Hardness:

 The hardness of a material measures how tightly the atoms are held together within it. This test is done either by scratching one substance with another and using the Moh's Scale. On the Moh's Scale, diamond is ranked 10 and graphite is ranked between 1 and 2. This suggests that diamond is about 40 times harder than graphite. Buckminsterfullerene crystals are also relatively soft, even though the individual C60 molecules are hard.  

The Moh's Scale measures the relative hardness of various substances. It uses ten reference minerals. The hardness of a substance is determined by scratching it against a reference mineral. If it scratches that mineral, then it is of equal hardness or harder than that mineral, otherwise it is softer then that mineral. The picture below shows the minerals that are used on the Moh's Scale. 

 

Diamond is ranked as number 10, the hardest substance on this scale. The softest mineral is talc. Graphite ranks between 1 and 2 on this hardness scale. The relation between the Moh's Scale and absolute hardness measured by other means is shown below: 

Other methods use indenters that apply a set amount of force on the surface of the test material. The profile of the resultant dent is then measured and calculated using a variety of other scales.

Brinell Hardness Test

The Brinell Hardness Test was one of the first quantitative tests developed to measure hardness. A tungsten carbide or hardened steel ball, with a diameter of 1.0 cm, is pressed into the material to be tested under a standard load. The load is maintained for 5 to 10 seconds to allow the material to undergo plastic deformation. After the load is removed, the spherical indentation left behind by the ball is measured. The load divided by the surface area of the indentation determines the hardness of the test material. This test is good for measuring the hardness of very hard and thick materials such as metals. 

Vicker Hardness Test

The operating principles of the Vicker Hardness Test are similar to that for the Brinell Hardness Test. The Vicker test uses a square-based diamond pyramid tip with a characteristic 136 degree angle as the indenter. Since determining the diagonal of a square impression is easier than determining the diameter of a circular impression, the hardness obtained by the Vicker test may be more accurate than the Brinell test. This test is also good for measuring the hardness of very hard and thick materials such as metals. 

Knoop Hardness Test

This test is a micro-hardness test, used to determine the hardness of specific locations on an inhomogeneous or very thin sample. An elongated diamond pyramid tip as the indenter. The impression left on the test material has a 130 degrees angle along the width with 172 degrees and 30 minutes angle along the length.

This big difference in hardness between the three forms of carbon is a consequence of each substance's crystal structures. The crystalline structure adopted by each substance is a reflection of how the carbon atoms are bonded together within each substance. 

The hardness of a substance is not the same in all directions. 

Even a highly symmetric crystal such as diamond have a distinct hardness for each of its crystalline faces. The cubic crystalline faces (100, 010, and 001 orientations) of diamond are much softer than a face perpendicular to its body diagonal (111 orientation). The carbon atoms are packed more densely, so more rigid, in this direction. This is the reason why natural diamonds are found as octahedrons. 

Mined diamond crystals are often found to be octahedral. The faces on the octahedron are mechanically harder than the faces on a cubic piece of diamond.  

Graphite is hard parallel to its basal plane, but is bendable normal to the layers. The bonds between the carbons within the graphite sheets are stronger than those in diamond. The forces that hold the sheets together, on the other hand, is very weak so the sheets can be easily peeled away. This is the reaon graphite feels so soft and lubricating. 

The bonds within each Buckminsterfullerene molecule are very strong. The forces that hold the molecules together to form its crystals are very weak, so its crystals are mechanically soft. A measure of a material's resistance to denting, scratching, and abrasion, related to the yield stress and tensile strength of the material. It is determined using indentation test, which measure the size of a hole formed by a hard indenter driven into the material, as in the Vickers and Brinell tests. It is sometimes classified using the Mohs test of mineral hardness (devised by German mineralogist Friedrich Mohs in 1812), which rates talc as hardness 1 and diamond as hardness 10.