To investigate the linear energy transfer (LET) dependence of the response of a PTW-60019 Freiburg microDiamond detector, its response was compared to the response of a plane-parallel Markus chamber in a 62 MeV/n mono-energetic carbon ion beam. Results obtained with two different experimental setups are in agreement. As recommended by IAEA TRS-398, the response of the Markus chamber was corrected for temperature, pressure, polarity effects and ion recombination. No correction was applied to the response of the microDiamond detector. The ratio of the response of the Markus chamber to the response of the microDiamond is close to unity in the plateau region. In the Bragg peak region, a significant increase of the ratio is observed, which increases to 1.2 in the distal edge region. Results indicate a correlation between the under-response of the microDiamond detector and high LET values. The combined relative standard uncertainty of the results is estimated to be 2.38% in the plateau region and 12% in the distal edge region. These values are dominated by the uncertainty of alignment in the non-uniform beam and the uncertainty of range determination.