The U b b e 1 o h d e effect, i.e. the expansion, or contraction, of the hydrogen bonds in crystals when deuterium is substituted to hydrogen, has not yet been well understood. Suggested interpretations based on a one-dimensional model, including possible resonance or anharmonicity effects seem oversimplified and unsatisfactory ,~nd the effect of t e m p e r a t u r e remains somewhat obscure.
These phenomena are however easily understandable in terms of a simple threedimensional model. The contributions of the three hydrogen frequencies to the expansion force, derived from spectroscopic data, are found to cancel each other-almost completely and the thermal variation of the rocking frequency contribution accounts for the reversal of the effect observed for ice between low temperature and the melting point. Expansion forces obtained in this way for potassium dihydrogen-phosphate and ice are in good numerical agreement with those obtained from experimental isotopic expansions, determined by X-rays, and known elastic constants. E x p e r i m e n t a l d a t a are however much too scarce and several new experiments are suggested in these fields.