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Photorefractive materials are being widely investigated for applications in holographic data storage. Inhomogenous illumination of these materials with an optical interference pattern redistributes charge, builds up internal electric fields and so changes the refractive index. Subsequent homogenous illumination results in light diffraction and reconstructs the information encoded in the original interference pattern. A range of inorganic and organic photorefractive materials are known, in which thousands of holograms of high fidelity can be efficiently stored, reconstructed and erased. But there remains a problem with volatility: the read-out process usually erases the stored information and amplifies the scattered light. Several techniques for 'fixing' holograms have been developed, but they have practical disadvantages and only laboratory demostrators have been built. Here we describe a resolution to the problem of volatility that should lead to the realization of a more practical system. We use crystals of lithium niobate - available both in large size and with excellent homogeneity - that have been doped with two different deep electron traps (iron and manganese). Ilumination of the crystals with incoherent ultraviolet light during the recording process permits the storage data (a red-light interference pattern) that can be subsequently read, in the absence of ultra-violet light, without erasure. Our crystals show up to 32 per cent diffraction efficiency, rapid optical erasure of the stored data is possible using ultraviolet light, and light scattering is effectively prevented.