X-ray powder-diffraction measurements performed at the ESRF between

10^{- 4}

and 22 GPa have been used to infer the equations of state (EOS) of both

^{12} C

and

^{13} C

diamonds. The experiments were carried out with a diamond-anvil cell and care was taken to obtain the most hydrostatic pressure conditions using nitrogen, argon, or ethanol:methanol:water mixtures as pressure transmitting media. The cell parameter determinations were precise enough to distinguish the small volume differences between the two isotopic end members. Fits of the data to Birch-Murnaghan EOS yield an isothermal bulk modulus of

^{12} C

diamond

[K_{0 T} = 446 (4) GPa

for

K_{0 T}^{'}

fixed to 4], in excellent agreement with the values inferred from ultrasonic and Brillouin scattering measurements. The EOS of

^{13} C

is very close to that of

^{12} C

diamond

[K_{0 T} = 438 (8) GPa

for

K_{0 T}^{'} = 4] .

This result is at variance with previous acoustic measurements which suggested that the bulk modulus of

^{13} C

diamond is 17% higher than that of

^{12} C

diamond.

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