Современные методы исследования и описания кристаллических структур - u045

1

FBGBKL?JKL<H H;S?=H B KI?PB:EVGH=H

H;J:AH<:GBY

JHKKBCKDHC N?>?J:PBB

<hjhg_`kdbc ]hkm^Zjkl\_gguc mgb\_jkbl_l

Obfbq_kdbc nZdmevl_l

dZn_^jZ g_hj]Zgbq_kdhc obfbb

KH<J?F?GGU? F?LH>U BKKE?>H<:GBY B HIBK:GBY

DJBKL:EEBQ?KDBO KLJMDLMJ

F_lh^bq_kdb_ mdZaZgby ^ey klm^_glh\ dmjkZ ^g_\gh]h hl^_e_gby

obfbq_kdh]h nZdmevl_lZ

KhklZ\bl_ev

dZg^ obf gZmd

K:FHCEH< : F

<HJHG?@

<<?>?GB?

2

< kh\j_f_gghc obfbb hkh[_ggh g_hj]Zgbq_kdhc ij_^klZ\e_gby h kljmdlmj_ b ijhkljZgkl\_gghf kljh_gbb j_Zevguo \_s_kl\ b]jZxl \Z`g_crmx jhev Gb jZajZ[hldZ ijbgpbibZevguo nmg^Zf_glZevguo ijh[e_f h[s_c nbabq_kdhc b g_hj]Zgbq_kdhc obfbb gb j_r_gb_ [hevrbgkl\Z ijbdeZ^guo obfbq_kdbo aZ^Zq ijZdlbq_kdb g_fukebfu [_a m]em[e_ggh]h ihagZgby \k_o Zki_dlh\ kljh_gby \_s_kl\Z b ij_`^_ \k_]h _]h ]_hf_ljbq_kdh]h kljh_gby ijhkljZgkl\_ggh]h jZkiheh`_gby Zlhfh\

Ihke_^gb_ ^_kylbe_lby hlf_q_gu klj_fbl_evguf ijh]j_kkhf \ jZa\blbb lhqguo bgkljmf_glZevguo f_lh^h\ bamq_gby ijhkljZgkl\_ggh]h kljh_gby obfbq_kdbo kh_^bg_gbc - j_gl]_gh]jZnbq_kdh]h ZgZebaZ g_cljhgh]jZnbb we_dljhgh]jZnbb we_dljhgghc b lmgg_evghc fbdjhkdhibb <k_ wlh kihkh[kl\h\Zeh ]em[hdhfm ijhgbdgh\_gbx kljmdlmjguo ij_^klZ\e_gbc ijZdlbq_kdb \h \k_ h[eZklb obfbb b fhe_dmeyjghc [bheh]bb ;_a wlbo ij_^klZ\e_gbc g_\hafh`gh mki_rgh_ jZa\blb_ fgh]bo jZa^_eh\ nbabdb fZl_jbZeh\_^_gby ]_hobfbb b fbg_jZeh]bb

;ukljuc jhkl h[t_fZ ^hklh\_jguo agZgbc h ijhkljZgkl\_gghf jZkiheh`_gbb Zlhfh\ \ kZfuo jZaebqguo \_s_kl\Zo y\ey_lky h^ghc ba hkgh\guo agZf_gZl_evguo q_jl kh\j_f_ggh]h _kl_kl\hagZgby <k_ kh\j_f_ggu_ mq_[gbdb b nmg^Zf_glZevgu_ fhgh]jZnbb ih g_hj]Zgbq_kdhc obfbb \ lhf beb bghf \b^_ bkihevamxl j_amevlZlu kljmdlmjguo bkke_^h\Zgbc gZdhie_ggu_ aZ ihke_^gb_ ^_kylbe_lby

H^gZdh bgl_gkb\gh_ jZa\blb_ wdki_jbf_glZevghc b l_hj_lbq_kdhc [Zau kljmdlmjghc obfbb qZklvx dhlhjhc y\ey_lky djbklZeehobfby \u^\b]Z_l gh\u_ aZ^Zqb b lj_[m_l khhl\_lkl\mxs_c w\hexpbb b \ f_lh^bd_ ij_ih^Z\Zgby < dmjk_ djbklZeehobfbb h^gZ ba lZdbo aZ^Zq aZdexqZ_lky \ lhf qlh[u ^hklZlhqgh ihegh b ]em[hdh ho\Zlblv hkgh\gu_ aZdhghf_jghklb kljh_gby djbklZeeh\ b dhgdj_lgu_ k\_^_gby h djbklZeebq_kdbo kljmdlmjZo \Z`g_crbo deZkkh\ obfbq_kdbo kh_^bg_gbc

Ohjhrh ba\_klgh qlh \k_ k\_^_gby h[ Zlhfgh-ijhkljZgkl\_gghf kljh_gbb \_s_kl\Z djbklZeehobfby ihemqZ_l ]eZ\guf h[jZahf \ j_amevlZl_ ^bnjZdpbhgguo b ij_`^_ \k_]h j_gl]_ghkljmdlmjguo bkke_^h\Zgbc djbklZeeh\ Kbkl_fZlbaZpby wlbo

^Zgguo mklZgh\e_gb_ h[sbo b qZklguo aZdhghf_jghkl_c \ kljh_gbb djbklZeeh\

ZgZeba aZ\bkbfhklb kljh_gby djbklZeeh\ hl bo obfbq_kdh]h khklZ\Z b ^Ze__ nbabdh- obfbq_kdbo k\hckl\ djbklZeeh\ hl bo kljh_gby - wlh h[eZklv djbklZeehobfbb H^gZdh ^_lZevgh_ jZkkfhlj_gb_ fh^_e_c dhlhju_ \ gZklhys__ \j_fy bkihevamxlky ^ey hibkZgby djbklZeebq_kdbo kljmdlmj j_Zevguo \_s_kl\ p_e_khh[jZagh ijh\_klb

3

kh\f_klgh k ZgZebahf hkgh\guo nbabq_kdbo ijbgpbih\ e_`Zsbo \ hkgh\_ bgkljmf_glZevguo f_lh^h\ ijbf_gy_fuo ^ey wdki_jbf_glZevgh]h bkke_^h\Zgby wlbo \_s_kl\ < gZklhys_f ihkh[bb ijb\_^_gh djZldh_ hibkZgb_ hkgh\guo wdki_jbf_glZevguo f_lh^h\ bkke_^h\Zgby djbklZeebq_kdbo kljmdlmj Z lZd`_ ^Zxlky ij_^klZ\e_gby h l_o l_hj_lbq_kdbo fh^_eyo kljh_gby djbklZeebq_kdbo l_e dhlhju_ fh`gh ihkljhblv gZ hkgh\Zgbb ihemq_gguo hiulguo ^Zgguo

=E:<: J?GL=?GH=J:NBQ?KDBC :G:EBA

1.1. F?LH> J?GL=?GH<KDH=H :G:EBA:

Ijb bkke_^h\Zgbb g_hj]Zgbq_kdbo l\_j^uo l_e \hagbdZ_l g_h[oh^bfhklv mklZgh\blv dhebq_kl\h nZa \ bamqZ_fhc kbkl_f_ kbg]hgbx \b^ kbff_ljbb kljh_gb_ we_f_glZjguo yq__d nZa \_ebqbgu iZjZf_ljh\ we_f_glZjguo yq__d obfbq_kdbc khklZ\ lbi j_Zevghc kljmdlmju djbklZeeZ ijbjh^m nZau - y\ey_lky eb bkke_^m_fh_ \_s_kl\h nZahc ihklhyggh]h beb i_j_f_ggh]h khklZ\Z \ ihke_^g_f kemqZ_ - h[eZklv ]hfh]_gghklb nZau kl_i_gv mihjy^hq_gghklb kljmdlmju \_ebqbgm djbklZeeblh\ \ ihebdjbklZeebq_kdhf fZl_jbZe_ fZ]gblgmx kljmdlmjm kh_^bg_gby b fgh]h_ ^jm]h_

H^gbf ba f_lh^h\ iha\heyxsbo ^hklZlhqgh mki_rgh j_rZlv ih^h[gu_ aZ^Zqb y\ey_lky j_gl]_gh]jZnbq_kdbc ZgZeba

J_gl]_gh\kdbfb emqZfb gZau\Zxlky we_dljhfZ]gblgu_ dhe_[Zgby k ^ebghc \hegu λ hl -3 ^h gf >ey bamq_gby kljmdlmju djbklZeeh\ ijbf_gyxl j_gl]_gh\kdb_ emqb k λ

≈ gf IhdZaZl_ev ij_ehfe_gby j_gl]_gh\kdbo emq_c f_gvr_ ohly b fZeh hlebqZ_lky hl g__

q = 1 − 1,3 ×10-5 ρλ2,

( 1.1 )

]^_ ρ - iehlghklv \_s_kl\Z \ ]/kf3, λ - ^ebgZ \hegu j_gl]_gh\kdh]h baemq_gby \ gf <\b^m [ebahklb q d _^bgbp_ nhdmkbjh\Zlv j_gl]_gh\kdb_ emqb ijb ihfhsb dZdbo- eb[h ebga g_\hafh`gh < j_gl]_gh\kdhc hilbd_ imqdb nhjfbjmxlky qZs_ \k_]h k ihfhsvx ^bZnjZ]f <hafh`gh b bkihevah\Zgb_ a_jdZe k iheguf \g_rgbf hljZ`_gb_f b

^bnjZdpbhgguo f_lh^h\ nhdmkbjh\Zgby imqdh\

Bklhqgbdhf j_gl]_gh\kdh]h baemq_gby kem`bl we_dljhggZy j_gl]_gh\kdZy ljm[dZ < g_c we_dljhgu bkimkdZ_fu_ gZdZe_gguf dZlh^hf \hevnjZfh\hc gblvx beb kibjZevx

mkdhjyxlky we_dljbq_kdbf ihe_f b gZijZ\eyxlky gZ f_lZeebq_kdbc Zgh^ Wg_j]by we_dljhgh\ ijb bo j_adhf lhjfh`_gbb \ \_s_kl\_ Zgh^Z ij_h[jZam_lky \ nhlhgu j_gl]_gh\kdh]h baemq_gby

hν = E1 − E2 ,

( 1.2 )

]^_ E1 , E2 - wg_j]by we_dljhgh\ khhl\_lkl\_ggh ^h b ihke_ khm^Zj_gby k Zgh^hf

MIII

2

FZdkbfZevgZy qZklhlZ nmax fbgbfZevgZy ^ebgZ \hegu lmin khhl\_lkl\m_l iheghc

hklZgh\d_ we_dljhgh\ ( E2 = 0 ).
hnmax = hc/lmin = E1 = eU,	( 1.3 )

]^_ U - mkdhjyxs__ gZijy`_gb_

Ihkdhevdm E2 fh`_l bf_lv ex[mx \_ebqbgm f_gvrmx E1 lh g_ij_ju\guc ki_dlj kh klhjhgu ^ebgguo \heg h]jZgbq_g ebrv ih]ehs_gb_f fy]dbo emq_c \ fZl_jbZe_ hdhrdZ ljm[db b \ \ha^mo_

?keb mkdhj_ggu_ we_dljhgu h[eZ^Zxl wg_j]b_c [hevr_c ihjh]Z \ha[m`^_gby l _

^hklZlhqghc qlh[u \u[blv ba ZlhfZ we_dljhg gZoh^ysbcky gZ \gmlj_gg_c h[hehqd_ gZ nhg_ g_ij_ju\gh]h ki_dljZ \hagbdZ_l ebgby oZjZdl_jbklbq_kdh]h j_gl]_gh\kdh]h baemq_gby We_dljhgu ZlhfZ i_j_oh^y k \g_rgbo h[hehq_d bf_xsbo [hevrmx wg_j]bx

E gZ \ZdZglgh_ f_klh \h \gmlj_gg_c h[hehqd_ bkimkdZxl nhlhgu

hn = E - E0

( 1.4 )

<_ebqbgZ hij_^_ey_lky oZjZdl_jghc ^ey dZ`^h]h we_f_glZ kbkl_fhc _]h wg_j]_lbq_kdbo mjh\g_c Ebgbb ki_dljZ jZa^_eyxlky gZ k_jbb K, L, M, N ... \ aZ\bkbfhklb hl lh]h k dZdhc h[hehqdb [ue m^Ze_g we_dljhg <gmljb dZ`^hc k_jbb bf__lky g_kdhevdh ebgbca1, a2 ..., b1, b2 ... \ khhl\_lkl\bb k mjh\g_f k dhlhjh]h kh\_jrbeky wg_j]_lbq_kdbc i_j_oh^

GZb[he__ bgl_gkb\gufb y\eyxlky ebgbb Ka1 i_j_oh^ we_dljhgZ LIII - KI ) b [ebadZy d g_c ih bgl_gkb\ghklb gh [he__ keZ[Zy ebgby Ka2 i_j_oh^ we_dljhgZ LII - KI ).

Bgl_gkb\ghklv ebgbb Kb1 i_j_oh^ we_dljhgZ - KI ) khklZ\ey_l - 25 % bgl_gkb\ghklb Ka1 >jm]b_ ebgbb bf_xl _s_ f_gvrmx bgl_gkb\ghklv QZklhlZ dZdhc- eb[h ebgbb baf_gy_lky ijb i_j_oh^_ hl h^gh]h we_f_glZ d ^jm]hfm ih aZdhgm Fhaeb

Ö n = (Z - s ),

( 1.5 )

]^_ Z - aZjy^ y^jZ c b s - ihklhyggu_

< j_gl]_ghkljmdlmjghf ZgZeba_ \ dZq_kl\_ fhghojhfZlbq_kdh]h baemq_gby qZs_

\k_]h bkihevamxlky ebgbb Ka1 b Ka2 f_lZeeh\ hl ojhfZ Z ^h fheb[^_gZ Z =

^ebgu \heg dhlhjuo e_`Zl \ bgl_j\Ze_ hl ^h gf

Wdki_jbf_glZevgu_ b l_hj_lbq_kdb_ hkgh\u j_gl]_ghkljmdlmjgh]h b nZah\h]h ZgZebaZ l\_j^uo l_e [ueb aZeh`_gu \ -191 ]] \ jZ[hlZo F EZmw1 b _]h

3

khljm^gbdh\ AgZy qlh fhev NaCl ] aZgbfZ_l \ l\_j^hf khklhygbb h[t_f jZ\guc kf3 b qlh \ wlhf h[t_f_ kh^_j`blky qbkeh :\h]Z^jh NA= 6,023×1023 dZ`^h]h ba bhgh\ Na+ b Cl− Z \k_]h ×1024 bhgh\ e_]dh jZkkqblZlv kj_^gb_ agZq_gby f_`Zlhfguo jZkklhygbc r0 = a/2, ijbgbfZy qlh bhgu Na+ b Cl− ihhq_j_^gh aZgbfZxl maeu dm[bq_kdhc yq_cdb \ djbklZeebq_kdhc kljmdlmj_ NaCl GZ hkgh\Zgbb wlh]h ^hims_gby ihemqZ_lky

r0	=	26 ,9		= 2,8 × 10	− 8	ñì	= 0,2 8í ì	( 1.6 )
		3	× 10 2 4
		1,2

LZdbf h[jZahf ihemq_ggZy \_ebqbgZ ^ey r0 khbaf_jbfZ k ^ebghc \hegu oZjZdl_jbklbq_kdh]h j_gl]_gh\kdh]h baemq_gby D - k_jbb Bkoh^y ba mkeh\by ^bnjZdpbb

	1 ≤	U 0	≤ 1 0	( 1.7 )
		λ

F EZmw ij_^iheh`be qlh \ khhl\_lkl\bb k aZdhgZfb ^bnjZdpbb k\_lZ

1 FZdk L_h^hj N_ebdk nhg EZmw - 1960 ) - g_f_pdbc nbabd eZmj_Zl Gh[_e_\kdhc ij_fbb H[eZklb bkke_^h\Zgby l_hjby bgl_jn_j_gpbb b ^bnjZdpbb k\_lZ

Hkgh\gh_ ^hklb`_gb_ EZmw - ij_^kdZaZgb_ ^bnjZd-pbhgghc dZjlbgu ijb ijhoh`^_gbb kd\hav djbklZeebq_kdmx j_r_ldm j_gl]_gh\kdbo emq_c Wdki_jbf_gl ih^l\_j^b\rbc ]bihl_am EZmw [ue hkms_kl\e_g < Njb^jbohf b I Dgbiibg]hf \ Fxgo_gkdhf mgb\_jkbl_l_ >bnjZdpbhggu_ dZjlbgu hl Zlhfh\ djbklZeeZ k l_o ihj gZau\Zxl eZmw]jZffZfb

djbklZee \ qZklghklb oehjb^Z gZljby fh`_l kem`blv \ dZq_kl\_ ^bnjZdpbhgghc j_r_ldb ^ey j_gl]_gh\kdbo emq_c Wdki_jbf_gl ih^l\_j^b\rbc ]bihl_am EZmw [ue [e_klys_ hkms_kl\e_g < Njb^jbohf b I

Dgbiibg]hf \ Fxgo_gkdhf mgb\_jkbl_l_ J_amevlZlu wlh]h hiulZ iha\hebeb jZkdjulv kljmdlmjm dZf_gghc kheb

MJ:<G?GB? <MEVN: - ;JW==:1.

4

HljZ`_gb_ \b^bfuo emq_c hl a_jdZeZ dZd ba\_klgh fh`_l bf_lv f_klh ih^ ex[uf m]ehf ijbq_f m]he iZ^_gby jZ\_g m]em hljZ`_gby < kemqZ_ ©hljZ`_gbyªj_gl]_gh\kdbo emq_c hl djbklZeeZ m]he iZ^_gby lh`_ jZ\_g m]em hljZ`_gby h^gZdh \ wlhf kemqZ_ hljZ`_gb_ \hafh`gh g_ ih^ ex[uf m]ehf ©HljZ`_ggucª fhghojhfZlbq_kdbc emq

j_ne_dk k nbdkbjh\Zgghc ^ebghc \hegu λ hljZ`Z_lky iZd_lhf ^Zgguo iZjZee_evguo djbklZeebq_kdbo iehkdhkl_c lhevdh ih^ kljh]h hij_^_e_ggufb m]eZfb ih^ ^jm]bfb `_ m]eZfb bf__l f_klh ih]ZkZgb_ Ijb ^jm]hc ^ebg_ \hegu λ1 hljZ`_gb_ hl l_o `_ iehkdhkl_c ( hkl ) ijhbahc^_l ih^ ^jm]bfb lh`_ kljh]h hij_^_e_ggufb m]eZfb

GZf g_h[oh^bfh jZah[jZlv ijbqbgu lZdh]h hkh[h]h ih\_^_gby j_gl]_gh\kdbo emq_c b \u\_klb gZ wlhc hkgh\_ nmg^Zf_glZevgh_ mjZ\g_gb_ hibku\Zxs__ wlhl ijhp_kk - mjZ\g_gb_ <mevnZ - ;jw]]Z

Imklv iZjZee_evgu_ j_gl]_gh\kdb_ emqb 1-6 gZijZ\e_gu ih^ m]ehf α d iehkdhklyf djbklZeeZ oZjZdl_jbamxsbfky bg^_dkZfb Fbee_jZ ( hkl ) b hlklhysbf ^jm] hl ^jm]Z gZ jZkklhygbb dhkl ( jbk < hlebqb_ hl \b^bfuo

emq_c hljZ`Z_fuo ih\_joghklvx a_jdZeZ ijb ex[hf m]e_ iZ^_gby ijbq_f m]he

1>Zggh_ mjZ\g_gb_ \u\_^_gh \ ] Zg]ebckdbfb mq_gufb Mbevyfhf =_gjb ;jw]]hf hlphf b Mbevyfhf Ehj_gphf ;jw]]hf kughf G_aZ\bkbfh hl gbo d ZgZeh]bqghfm mjZ\g_gbx ijbr_e ijhn_kkhj Fhkdh\kdh]h mgb\_jkbl_lZ Xjbc <bdlhjh\bq <mevn ^ey h[tykg_gby hiulZ F EZmw

5

Jbk Ko_fZ ihykgyxsZy \u\h^ mjZ\g_gby <mevnZ - ;jw]]Z

iZ^_gby jZ\_g m]em hljZ`_gby j_gl]_gh\kdb_ emqb ijhgbdZxl \ ]em[v

djbklZeeZ b ©hljZ`_gb_ª ijhbkoh^bl g_ lhevdh hl ih\_joghklb gh b hl gb`_e_`Zsbo iehkdhkl_c jbk Z [ A^_kv njhgl iZ^Zxsbo emq_c h[hagZq_g HH’ njhgl

6

©hljZ`_gguoª - HH’’ . Ba jbkmgdZ \b^gh qlh dZ`^uc ke_^mxsbc emq gZijbf_j 2,

^he`_g ijhclb imlv gZ 2x [hevrbc ih

kjZ\g_gbx k ij_^u^msbf \ gZr_f kemqZ_ emqhf 1. Ijb wlhf hq_\b^gh qlh x = d sinΘ ]^_ Θ - m]he iZ^_gby b hljZ`_gby emq_c Gh g_ \kydbc m]he α y\ey_lky [jw]]h\kdbf m]ehf Θ ^ey dhlhjh]h \hafh`gh h[jZah\Zgb_ ©hljZ`_ggh]hªj_ne_dkZ LZd dZd \k_ emqb f_`^m njhglhf iZ^_gby HH’ b njhglhf hljZ`_gby ijhoh^yl jZagu_ imlb b m njhglZ hljZ`_gby hgb ^he`gu bgl_jn_jbjh\Zlv lh h[jZah\Zlvky hljZ`_gguc j_ne_dk fh`_l lhevdh \ lhf kemqZ_ _keb j_amevlbjmxsZy Zfieblm^Z \k_o emq_c [m^_l hlebqgZ hl gmey Z ijZdlbq_kdb - ^hklZlhqgh agZqbl_evgZ qlh[u [ulv aZj_]bkljbjh\Zgghc Ijb hljZ`_gbb ijbfblb\ghc j_r_ldhc h[gZjm`b\Z_lky qlh ^ey wlh]h 2x ^he`gh [ulv jZ\gh p_ehfm qbkem ^ebg \heg, beb nλ. Lh]^Z

n λ = 2 dhkl sinΘ	( 1.8 )
LZdbf h[jZahf ihemqZ_lky mjZ\g_gb_ <mevnZ-;jw]]Z
DZd \b^gh gZ jbk d, ijb wlhf \k_ emqb kh\iZ^Zxl ih nZa_ nZah\uc m]he jZ\_g b

kha^Zxlky hilbfZevgu_ mkeh\by ^ey ©hljZ`_gbyª ?keb m\_ebqblv m]he iZ^_gby lZd qlh[u 2x klZeh > λ gZijbf_j λ. Ba jbk k hq_\b^gh qlh \hagbdZxl emqb \ ijhlb\hiheh`guo nZaZo b j_amevlbjmxsZy Zfieblm^Z dZ`^uo q_luj_o emq_c jZ\gZ gmex

Bf__l f_klh ih]ZkZgb_ j_ne_dkZ

Fgh`bl_ev n gZau\Zxl ihjy^dhf ki_dljZ LZd dZd sinΘ = nλ/2dhkl lh ijb nbdkbjh\Zgguo agZq_gbyo λ b dhkl \ aZ\bkbfhklb hl agZq_gbc n kbgmk m]eZ ^bnjZdpbb sinΘ ijbgbfZ_l jZagu_ agZq_gby ijhihjpbhgZevgu_ wlbf qbkeZf ?keb ^ey n = 1 sinΘ = 0,300 ( Θ = 17D 27’ lh ^ey n = 2

sinΘ = 0,600 ( Θ = 36D 52’ ^ey n = 3 sinΘ = 0,900 ( Θ = 76D 10’ >ey

n = 4 sinΘ > j_ne_dk g_\hafh`_g >Z`_ _keb ijb n = 1 sinΘ hq_gv fZe dZd \ ijb\_^_gghf ijbf_j_ ijZdlbq_kdb \hagbdZxl ki_dlju ebrv i_j\uo

lj_o ihjy^dh\ ?keb `_ sinΘ i_j\h]h j_ne_dkZ [hevr_ l _ Θ > 76D 10’ ), lh hljZ`_gby ^Z`_ \lhjh]h ihjy^dZ hl ^Zggh]h dhkl g_\hafh`gu sinΘ > 1 ).

Ijb bamq_gbb ki_pbZebabjh\Zgguo fhgh]jZnbc beb hjb]bgZevguo klZl_c \ i_jbh^bq_kdhc i_qZlb ihk\ys_gguo ijh[e_fZf bkke_^h\Zgby djbklZeebq_kdhc

kljmdlmju f_lh^hf j_gl]_gh\kdh]h ZgZebaZ fh`_l

7

\hagbdgmlv \iheg_ mf_klguc \hijhk ihq_fm ijb jZkq_lZo \hafh`guo j_ne_dkh\ ih mjZ\g_gbx ijbgbfZ_lky ihjy^hd ki_dljZ n b \ dZdhc f_j_ baf_gylky \u\h^u ijb n b l ^ G_h[oh^bfh hl\_lblv qlh \u\h^u g_ baf_gylky Ijb aZibkb mjZ\g_gby \ \b^_

	d h k l	=	λ
			2 sin Θ	,	( 1.9 )
	n

]^_ n - ihjy^hd ki_dljZ p_eh_ qbkeh jZ\gh_ b l ^

Ihkdhevdm

	dhkl	= dnhnknl = dh * k * l *		( 1.10 )
	n
gZijbf_j
d 111 = d 222 ;			d 111 = d 333
2			3

Ih^klZ\eyy \ fh`gh ihemqblv

	dh * k * l* =	λ
		2 sin Θ	( 1.11 )

>jm]bfb keh\Zfb hl iehkdhklb ( h*k*l*) \hagbdZ_l j_ne_dk ih^qbgyxsbcky mjZ\g_gbx <mevnZ - ;jw]]Z b \ua\Zgguc ki_dljZfb -]h -]h b l ^ ihjy^dZ

1.3. MKLJHCKL<H IJB;HJH< >EY J?GL=?GH=J:NBQ?KDBO

BKKE?>H<:GBC

IjbgpbibZevgZy ko_fZ ijb[hjZ ^ey ijh\_^_gby j_gl]_gh]jZnbq_kdbo bkke_^h\Zgbc djbklZeebq_kdhc kljmdlmju ijb\_^_gZ gZ jbk Hkgh\guf