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"Science fiction has gotten more accurate as we've gotten closer to the present, because science fiction stories have not only attracted, but also generated current scientists."
- Larry Niven

1D Diamond Crystal  
  A continuous pseudo-one dimensional diamond crystal- maybe a nanotube?  

The key engineering feat of this novel requires an extremely light material with great tensile strength. Clarke comes up with a carbon-based material.

"So you do have an invisible wire. Clever - but what use is it, except for parlour tricks?"

"I can't blame you for jumping to that conclusion. But it's quite wrong. The reason you can't see this sample is that it's only a few microns thick. Much thinner than a spider's web."

"...What is it?"

"The result of two hundred years of solid-state physics. For whatever good that does, it is a continuous pseudo-one dimensional diamond crystal - though it's not actually pure carbon. There are several trace elements in carefully controlled amounts. It can be mass-produced only in the orbiting factories, where there's no gravity to interfere with the growth process."

"Fascinating ... I can appreciate that this may have all sorts of technical applications. It would make a splendid cheese cutter."

From The Fountains of Paradise, by Arthur C. Clarke.
Published by Ballantine in 1978
Additional resources -

This sounds very much like a nanotube:

Carbon nanotubes discovered in 1991 by Sumio Iijima resemble rolled up graphite, although they can not really be made that way. Depending on the direction that the tubes appear to have been rolled (quantified by the 'chiral vector'), they are known to act as conductors or semiconductors. Nanotubes are a proving to be useful as molecular components for nanotechnology.

Strictly speaking, any tube with nanoscale dimensions, but generally used to refer to carbon nanotubes, which are sheets of graphite rolled up to make a tube. A commonly mentioned non-carbon variety is made of boron nitride, another is silicon. These noncarbon nanotubes are most often referred to as nanowires. The dimensions are variable (down to 0.4 nm in diameter) and you can also get nanotubes within nanotubes, leading to a distinction between multi-walled and single-walled nanotubes. Apart from remarkable tensile strength, nanotubes exhibit varying electrical properties (depending on the way the graphite structure spirals around the tube, and other factors, such as doping), and can be superconducting, insulating, semiconducting or conducting (metallic).

Nanotubes can be either electrically conductive or semiconductive, depending on their helicity, leading to nanoscale wires and electrical components. These one-dimensional fibers exhibit electrical conductivity as high as copper, thermal conductivity as high as diamond, strength 100 times greater than steel at one sixth the weight, and high strain to failure.

A nanotube's chiral angle--the angle between the axis of its hexagonal pattern and the axis of the tube--determines whether the tube is metallic or semiconducting.

Apparently, nanotube crystals were observed as early as 1952 by Soviet scientists, but the papers were only available in Russian. Another paper was published in 1970, but I don't think that their properties were explored until after Clarke wrote his book.

Read more about nanotubes and buckyballs.

Consider also an earlier application of a similar idea - the Sinclair molecule chain from a 1968 Larry Niven story.

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Additional resources:
  More Ideas and Technology from The Fountains of Paradise
  More Ideas and Technology by Arthur C. Clarke
  Tech news articles related to The Fountains of Paradise
  Tech news articles related to works by Arthur C. Clarke

1D Diamond Crystal-related news articles:
  - Nanofibers In Unlimited Lengths Now Available
  - Carbon Nanotube Knife Like Cheese Slicer
  - Diamond Nanothreads For Space Elevators?
  - 'Diamond Nanothreads' Now, Someday Space Elevators?
  - Carbyne, The Ultimate Form Of Carbon

Articles related to Material
MIT Self-Assembling Reprogrammable Materials
Tiny Mining - Extract Precious Industrial Minerals From Your Own Body
Polyaramide Is Stronger Than Steel, Light As Plastic
Trinitite, Pentagrams And Isaac Asimov

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