Formula Bragg. Diffraction da wani sarari raga

Wannan labarin ya gabatar da wani dabara Bragg, karatu ta muhimmanci ga zamani duniya. Mun bayyana hanyoyin for binciken abubuwa da aka sanya yiwu ta gano electron diffraction a kan daskararru.

Kimiyya da rikice-rikice

Gaskiyar cewa daban-daban da al'ummomi ba za su fahimci juna, ko da Turgenev rubuta labari "iyaye da 'ya'ya." Kuma da gaskiya ne wannan: da iyali na zaune a shekara ɗari, da yara girmama dattawa, duk tallafawa juna, sa'an nan a sake - da kuma duk abin da canje-canje. Kuma duk al'amarin a kimiyya. Ba abin mamaki cocin Katolika kamar yadda tsayayya ci gaban da na halitta sanin duk wani kokari zai iya haifar da wani uncontrolled canji a duniya. Daya samu musanya ji na kiwon lafiya, da kuma yanzu da haihuwa mutane sun yi mamaki da suka duba saukar, zũriyarsu wanke hannu kafin cin abinci, da kuma brushing su hakora. Labari Kaka ta musu ne su gyaɗa kansu: "Me ya sa, mu zauna da kyau ba tare da shi, kuma bãbu abin da ta haifi ashirin yara. Kuma duk wannan shi ne your tsarki kawai cutar da kuma daga sharrin daya. "

Daya cikin jarrabawa a wuri na taurari - kuma a yanzu a kan kowane kusurwa, matasa ilimi mutane tattauna da tauraron dan adam da kuma meteors, nesa da kuma yanayin da Milky Way, yayin da mazan ƙarni na fushi: "Maganar banza da wani, abin da yake da amfani da m sarari kuma wani sarari suKe duniyoyin, abin da ke bambanci, a matsayin juyawa Mars kuma Venus zai tafi mafi dankalin turawa ya yi girma, dã ya kasance mafi amfani. "

A nasara da fasaha, da ta samu ta gaskiya cewa da aka sani diffraction grating sarari - kuma a kowane sauran aljihu ne a smartphone. A lokaci guda mazan mutane gunaguni: "Babu wani abu mai kyau ne ba a cikin wadannan sauri saƙonni, ba su da wani abu da cewa wannan wasika." Duk da haka, kamar yadda paradoxical kamar yadda sauti, da masu daban-daban na'urori gane su a matsayin irin wani ba, kusan kamar iska. Kuma 'yan mutane tunani game da sunadaran da suke aiki da kuma babban hanyar da tunanin mutum ya yi wasu biyu ko uku, shẽkara ɗari.

A alfijir karni na ashirin da

A cikin karni na sha tara marigayi, mutãne ne da fuskantar matsalar ilmi da duk bude events. An yi imani da cewa a cikin kimiyyar lissafi da muka riga ya san kome da kome, da kuma ta zauna ita kaɗai don gano bayani. Duk da haka, an gano Planck ta kamfani mai suna Quanta da discontinuity takaice jihohi zahiri kife baya ideas game da tsarin kwayoyin halitta.

Opening fadi daya bayan daya, da masu bincike fizge ideas daga juna hannuwanku. Shiriritar Tashi, gwada, tattauna, sun ƙaryata. Daya tabbatar da abu haifar da daruruwan sabon, kuma akwai da yawa mutane shirye ya nemi amsoshin.

Daya daga jujjũyãwar maki cewa sun canza da ji na duniya, ya bude daga cikin dual yanayin na farko barbashi. Ba tare da shi, da dabara Bragg dã ba su bayyana. A ake kira kalaman-barbashi biyuntakar bayyana dalilin a wasu lokuta, da electron behaves matsayin jiki da ciwon tari (Ina nufin corpuscle, barbashi), da kuma a cikin sauran - kamar ethereal kalaman. Masana kimiyya sun dogon jãyayya, ba tukuna zo a ƙarshe - wannan daban-daban Properties na microworld abubuwa da duka biyu.

Wannan labarin ya bayyana dokar Bragg, wanda ke nufin cewa mu da sha'awar a cikin kalaman Properties na firamare barbashi. Domin da gwani, wadannan tambayoyi su ne ko da yaushe shubuha, saboda shawo kan dokin da oda na nanometers a size, mun rasa yaƙĩni - zo a cikin sakamako da manufa na Heisenberg. Duk da haka, domin mafi dalilai shi rasa isasshe m kimantawa. Saboda haka wajibi ne a fara da bayyana wasu siffofin na Bugu da kari kuma subtraction na talakawa tãguwar ruwa, wanda shi ne mai sauki isa ga tunanin da kuma fahimta.

Waves da sinuses

'Yan mutane a cikin shimfiɗar jariri, da ƙaunar wannan reshe na aljabara kamar yadda trigonometry. Ba tare da kuma cosine, tangent da cotangent suna da nasu tsarin na Bugu da kari, subtraction, da kuma sauran canje. Zai yiwu yara, ba su fahimta da wannan, don haka ban sha'awa ga karatu. Kuma da yawa sun yi mamaki game da dalilin da ya sa yi duk wannan shi ne ya cancanta, a cikin abin da wani ɓangare na rayuwar yau da kullum wannan ilimi za a iya amfani.

A duk ya dogara da yadda na bincike mutane. Wasu mutane rasa ilimi kamar da rana haskakawa a lokacin da rana da kuma da watã da dare, ruwa ne rigar, da wuya dutse. Amma akwai kuma wadanda suke da sha'awar, kamar yadda shirya kome mutum gani. Domin rashin gudanar da bincike da kuma bayyana mafi amfani daga nazarin kalaman kaddarorin ya'ya, Oddly isa, da kimiyyar lissafi na firamare barbashi. Alal misali, electron diffraction ɗã'a ga daidai da wadannan dokoki.

A farkon farawa, aiki a kan tunanin: ka rufe idanunka da kuma bari da kalaman kwashe kansu.

Tunanin wani iyaka sinusoid kumbura kwarin kunya, kumbura kwarin kunya. Babu wani abu a cikin shi ba a canza, da nisa daga saman daya ɗan tutun rairai zuwa wani, daidai ne a matsayin ko'ina kuma. Gangara na line lõkacin da ta ke daga wata iyakar zuwa m, daidai ne a gare kowane yanki na kwana. Idan akwai wani yawan biyu m ba tare da kalaman, sa'an nan da aiki zama mafi rikitarwa. Diffraction a kan wani sarari raga ne kai tsaye dogara a kan Bugu da kari da dama taguwar ruwa. The dokokin hulda dogara da dalilai da dama.

A farko - lokaci. Abin da sassa shãfe biyu masu lankwasa. Idan kalla su daidaita ga karshe millimeter, idan karkata kusassari na masu lankwasa ne m - duk Figures aka ninki biyu, da humps ne biyu sau mafi girma, da kuma m - sau biyu a matsayin mai zurfi. Idan a kan m - a kalla daya kwana da dama a kalla wani, tãguwar ruwa soke juna fita, duk vibrations suna tuba zuwa sifili. Kuma idan da kasoshin lokatan ba daidai kawai jera - wato, a kalla daya kwana da dama a kan Yunƙurin ko fall a cikin sauran, hoton zama quite wuya. Kullum, da dabara qunshi wani Bragg kwana kawai, kamar yadda zai zama bayyana daga baya. Duk da haka, dokokin hulda tsakanin taguwar ruwa don taimaka yi ta ƙarshe mafi cikakken.

Na biyu - mawadãta. Wannan shi ne tsawo daga humps kuma hollows. Idan wani kwana tsawo na daya santimita, da kuma sauran - biyu, sa'an nan suka kamata a saka bi da bi. Wannan ne, idan wani matsakaicin kalaman tsawo na biyu santimita dama tsananin a cikin tãguwar ruwa tare da mafi tsawo na daya santimita, ba su soke juna, amma kawai rage-rage tsawo na farko da kalaman na disturbances. Alal misali, diffraction na electrons dogara a kan oscillation amplitude, wanda kayyade su da makamashi.

Na uku - kudi. Wannan tazara tsakanin m maki da kwana, irin su Maxima ko minima. Idan mitoci ne daban-daban, sa'an nan a wani matsayi biyu masu lankwasa kololuwa daidaita, bi da bi, gaba daya folded. wannan ba shi ne na gaba lokaci faruwa, da karshe iyakar zama m da ƙananan. Sa'an nan a kalla daya kalaman da dama tsananin a kan a kalla daya, ba da mafi ƙasƙanci sakamakon a wannan danniyan. A sakamakon haka, kamar yadda ka sani, shi ne ma sosai hadaddun, amma lokaci-lokaci. Hoto jima ko daga baya sake, da kuma sake biyu Maxima daidaita. Saboda haka, a kan aikace-aikace na tãguwar ruwa tare da daban-daban mitoci bayyana sabon m mawadãta oscillation.

Fourth - shugabanci. Yawancin lokaci, a lokacin da la'akari da biyu irin wannan kalaman (a cikin wannan harka ba tare da kalaman), an yi imani da cewa su ne a layi daya ga juna ta atomatik. Duk da haka, a cikin real duniya abubuwa ne daban-daban, da shugabanci na iya zama wani abu a cikin uku-girma sarari. Saboda haka, kara zuwa ko mu cire zai kawai tãguwar ruwa tafiya a layi daya. Idan sun motsa a gaban kwatance, babu hulda tsakanin su. Dokar Bragg tsaye daidai ne a kan gaskiyar cewa kawai a layi daya bim suna kafa.

Tsangwama da kuma diffraction

Duk da haka, electromagnetic radiation - shi ne ba daidai wani ba tare da kalaman. Huygens 'manufa jihohin da kowane batu na matsakaici ga abin da wavefront ya isa (ko tashin hankali) ne a sakandare tushen siffar zobe tãguwar ruwa. Saboda haka, a kowane lokaci da baza, ce, wani zango na haske a duk sau zoba. Wannan shi ne tsangwama.

Wannan sabon abu ne dalilin cewa haske musamman, da kuma electromagnetic taguwar ruwa kullum iya tanƙwara a kusa da cikas. A karshen al'amari ne ake kira diffraction. Idan mai karatu bai tuna da shi daga makaranta, za mu nuna cewa biyu slits a wani duhu allo, hasken da talakawa fari haske a cikin wata rikitarwa Maxima da minima na haske tsarin, watau tube ba zai zama biyu m, kuma da yawa da sãɓãwar launukansa a tsanani.

Idan tsiri ba irradiated da haske, kuma bombard quite a jiki electrons (ko, misali, alpha barbashi), za mu samu daidai da wannan hoton. A electrons ake diffracted da kuma tsoma baki. Shi ne a cikin wannan bayyana su kalaman yanayi. Ya kamata a lura cewa Bragg diffraction (sau da yawa ake magana a kai kawai Bragg) kunshi a cikin karfi watsi da taguwar ruwa a lokaci-lokaci lattices zo daidai da zamani da ya faru da kuma warwatsa kalaman.

m

Tare da wannan magana, kowane iya samun nasu jam'iyya. Duk da haka, m - tabbataccen reshe na kimiyyar lissafi da cewa karatu da tsarin da kaddarorin da lu'ulu'u, da tabarau da kuma tukwane. Bayyana a kasa ne kaɗai ya sani cewa da zarar cikin masana kimiyya sun ɓullo da wani Dalili na X-ray analysis.

Saboda haka, crystal - ne a jihar da abu a lokacin da nuclei na atoms zauna a da kyau-tsare matsayi a sarari zumunta ga juna, da kuma free electrons a matsayin electron bawo an taƙaita. Babban halayyar da m jiki - periodicity. Idan mai karatu sau daya ne sha'awar kimiyyar lissafi ko sunadarai, mai yiwuwa baba up wani image a kansa na crystal raga na gishiri (ma'adinai sunan - halite, dabara NaCl).

Iri biyu kwayoyin halitta ne sosai kusa contact, kafa a isasshe m tsarin. Sodium da kuma chloro interleaved fom in duk uku girma na cubic raga, da tarnaƙi daga waxanda suke perpendicular zuwa juna. Saboda haka, lokaci (ko naúrar cell) - wani shigen sukari, cikinsa da uku vertices dokoki sunadaran daya jinsin, da sauran uku - wani. A cajin juna irin wannan cubes, yana yiwuwa a samu wani iyaka crystal. All kwayoyin halitta suna located cikin biyu ma'aunai suna lokaci zuwa lokaci sa crystallographic jirgin sama. Wannan shi ne, naúrar cell wata uku-girma, amma daya jam'iyyar, maimaita sau da yawa (a cikin manufa hali - wani iyaka yawan sau), shi Forms guda surface na ƙarau. Wadannan saman suna da yawa kuma suna layi daya da juna.

A interplanar nesa - wani muhimmin nuna alama cewa ƙayyade, misali, m jihar zaman lafiya. Idan a biyu girma, wannan nesa ne karami, da uku - a manyan, sa'an nan abu ne readily exfoliates. Yana bayyana, misali, Mica, wanda ya maye gurbin baya mutane gilashin a cikin windows.

Lu'ulu'u da kuma ma'adanai

Duk da haka, rock gishiri - mai sauqi qwarai misali: iri biyu kawai kwayoyin zarra da hujjõji cubic fasali. Sashe na Geology, da ake kira mineralogy, karatu da crystal jiki. Su peculiarity shi ne cewa daya sinadaran dabara hada 10-11 jinsunan kwayoyin halitta. Kuma suna da tsarin ne musamman hadaddun: tetrahedrons, cubes da a haɗa vertices a kusurwoyi mabambanta samar da wata porous tashoshi na daban-daban siffofi, tun fil azal, hadaddun dara ko wandar-wandar tafiyar maciji connection. Irin wannan, alal misali, tsarin ne wuce yarda da kyau, quite rare da zalla Rasha ornamental dutse charoite. Ya m alamu haka lafiya ba za su iya kunna kai - Saboda haka sunan ma'adinai. Amma ko da a cikin rikitarwa tsarin da ba a layi daya to juna crystallographic jirgin sama.

Wannan damar saboda gaban diffraction na electrons a crystal raga don gane da tsarin.

Tsari da kuma electrons

Don mayalwaci bayyana hanyoyin da karatu da tsarin al'amari, dangane da diffraction na electrons, wanda zai iya tunanin cewa bukukuwa jefa cikin akwatin. Sa'an nan ƙidaya nawa bukukuwa bounced baya da kuma a abin da kwana. Sa'an nan, da shugabanci a cikinsa ya fi na bukukuwa bouncing, hukunci a kan tsari akwatin.

Hakika, wannan shi ne wani m ra'ayin. Amma bisa ga wannan danyen model, da shugabanci a cikin abin da mafi girma da yawan kwallaye bouncing - a diffraction ganiya. Saboda haka, electrons (ko X haskoki) bombarding surface na ƙarau. Wasu daga cikin su ne "makale" a cikin al'amarin, kuma amma wasu suna rubuta. Bugu da ƙari, suna nuna ne kawai daga crystallographic jirage. Tun lokacin da jirgin sama ne ba daya ba, amma da yawa daga gare su, sa'an nan kuma kara kawai nuna tãguwar ruwa ne a layi daya ga juna (mu tattauna a sama). Kamar wancan shi samu alama a cikin wani bakan, inda gani tsanani dogara a kan kwana na abin da ya faru. Diffraction ganiya nuna kasancewar wani jirgin sama a wani kwana karatu. A sakamakon hoton da aka bincikar ya sami ainihin tsarin da crystal.

dabara

A analysis ne da za'ayi a cewar wasu dokoki. Suna dogara ne a kan wata dabara Bragg. Yana kama da wannan:

2D sinθ = nλ, inda:

• d - da interplanar jerawa.
• θ - zamewa kwana (da kwana karin zuwa kwana na gani).
• n - da oda na diffraction ganiya (tabbatacce lamba, Ina nufin 1, 2, 3 ...);
• λ - zango na aukuwa radiation.

Kamar yadda mai karatu zai iya gani, kwana ba dauka ko da daya da aka samu kai tsaye a cikin nazari da kuma ƙarin cikinta. Ya kamata mu ma bayyana game da darajar n, wanda nufin da manufar "diffraction ganiya." Tsangwama The dabara kuma ya ƙunshi wani m lamba da cewa ƙayyade domin na matsakaicin kiyaye.

A illuminance na allo a biyu-tsaguwa gwaji, misali, ya dogara da cosine hanya bambanci. Tun da cosine - aiki akai-akai, bayan da duhu allo, a cikin wannan yanayin akwai ba kawai babban ganiya, amma kuma 'yan more suma ratsi a kan sãsanninta. Muna zaune a cikin wani manufa duniya, wanda shi ne gaba daya amenable to ilmin lissafi dabarbari, wadannan makada zai zama wani iyaka lamba. Duk da haka, a gaskiya yawan lura haske yankunan da yaushe iyakance kuma dogara a kan zango, tsaguwa nisa, da kuma nĩsa a tsakãninsa da tushen haske.

Tun diffraction - a kai tsaye sakamako na kalaman yanayin haske da na farko barbashi, Ina nufin ko suna da na tsangwama, sa'an nan da dabara ya hada da wani Bragg domin diffraction ganiya. Af, wannan al'amari ya sa shi sosai wuya a farko gwaji lissafin. A lokacin, dukan rikirkida alaka reversals na jirage da kuma lissafi na mafi kyau duka tsarin daga diffraction juna, yi ta inji. Su lissafi daidai da kololuwa raba mamaki, da kuma abin da - na biyu ko na uku domin na babban Lines a jere.

Kafin gabatarwar kwakwalwa a wurare dabam dabam tare da wani sauki dubawa (mun gwada sauki, tun da dama lissafin shirin - tukuna nagartaccen kayan aikin) shi aka yi duka da hannu. Kuma duk da dangi brevity na wanda yana da wani lissafi na Bragg, da gaskiya, don tabbatar da gaskiya da dabi'u samu, shi ya ɗauki lokaci mai tsawo da kuma kokarin. Masana kimiyya sun gwada da kuma retested - ba wormed hanyarsa ta zuwa ga inda wani maras babba matsakaicin, wanda zai iya ganimar da lissafin.

Ka'idar da yi

Wonderful samu, m biyu Wolfe da Bragg ya shiga hannun 'yan adam ne ba makawa ga kayan aiki da nazari na boye har Tsarin daskararru. Duk da haka, kamar yadda muka sani, ka'idar - abu mai kyau, amma in yi ta ne ko da yaushe kadan daban-daban. Just sama shi ne wani tambaya na lu'ulu'u ne. Amma wani ka'idar yana nufin manufa hali. Wannan shi ne iyaka aibi-free sarari a cikin abin da tsarin maimaitawa dokokin ba su keta.

Duk da haka, da real, ko da sosai tsabta da kuma girma a cikin dakin gwaje-gwaje, crystalline abu lahani yawaita. Daga cikin halitta tsarin samu cikakken misali - a babban rabo mai girma. Yanayi Bragg (bayyana ta sama dabara) zuwa xari bisa dari daga cikin lokuta da shafi real crystal. Domin su, a cikin wani hali, akwai irin wannan aibi, kamar yadda wani surface. Kuma bari mai karatu bai dame da Wauta na wasu daga cikin kalamai: surface ne ba kawai tushen lahani, amma kuma da lahani.

Alal misali, da samar da makamashi na shaidu ta kafa a cikin crystal ne daban-daban daga abin da darajar iyakar zones. Wannan yana nufin cewa wajibi ne a gabatar da wani irin yiwuwa kuma gibba. Wannan shi ne, a lokacin da experimenter kuranye electron gani bakan ko X-ray daga m jiki, su sami ba kawai kan kusurwa, ya kuma kwana da kuskure. Alal misali, θ = 25 ± 0.5 digiri. A jadawali aka bayyana ta da cewa da diffraction ganiya (da dabara na wanda shine Bragg lissafi) yana da nisa, kuma shi ne wani tsiri, kuma ba tsananin cikakken bakin ciki line a wuri na darajar.

Myths da kurakurai

Sabõda haka, shi dai itace, duk da lakabi, ba gaskiya ba ne?! Don wasu har. Idan kun yi awo da zazzabi da kanka da kuma samun 37 a ma'aunin zafi da sanyio, wannan ba gaba ɗaya cikakke. Jikinka zafin jiki ne daban-daban daga m dabi'u. Amma ku babban abu cewa ta ke hauka cewa kun kasance majinyata, kuma yana da lokaci da za a bi. Kuma ku da likita ba kome cewa a gaskiya da ma'aunin zafi da sanyio nuna 37.029.

Kuma a cikin kimiyya - Muddin kuskure ba ya hana yin tabbataccen karshe, shi ne a dauki la'akari, amma mayar da hankali ne a kan primary muhimmancin. Bugu da kari, statistics nuna: har da kuskure ne kasa da kashi biyar bisa dari, shi za a iya bari. A sakamakon samu a gwaje-gwajen da na wanda da wadannan yanayin Bragg ma da wani kuskure. Masana kimiyya wanda ake yi lissafin, shi ne yawanci nuna. Duk da haka, domin takamaiman aikace-aikace, a cikin wasu kalmomi, fahimtar abin da tsarin a crystal, da kuskure ne ba da muhimmanci sosai (idan dai shi ne kananan).

Shi ne ya kamata a lura da cewa kowane na'urar, ko da a cikin makaranta line, akwai ko da yaushe da rashin tabbas. Wannan adadi daukan la'akari da ma'aunai da kuma, idan ya cancanta, a hada a total kuskure sakamakon.