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Ape­ri­od­ic crys­tals are long range or­dered struc­tures which lack trans­la­tion­al in­vari­ance. They are found in a large va­ri­ety of sys­tems (min­er­als, or­gan­ic com­pounds, sin­gle el­e­ment un­der pres­sure, ox­ides, fer­ro-electrics, in­ter­metal­lic com­pounds) and en­com­pass in­com­men­su­rate­ly mod­u­lat­ed struc­tures, in­com­men­su­rate com­pos­ites and qua­sicrys­tals.


The struc­ture de­ter­mi­na­tion of ape­ri­od­ic crys­tals and the in­flu­ence of the ape­ri­od­ic or­der on their phys­i­cal prop­er­ties have made tremen­dous progress in re­cent years. How­ev­er the high di­men­sion­al de­scrip­tion and su­per­space ap­proach used to de­scribe the atom­ic struc­ture of ape­ri­od­ic crys­tal re­mains dif­fi­cult to grasp for the non spe­cial­ist.

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To promote this very specific approach, the Com­mis­sion on Ape­ri­od­ic Crys­tals and the Com­mis­sion on Teach­ing Crys­tal­log­ra­phy of the In­ter­na­tion­al Union of Crys­tal­log­ra­phy (IU­Cr) have de­cid­ed to or­ga­nize a school on Ape­ri­od­ic Crys­tals. The school is jointly organised with the CNRS and European C-MetAC network.

The tar­get­ed au­di­ence is clear­ly a non-spe­cial­ist one: Phd stu­dents, young or ex­pe­ri­enced sci­en­tists work­ing in the field of crys­tal­log­ra­phy, chem­istry, ma­te­ri­al sci­ence or sol­id state physic and will­ing to have a ba­sic un­der­stand­ing of ape­ri­od­ic crys­tals.The school will be or­ga­nized on 5 days in Normandy, north-west of France. Ex­perts in the field of ape­ri­od­ic crys­tal will give lec­tures, in a tu­to­ri­al way and on a step by step ba­sis. The num­ber of par­tic­i­pants will be lim­it­ed to 40 in or­der to fa­cil­i­tate ex­changes. Af­ter an in­tro­duc­tion to the high di­men­sion­al con­cept, the ba­sis of the struc­ture de­ter­mi­na­tion of ape­ri­od­ic crys­tal will be in­tro­duced for each class of ape­ri­od­ic crys­tals. Var­i­ous ex­am­ples will then be pre­sent­ed, to­geth­er with overviews on phase tran­si­tions, phonons and pha­sons, sim­u­la­tions and ape­ri­od­ic crys­tal sta­bil­i­ty.Tu­to­ri­al in small groups (20) will al­so be or­ga­nized in or­der to prac­tice the no­tions learned in the lec­tures.

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