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First of all I know about quartz but I don't know about quartz fibre. I was doing chapter on elasticity and their I found a statement that quartz fibre is close to the perfectly elastic material.

My question is what is quartz fibre and what makes it the most elastic material?

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Quartz can be crystalline, or amorphous. The amorphous form, after softening in a flame, can be pulled, like taffy, to form filaments. But, it's rather more exciting than that; in the words of C. V. Boys Sci. Am. Supplement 717

The apparatus consists of a small crossbow, and an arrow made of straw with a needle point. To the tail of the arrow is attached a fine rod of quartz which has been melted and drawn out in the oxyhydrogen jet. I have a piece of the same material in my hand, and now after melting their ends and joining them together, an operation which produces a beautiful and dazzling light, all I have to do is to liberate the string of the bow by pulling the trigger... In this way threads can be produced of great length, of almost any degree of fineness, of extraordinary uniformity, and of enormous strength.

The resulting quartz fiber is tempered by its rapid cooling in air, so that the surface of the fiber is held in compression. Because the surface chills first, it freezes at a large diameter, and the material inside the surface, as it shrinks and cools, pulls radially on that surface. This means the resulting fiber, like tempered glass, is nearly immune to surface cracks, or even microcracks. Cracks only grow when the material is in tension, never in compression.

Quartz fibers made by this process are devoid of imperfections (because any nonuniformity of the material would cause a break during stretching), and nearly immune to microcracks, and have no ductility to speak of. Crystalline materials can fracture on crystal planes, metals can exhibit ductile flow, and most materials have microcracks which can pick up contaminants and create weaknesses.

According to the inventor of this kind of fiber, it's the best available torsion spring (and his other accomplishments seem to prove that point). Best, though, doesn't mean 'most elastic' in the sense of great elongation possibilities; it just means good conformance with ideal spring behavior.

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