Final answer:
To analyze the vibration modes of a system of atoms using (x,y,z) coordinates, we examine the displacement of each atom from its equilibrium position in each direction. The number of modes depends on the number of atoms and degrees of freedom in the system, which is calculated by multiplying the number of atoms by 3 in a 3D system.
Step-by-step explanation:
In order to analyze the vibration modes of a system of atoms, we can use the (x,y,z) coordinates of each atom. By examining the displacement of each atom from its equilibrium position in each direction, we can determine the vibrational modes.
The number of modes will depend on the number of atoms and degrees of freedom in the system. In a 3D system, each atom will have 3 degrees of freedom (one for each Cartesian coordinate). Thus, the total number of modes can be calculated by multiplying the number of atoms by 3.