Standing more than 3m tall, the model was built by Dr Robert Krickl from nearly 40,000 balls and 10km of sticks.
The world record attempt will be adjudicated by the Guinness Book of Records on 23 November.
It will be on public display until 30 November, and has already been commemorated on an Austrian postage stamp.
"I want to show - to visualise - how our world looks when it`s magnified about a billion times," Dr Krickl, a crystallographer turned science communicator, told Science in Action on the BBC World Service.
""Because of the regular pattern it is built up from, which causes hundreds of the "ions" to form precise lines from multiple angles, the huge model has a rather dazzling appearance.
It also has particular significance this week, Dr Krickl said.
"This week it`s the 100th anniversary of the Nobel Prize for discovering what I show with this model: the arrangement of atoms in crystals."
The British father-and-son team of William and Lawrence Bragg won the physics Nobel in 1915 for originating the technique that is now known as X-ray crystallography.
"This discovery really had a major impact on science and our understanding of the world," Dr Krickl said. "It led to the determination of the structure of DNA, of viruses, of proteins - and on the other hand, of materials used in our daily lives, for technology to build faster, better lighter machines."
To mark this anniversary, on Thursday he welcomed representatives from the British Council and the British Embassy to view the nearly completed structure.
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