The Mohs Scale Of Hardness

In 1822 a German mineralogist called Friedrich Mohs set up a scale of hardness for minerals.
Mohs selected 10 popular minerals and tested them for scratchability. His system was beautifully simple. A mineral will scratch all softer minerals with a lower hardness number.
Much dust and grit in the environment (excluding house dust which is mainly dead skin etc.) consists of quartz which is number 7 on Mohs' scale.
Hence a gemstone should have a hardness of 7 or more if it is to retain a good polish. As well as hardness, gemstones also need toughness to withstand the rigours of daily wear.
Nephrite jade is the toughest gemstone although it is 6 to 7 on the Mohs scale.
Below is the categorisation Friedrich Mohs determined.

1. Talc

Talc can be scratched with a fingernail to form fine powder and is the softest mineral.

2. Gypsum

Gypsum can be scratched with a finger nail.
It is calcium sulfate dehydrate and is used to make plaster, plasterboard, insulation board, acoustic ceiling adhesives and more for use in the building industry.

3. Calcite

Calcite can be scratched with a finger nail.

A common and highly variable mineral in form and colour.
Calcite is the predominant mineral in limestone and marble. These two rocks form a significant portion of the earth's crust.
Calcite has more uses than almost any other mineral. It is used as a construction material, a soft abrasive, agricultural soil treatment, construction aggregate, pigment, in pharmaceuticals as an acid neutraliser and more.
Chrysocolla has a hardness of 3.

4. Fluorite

Fluorite is easily scratched with a knife.
Also known as Feldspar, Fluorite is a combination of fluorine and calcium and has many industrial uses. It is used in a wide variety of chemical, metallurgical and ceramic processes.
Specimens with exceptional diaphaneity and colour are cut into gems or used to make ornamental objects.
Blue John is a variety of fluorite and is found in Castleton, Derbyshire. This is the purpley blue colour but fluorite also occurs in yellow and green.
Other gemstones with a Mohs hardness of 4 include rhodochrosite and malachite.

5. Apatite

Apatite can easily be scratched with a knife.
Apatite refers to a group of phosphate minerals which includes fluorapatite, chlorapatite, hydroxylapatite, carbonate-rich apatite and francolite. Fluorapatite is the most common of these minerals.
The primary use of apatite is in the manufacture of fertilizer - it is a source of phosphorus. It is also used as a gemstone due to its gorgeous vivid turquoise colour and vitreous texture.
Lapis lazuli has a hardness of 5.5.
Opals are between 5.5 and 6.5 on the scale

6. Orthoclase

Orthoclase can be scratched with a steel file.
It is an important tectosilicate mineral which forms igneous rock. Alternate names are alkali feldspar and potassium feldspar. The feldspars are the most abundant mineral group in the Earth's crust.
Orthoclase is a common raw material used in the manufacture of some glasses and ceramics such as porcelain, and as a constituent of scouring powder.
Moonstone and Labradorite are largely composed of orthoclase and amazonite also belongs to the alkali feldspar gemstones.
Rhodonite, turquoise, jade, nephrite, chalcedony, jasper, tanzanite, peridot and garnet have hardnesses between 6 and 7.

7. Quartz

Quartz will scratch window glass.
Age cannot wither her, nor custom stale her infinite variety - was Enobarbus talking about Cleopatra or the quartz mineral?
Quartz is the second most common mineral in the earth's crust but what variety!
Colourless, transparent rock crystal is the purest form of quartz. 
However chemical impurities in the rock give us amethyst, citrine, rose and smokey quartz, chalcedonies, jaspers, chrysoprase, agates, cat's eye, tiger's eye, hawk's eye and more.
Beryl which is aquamarine and emerald, has a Mohs scale rating of 7.5 and iolite falls between 7 and 7.5.

8. Topaz

Historically, it was thought that topaz only occurred in yellow and that all yellow gems were topaz.
We now know that this is not the case and topaz occurs in colourless, blue, yellow, brown and pink. The colour depends on the percentage of fluorine or water present in the rock. Golden brown and pink topaz contains more water whereas blue and yellow topaz is fluorine rich.
Topaz is usually faceted and can occur in huge crystals weighing many kilos.

9. Corundum

Corundum is ruby and sapphire.
Ruby and sapphire are two of the precious gemstones popular for engagement rings, special birthdays and anniversaries and of course the crown jewels.
The beauty of these gemstones lies in their rich and intense colours. Their hardness gives them a brilliant and lasting polish. 
Ruby is given its magnificent crimson red colour by chromium. All other corundum without chromium is sapphire.
Sapphire is most well known for the shades of blue but also occurs in yellow, pinkish-orange (known as padparadscha) and green.
Some of the finest rubies are mined in Myanmar (formerly Burma) and the richest source of sapphires is Sri Lanka.

10. Diamond

So finally we arrive at the hardest mineral - diamond.
You don't need me to tell you why diamonds are prized but just for completeness, I will! Diamonds are prized for their lustre, dispersion and lasting fiery brilliance. It's hard to believe diamonds are a form of carbon like graphite and charcoal.
Diamond's exceptional properties arise from its crystal structure in which the bonding between carbon atoms is immensely strong an uniform.
How to judge the quality of a diamond?
The four Cs apply - colour, clarity, cut and carat weight. To go into detail about each of these requires a whole article in its own right - one for another time!