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Does deuterium peroxide exist? Wikipedia has no reference. Also, the sites for delivery of chemicals like "Pubchem" or "Chemspider" have no reference.

In my book, a preparation of $\ce{D2O2}$ is given,

$$\ce{K2S2O8 + 2D2O -> 2KDSO4 +D2O2}$$

If $\ce{D2O2}$ exist, what are its physical properties (structure and appearance etc.)?

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    $\begingroup$ It does exist. A quick SciFinder search brings up around 50 papers, mostly dealing with rotational/vibrational spectra - don't know if larger quantities have been prepared. As for the structure: it's pretty similar to that of hydrogen peroxide, but has a slightly shorter O-D distance. Here is a reference for its structure. $\endgroup$
    – snurden
    Jul 20, 2015 at 10:25
  • $\begingroup$ It's simply deuterated H2O2 so of course it exists and is quite similar. $\endgroup$
    – Mithoron
    Jul 20, 2015 at 16:17

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It does exist. At least Google shows one supplier situated in New Jersey.

ID 1130 Deuterium Peroxide (30% in D2O) D2O2 98 5 5.0g / 10.0g

Though for some reason I could not find any reputable supplier like Cambridge Isotopes or Sigma-Aldrich (strange!). As far as physical properties are concerned, as pointed out by @snurden there exists a significant amount of literature. Here is one article from the Canadian Journal of Chemistry that includes study of many properties (behind a pay wall though).

Abstract:

Abstract of above paper

And to answer final part of your question: Result of same paper

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