocal lattice vectors b1, b2 and b3 from the unit cell s lattice vectors a1, a2 and a3 in real space, and print out the volume of the unit cell. Store the x, y, z coordinates of a and b in arrays. Test on SC, BCC, FCC to make sure the code is correct. Note that the reciprocal lattice vectors for primitive cell of BCC is FCC and vice versa. 2. Write a function that takes a coordinate (x1, y1, z1) with a1,a2,a3 as the unit cell, apply periodic boundary conditions, return the fractional coordinates n1, n2, n3 (in the range of (-0.5, 0.5]) and the (x2, y2, z2) Hint, call the code of reciprocal to have (b1,b2,b3) as global arrays, then take the dot product and mod. Why 2? can be ignored? ?2 ?3 ?1 ?2 ?3, ?3 ?1 ?1 ?2 ?3, ?1 ?2 ?1 ?2 ?3, or ?1= 2? ?2= 2? ?3= 2? ?2 ?3 ?1 ?2 ?3 ?3 ?1 ?1 ?2 ?3 ?1 ?2 ?1 ?2 ?3 ?1= ?2= ?3= , ,
3. Neighbor list Input a1, a2 and a3 vectors, atomic positions in the unit cell, distance cutoff. Calculate the neighbor list of each atom according to the distance cutoff. Write the first-nearest neighbor list of all atoms in a file for submission. Hint, use reciprocal and PBC code to store all the information into neighbor list arrays and distance arrays. Hint: make sure the cutoff is correct for nearest neighbors. Check your correctness with unit cells of simple cubic, BCC, FCC and diamond. diamond/zinc blende How many first nearest neighbors for SC, BCC, FCC and diamond? How to represent a neighbor list in concise and accurate way? Submit neighbor list, code and README in a zip file Due date: Oct 7rd23:59
Recap on the concept of simulation box 5 0 1 2 3 0 12 13 14 15 12 5 ?2 ?5= (5 ?11= (15 4, 5 4, 10 4) 8 9 10 11 8 Position vector: (Cartesian) [0,5] 4) 4 5 6 7 4 ?5= (1 ?11= (3 4, 1 4, 1 Position vector: (fractional) [0,1] 4) 2) 0 1 2 3 0 ?1
Recap on Periodic Boundary in 2D Lattice constant: 5/4 0 1 2 3 0 12 13 14 15 12 Apply PBC to Displacement Vector [-0.5,0.5] ?2 8 9 10 11 8 Displacement in Recip. Space Back to Real space 4 5 6 7 4 0 1 2 3 0 ?1
Example of a neighbor list (2D) (a=5/4, 1stnearest neighbor) 5 Example of NeighborList , for a=1.25 Label 2 ... 4 9 11 12 0 1 2 3 0 Label 1 ... 8 8 8 8 Distance ... 1.25 1.25 1.25 1.25 12 13 14 15 12 Cutoff 8 9 10 11 8 Neighbor-list should have indices corresponding to distances, the exact order or implementation doesn t matter! 4 5 6 7 4 0 1 2 3 0
