Knoop hardness is a microhardness scale developed by Frederick Knoop, Chauncey Peters and W. B. Emerson at the United States National Bureau of Standards, the predecessor of NIST, in 1939. It expresses the resistance of a material to indentation by a precisely shaped diamond pyramid under a defined load and is widely used in gemmology, ceramics, and the heat-treatment industries to compare materials whose hardness is too high or too low to be conveniently expressed on the more familiar Mohs scale. The Knoop scale is a true quantitative scale rather than the relative ordinal Mohs scale.

Method

A Knoop test uses an elongated rhombohedral diamond indenter with apical angles of 172 degrees 30 minutes and 130 degrees, pressed into the polished surface of the test material under a controlled load between 10 grammes-force and 1 kilogramme-force. The resulting elongated rhombohedral impression is measured along its long diagonal under a microscope, and the Knoop hardness number, designated HK, is calculated as the load divided by the projected area of the impression, in kilogrammes-force per square millimetre. The shallow geometry of the Knoop indenter, compared to the Vickers diamond pyramid used for the parallel test, makes Knoop especially suitable for thin sections and small grains, conditions encountered in mineralogy and gemmology.

Values for common gem materials

Diamond, the hardest known natural material, has a Knoop hardness of approximately 8000 to 8500 HK on the cubic plane and 9500 to 10000 HK on the octahedral plane, the directionality reflecting diamond's anisotropic hardness, which is the principle on which polishing the stone depends. Corundum, ruby and sapphire, sit at approximately 1800 to 2000 HK. Topaz is around 1250 to 1450 HK. Quartz is approximately 700 to 800 HK. The Knoop scale therefore reveals the substantial gap between successive Mohs steps that the ordinal Mohs scale conceals: Mohs 9 corundum is roughly four times harder than Mohs 8 topaz on the Knoop scale, while Mohs 10 diamond is roughly five times harder than Mohs 9 corundum.

Use in gemmology

The Knoop scale is used in gemmology principally for two purposes: comparing materials of similar Mohs hardness to predict relative wear in jewellery, and informing the selection of polishing media and lap speeds in the cutting trade. Diamond's directional Knoop hardness is the basis of the cutter's understanding that the stone polishes well only along certain crystallographic directions, a property the cutter exploits by orienting the rough on the dop accordingly. The scale is also used in the testing of synthetic and treated materials, where Knoop measurements can sometimes distinguish, for example, glass simulants from genuine quartz, since the ordinal Mohs scratch test cannot resolve materials within a single Mohs step.

Limitations

The Knoop test is a destructive test in the sense that it leaves a small permanent indentation on the polished surface, which limits its application on finished jewellery. It is therefore principally a laboratory and rough-material test rather than a finished-stone identification tool. The Vickers test, with its symmetric square-pyramid indenter, gives broadly correlated values and is preferred in some metallurgical contexts; for gem materials Knoop is the more common reference.