▁a ▁mass ▁of ▁a ▁cer am ic ▁greatly ▁increases . ▁ ▁So ▁in ▁general , ▁nan oph ase ▁materials ▁have ▁greater ▁surface ▁areas ▁than ▁that ▁of ▁a ▁similar ▁mass ▁material ▁at ▁a ▁larger ▁scale . ▁ ▁This ▁is ▁important ▁because ▁if ▁the ▁surface ▁area ▁is ▁very ▁large ▁the ▁particles ▁can ▁be ▁in ▁contact ▁with ▁more ▁of ▁their ▁surr ound ings , ▁which ▁in ▁turn ▁increases ▁the ▁react ivity ▁of ▁the ▁material . ▁ ▁The ▁react ivity ▁of ▁a ▁material ▁changes ▁the ▁material ' s ▁mechanical ▁properties ▁and ▁chemical ▁properties , ▁among ▁many ▁other ▁things . ▁ ▁This ▁is ▁especially ▁true ▁in ▁nan oph ase ▁cer am ics . ▁ ▁Properties ▁of ▁Nan oph ase ▁Cer am ics ▁Nan oph ase ▁cer am ics ▁have ▁unique ▁properties ▁than ▁regular ▁cer am ics ▁due ▁to ▁their ▁improved ▁react ivity . ▁ ▁Nan oph ase ▁cer am ics ▁exhib it ▁different ▁mechanical ▁properties ▁than ▁their ▁counter part ▁such ▁as ▁higher ▁hard ness , ▁higher ▁f ract ure ▁t ough ness , ▁and ▁high ▁du ct ility . ▁ ▁These ▁properties ▁are ▁far ▁from ▁cer am ics ▁which ▁behave ▁as ▁brit t le , ▁low ▁du ct ile ▁materials . ▁ ▁T itan ium ▁D io x ide ▁ ▁T itan ium ▁dio x ide ▁( ), ▁has ▁been ▁shown ▁to ▁have ▁increased ▁hard ness ▁and ▁du ct ility ▁at ▁the ▁nan osc ale . ▁ ▁In ▁an ▁experiment , ▁gra ins ▁of ▁tit an ium ▁dio x ide ▁that ▁had ▁an ▁average ▁size ▁of ▁ 1