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The phrase "a higher hardness of" is correct and usable in written English.
It can be used when discussing the comparative hardness of materials or substances in scientific or technical contexts.
Example: "The new alloy exhibits a higher hardness of 200 Vickers compared to the previous version."
Alternatives: "greater hardness of" or "increased hardness of".
Exact(7)
This effect could be explained only by a higher hardness of the material.
The lower transformation temperature produces finer and denser carbides, and results in a higher hardness of ferrite.
Additionally, microhardness results also confirm that Cu ball bonds reveal a higher hardness of 111 VHN than that of initial Cu ball (84 VHN).
The nanolayered CrN/WN coatings exhibited a higher hardness of approximately 30 GPa, which was superior to that of the nanocomposite CrWN coating.
Under optimized deposition conditions, the TiAlN/SiNx multilayer coating showed a higher hardness of about 3200 HV and better wear resistance than the TiAlN monolayer coating.
The results suggested that the increase in the percentage of polymers, as well as in the compression time, resulted in a higher hardness of the matrix with a reduced rate release of the PHCl.
Similar(53)
After heat-treatment, it decomposed into a bainitic structure with a high hardness of 884 HV.
The DLC coatings have a high hardness of >18 GPa, a low friction coefficient of 0.12 and a low wear rate of (1.7 ± 0.2) × 10−15 m3/N·m.
The featureless phase with a high hardness of 1155 HV was characterized as a metastable solid solution of ε phase.
In addition, this NGMG sustains the good mechanical properties of metallic glasses, showing a high hardness of ∼5.3 GPa.
The coatings with a N content of 25.5 at.% possessed a highest hardness of 25.4 GPa and a highest H/E ratio of 0.096.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com