 Marcos A. Pimenta

ID: marcos-a-pimenta

Marcos A. Pimenta coauthored the 2015 Raman investigation of isotopic composition in graphene.^[ref]

k

and an effective vibrating mass

m

, the mode frequency is proportional to

k / m

. Replacing carbon-12 by carbon-13 changes mass without changing the number of protons; comparing isotopes can therefore help separate mass effects from changes in the bonding model.

For an original unchanged-stiffness estimate, a mode at

1580 c m^{- 1}

in ideal carbon-12 material would move to

ν_{13} = 1580 \frac{12}{13} \approx 1518.0 c m^{- 1}

in the corresponding ideal carbon-13 model. The approximately

3.92%

frequency reduction is smaller than the

8.33%

mass increase because frequency depends on the inverse square root of mass.

If stiffness changes too, the ratio instead contains both effects:

\frac{ν _{2}}{ν _{1}} = \frac{k _{2}}{k _{1}} \frac{m _{1}}{m _{2}} .

A frequency shift alone then cannot identify a stiffness change without composition information. This connects Raman spectroscopy to an inverse problem: a measured peak position constrains a combination of model parameters. The numerical frequencies above are an illustrative calculation, not a reproduction of Pimenta's experimental data.

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