Hardness and the Mohs Scale

Introduction

Why can a steel knife scratch glass only with difficulty, while a diamond scores it easily? The answer is hardness — the ability of a material to resist being scratched. Hardness is a physical property that is easy to test and very important in choosing materials for tools, jewellery, cutting edges and protective surfaces.

Core explanation

Definition. Hardness is a material's resistance to being scratched or dented. A harder material can scratch a softer one, but not the other way round.

The Mohs scale. In 1812 the German mineralogist Friedrich Mohs ranked ten minerals by scratch resistance:

Mohs number Mineral Everyday comparison --- --- --- 1 Talc Crumbles under a fingernail 2 Gypsum Scratched by a fingernail (about 2.5) 3 Calcite Scratched by a copper coin (about 3) 4 Fluorite Scratched easily by a steel knife 5 Apatite Scratched by a knife with effort 6 Orthoclase feldspar Scratches glass (glass about 5.5) 7 Quartz Scratches steel and glass easily 8 Topaz 9 Corundum (ruby, sapphire) 10 Diamond Scratches everything else

Each mineral scratches all those below it. An unknown sample that scratches fluorite but is scratched by apatite has a hardness between 4 and 5.

The scale is a ranking, not a measurement. The numbers show order only. Diamond (10) is not "slightly harder" than corundum (9): by precise measurement it is several times harder. Scientists use instruments that press a hard point into a surface and measure the dent for accurate, quantitative hardness values.

Hardness is not the same as strength. Glass is hard (difficult to scratch) but brittle (it shatters easily). Rubber is soft but tough. Choosing a material means considering several properties together.

What makes materials hard? Hardness depends on how strongly the particles are held together. In diamond, every carbon atom is joined to four others by strong covalent bonds in a rigid three-dimensional network, so it is extremely hard. In talc, layers of particles are held together only weakly and slide over each other easily.

Step-by-step reasoning

To estimate the hardness of an unknown mineral:

1. Try to scratch it with a fingernail (2.5). If it scratches, hardness < 2.5. 2. Otherwise try a copper coin (3), then a steel nail or knife (about 5.5). 3. Try scratching a glass plate with the sample (glass 5.5). 4. Rub away the powder to make sure a real groove, not a streak of powder, was made. 5. State the range, for example "between 3 and 5.5".

Visual explanation

Picture a vertical ladder with ten rungs labelled with the Mohs minerals, talc at the bottom and diamond at the top. Beside the ladder, everyday tools are placed at their approximate heights: fingernail at 2.5, copper coin at 3, glass and steel at about 5.5, and a steel file at about 6.5.

Real-world analogy

A scratch test is like a knockout tournament: each player (material) either beats or loses to another. By seeing who beats whom, you can rank all the players in order, even without a precise score for each one.

Real-world example

Diamond-tipped saws and drill bits cut stone, concrete and glass because diamond is harder than all of them. Sapphire (corundum, 9 on the Mohs scale) is used for the faces of high-quality watches because everyday objects, including sand grains (mostly quartz, 7), cannot scratch it.

Why?

Why does a softer material not scratch a harder one? To scratch a surface, the particles of the scratching object must push apart and displace the particles of the surface. If the surface particles are held more strongly than those of the scratching object, the scratching object wears away first instead.

Common misconception

"Hard materials are unbreakable." Diamond is the hardest natural material, yet it can be split with a sharp blow along certain planes, and glass is hard but shatters when dropped. Hardness is resistance to scratching, not resistance to breaking.

Worked example

Question: A mineral scratches calcite but not fluorite, and a steel knife scratches it. Estimate its Mohs hardness.

Reasoning: It scratches calcite, so it is harder than 3. It does not scratch fluorite, so it is softer than 4 (or equal to it). A knife scratches it, which is consistent.

Answer: Between 3 and 4.

Quick check

1. Which mineral is at the top of the Mohs scale? Answer: Diamond, with a hardness of 10.

Exam focus

Remember that the Mohs scale is a comparative ranking based on scratching. Questions may give a list of scratch results and ask you to place an unknown on the scale. Distinguish hardness (scratch resistance) from strength and brittleness.

Advanced insight

Materials scientists have made substances that rival diamond, such as cubic boron nitride, which is used for cutting hard steels because it does not react with iron at high temperatures the way diamond does. Measured with modern indentation tests, the gap between diamond and the next-hardest natural mineral is much larger than the Mohs numbers suggest.

Summary

Hardness is resistance to being scratched. The Mohs scale ranks ten minerals from talc (1) to diamond (10); each scratches those below it. It is a comparative ranking, not an even scale. Hardness depends on how strongly particles are held together and is different from strength or toughness.

Practice questions

1. A sample is scratched by a copper coin but not by a fingernail. Estimate its hardness. Answer: Between 2.5 and 3. 2. Why is diamond used on the tips of drills for cutting rock? Answer: It is harder than any rock, so it scratches and cuts the rock without being worn away quickly. 3. Explain why glass is described as hard but brittle. Answer: It resists scratching (hard) but shatters easily when struck (brittle). 4. Why can quartz sand scratch a glass window? Answer: Quartz (7) is harder than glass (about 5.5).