Dear Param Shivam Singh ,

Before being able to answer your question, we'll need to know a few things:

• Does black = undoped and purple = doped?
• Does purple = partial substitution?
• Is the dopant heavier than the atom/ion that used to sit at that site?
• Does the frequency increase as you move to the right along the x-axis?

If so, then I think that both peaks correspond to the same vibrational mode. The peak on the right corresponds to the vibration including the original, lighter atom/ion and the peak on the left corresponds to the vibration including the heavier dopant. You can understand this intuitively using a simple model of two masses (m1 and m2) connected by a spring with a force constant k. The stretching frequency for this system is given by

f = sqrt(k / u)

where

u = (m1 * m2) / (m1 + m2)

If you increase one of the masses (analogous to doping), then u increases and f decreases. This could explain your result but only if you can answer "yes" to those four questions above.

Please let me know if you have any further questions.

Best,

Rob

Dear Param Shivam Singh ,

Before being able to answer your question, we'll need to know a few things:

• Does black = undoped and purple = doped?
• Does purple = partial substitution?
• Is the dopant heavier than the atom/ion that used to sit at that site?
• Does the frequency increase as you move to the right along the x-axis?

If so, then I think that both peaks correspond to the same vibrational mode. The peak on the right corresponds to the vibration including the original, lighter atom/ion and the peak on the left corresponds to the vibration including the heavier dopant. You can understand this intuitively using a simple model of two masses (m1 and m2) connected by a spring with a force constant k. The stretching frequency for this system is given by

f = sqrt(k / u)

where

u = (m1 * m2) / (m1 + m2)

If you increase one of the masses (analogous to doping), then u increases and f decreases. This could explain your result but only if you can answer "yes" to those four questions above.

Please let me know if you have any further questions.

Best,

Rob

Robert Wexler

Thank you so much Sir,

All those four question above are in 'Yes'.

dopant (partial) is heavier than Site element.

Now matter is clear !!😊

If possible , please give me any reference related to this.

I don't see an x-axis. Is this doped carbon? What is the material being doped with?

Without knowing the x-axis, I can offer three possibilities:

A) if it is around 1450 and 1600 cm^-1 and it is Carbon, then it could be from the material becoming more amorphous.

B) the dopant has a higher mass, then the bonds in the pristine sample are being shifted with intensity that should correlate to the concentration of dopant.

C) the symmetry change of the dopant domains is causing a different peak.