QUASICRYSTAL DA AKA YI TA HANYAR MURƊA TSARIN CRYSTAL BIYU DA 45°

Crystal tsari ne da ke maimaituwa: ka matsar da shi mataki ɗaya sai ya faɗa kan kansa. Quasicrystal sun karya wannan ƙa’ida. Kamar yadda takardar ta tuna, sun nuna cewa tsari na nesa (long-range order) zai iya kasancewa ba tare da wani maimaitawa ba. Atom ɗinsu suna bin tsari mai tsauri, tabbatacce wanda ke ba da tsarin diffraction masu kaifi — amma da daidaiton juyawa, kamar ninki biyar, takwas, goma ko goma sha biyu, da suke ba za su yiwu ba a crystal mai maimaituwa. An danganta irin wannan tsari da halaye na musamman na electron, haske da na inji.

Matsalar ita ce yawancin quasicrystal an same su ne a wasu gaurayen ƙarafa (alloys) na musamman, ko a matsayin siraran tsari sosai a kan wasu fuskoki na musamman. Hakan yana barin ɗan iko kaɗan kan daidaiton juyawarsu, sinadaransu ko yadda ake gina su cikin na’urori.

Murɗa maimakon ganowa

Ra’ayin da aka bincika a nan shi ne a mai da kusurwar murɗawa kanta maɓallin sarrafawa. Tarin abubuwa masu girma biyu (two-dimensional) da aka murɗa sun riga sun nuna cewa za a iya tilasta daidaiton juyawa da aka hana ta hanyar lissafin siffofi (geometry), amma tsarinsu suna riƙe da juna ne a raunane. Oxide masu sarƙaƙiya sun bambanta: fuskokinsu za su iya haɗuwa ta sinadarai idan sun taɓa juna, kuma su canza tsarinsu na electron a cikin haka.

Shivasheesh Varshney, Bharat Jalan, Richard D. James da wata babbar tawaga a Jami’ar Minnesota, tare da abokan aiki ciki har da Caltech, MIT, Jami’ar Fasaha ta Denmark da Jami’ar Antwerp, sun yi aiki da strontium titanate, wani oxide da atom ɗinsa ke zaune a kan grid mai murabba’i mai faɗin ångström 3.905. Sun shuka siraran tsarin crystal guda a kan wani tsari na sadaukarwa, suka sake su, suka juya su a kusurwoyin da aka zaɓa, suka ɗora su a kan wani tallafi, sannan suka gasa tarin a 900 °C a cikin oxygen.

• Tsari biyu a 45° suna samar da tsari na ninki takwas, mai kusurwa takwas.
• Tsari uku a matakan 30° a jere, da siririn tsari a tsakiya, suna samar da tsari na ninki goma sha biyu, mai kusurwa goma sha biyu.

Aune-aunen X-ray sun nuna cewa kusurwoyin murɗawa sun kai inda aka nufa a cikin ±0.2 digiri, ko wane tallafi ne.

Ganin daidaiton juyawa da aka hana

Electron diffraction yana nuna zobban ɗigo takwas masu tazara daidai ga tarin 45° da goma sha biyu ga tarin tsari uku, kuma ɗigon suna da kaifi, alamar tsari na nesa. Hotunan matakin atom sun dace da shimfiɗar tayal ta lissafi da ke cikin littattafai ta waɗannan quasicrystal: murabba’i da rhombus na 45° a yanayin ninki takwas, da murabba’i da rhombus a rabo na 1 zuwa √2; alwatika, murabba’i da rhombus na 30° a yanayin ninki goma sha biyu.

Tsarin ninki takwas (tsari biyu na 45°) da ninki goma sha biyu (tsari uku na 30°/30°) da aka gani ta electron diffraction, hoton atom da nazarin Fourier, da shimfiɗar tayal da ke cikin juna waɗanda girmansu ke ƙaruwa da 1 + √2 da 2 + √3. — Figure 2, Varshney et al. (2026), arXiv:2610.09222.

Tsare-tsaren kuma suna kama da kansu (self-similar). Gungun tayal suna sake bayyana a ma’auni mafi girma da mafi girma: a yanayin ninki takwas, kowane ƙarni ya fi na baya girma da 1 + √2 ≈ 2.414; a yanayin ninki goma sha biyu, da 2 + √3 ≈ 3.732. Kwaikwayon kwamfuta da ke amfani da mu’amalolin atom da na’ura ta koya (machine-learned) sun nuna cewa tsarin yana tsira daga sassautawa (relaxation) da motsi a zafin ɗaki, kuma wani ma’aunin tsarin quasicrystal yana kaiwa ƙololuwarsa ne kawai a daidai 45°.

Iyaka da ta haɗe, ba kawai an ɗora ba

Gasawa tana da muhimmanci. Kafin ita, wani tsarin saura mai kauri nanomita 1 zuwa 3 yana raba tsarin. Bayanta, na’urar hangen nesa tana nuna iyaka da ke da kaifi a cikin kusan tsarin atom ɗaya, tare da shimfiɗun crystal da ke ci gaba a ƙetarenta. Electron spectroscopy ta bayyana atom na titanium a wani yanayin caji daban (Ti³⁺) a daidai iyakar — alamar ainihin haɗin sinadarai.

Iyakar kuma tana sake fasalin tsarin electron. A tsarin da kaurinsu nanomita 1.5 kawai, sha na X-ray da aka auna a kan yankunan tsari ɗaya da tsari biyu da aka murɗa da ke maƙwabtaka ya nuna cewa iyakar 45° tana sake rarraba orbitals na electron kuma tana ƙarfafa haɗi a ƙetaren iyakar. Lissafi suna nuni ga tsarin ƙananan electric dipoles masu juyawa kamar guguwa a iyakar.

Kusurwa ta musamman ga haske

A ƙarshe, tawagar ta bugi tarin da wani bugun terahertz mai ƙarfi kuma ta leƙa su da hasken laser mai polarization na da’ira. A kusurwoyin murɗawa na tsaka-tsaki, iyakar tana ƙara nata siginar. A daidai 45°, wannan siginar iyakar tana sokewa kuma ba za a iya bambanta ta da ta ƙasan tushe (substrate) ba — kuma bayan gasawa kawai. Kusurwar quasicrystal ta fice a matsayin wani wuri na musamman.

Sabon maɓalli don ƙirƙirar kayayyaki

A wannan hanya, marubutan suka yi jayayya, ba sai an nemo tsarin quasicrystal a wani gauraye na musamman ba: za a iya saita shi da murɗawa, a cikin oxide inda electron, spin da tsarin crystal ke haɗe sosai, kuma a matsar da shi zuwa tallafi daban-daban. Yadda tarin ninki goma sha biyu ke sake fasalin tsarin electron an bar shi ga aiki na gaba.