Научные основы синтеза и технологии производства
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D f_lh^Zf ijb]hlh\e_gby dZlZebaZlhjh\ ij_^ty\ey _lky jy^ lj_[h\Zgbc hgb ^he`gu h[_ki_qb\Zlv ihemq_ gb_ dZlZebaZlhjh\ h[eZ^Zxsbo aZ^Zggufb obfbq_kdbf b nZah\uf khklZ\hf b \_ebqbghc m^_evghc ih\_jogh klb hilbfZevghc ihjbklhc kljmdlmjhc [ulv \hafh`gh ijhklufb b wdhghfbqgufb Djhf_ lh]h ijhp_kk ijb]h lh\e_gby ^he`_g ]ZjZglbjh\Zlv obfbq_kdmx [_a\j_^ ghklv ^ey hdjm`Zxs_c kj_^u >@ < ihke_^gb_ ]h^u \ k\yab k mkbeb\Zxsbfky bgl_j_ khf d \h^hjh^ghc wg_j]_lbd_ \hajhkeZ ihlj_[ghklv \ dZlZebaZlhjZo b khj[_glZo ijbf_gy_fuo \ ijhba\h^kl \_ \h^hjh^Z b \h^hjh^kh^_j`Zsbo ]Zah\ f_lh^hf dhg \_jkbb m]e_\h^hjh^gh]h kujvy Dhg\_jkby fhghhdkb^Z m]e_jh^Z \h^yguf iZjhf DZlZeblbq_kdZy dhg\_jkby fhghhdkb^Z m]e_jh^Z y\ey_lky khklZ\ghc qZklvx ijhp_kkZ ihemq_gby \h^hjh ^Z \ ijhfure_gghklb gZ hkgh\_ ijbjh^gh]h ]ZaZ < k\yab k jhklhf ijhba\h^kl\Z \h^hjh^Z ^ey kbgl_aZ Zf cº° ²Òä Î y cº° ²Òä º­mÈ Òä ij lËÓ fbZdZ b ^jm]bo p_e_c jhev wlhc j_Zdpbb \ obfbq_kdhc ijhfure_gghklb \hajZklZ_l >@ Dhg\_jkby fhghhdkb^Z m]e_jh^Z ijhl_dZ_l kh]eZkgh mjZ\g_gbx j_Zdpbb KH G2H KH2 G2; ∆G°298 = –41 d>`fhev < kh\j_f_gguo ko_fZo ijhba\h^kl\Z ZffbZdZ hklZ lhqguc fhghhdkb^ m]e_jh^Z ]b^jbjm_lky k h[jZah\Zgb _f f_lZgZ Z lZd`_ ^jm]bo hj]Zgbq_kdbo kh_^bg_gbc dhlhju_ gZdZieb\Zxlky \ pbjdmeypbhgghf ]Za_ b m^Z eyxlky gZ klZ^byo ijh^m\hd \f_kl_ k \h^hjh^hf Zahlhf b ZffbZdhf Q_f [hevr_ \ j_Zdpbhgghf ]Za_ hklZ_lky KH l_f [hevr_ \h^hjh^Z jZkoh^m_lky gZ _]h ]b^jbjh \Zgb_ b l_f \ur_ ihl_jb Zahlh\h^hjh^ghc kf_kb m^Z ey_fhc gZ klZ^byo ijh^m\hd >@ < djmiguo Z]j_]ZlZo ijhba\h^kl\Z ZffbZdZ hkms_ kl\ey_lky ]em[hdZy dhg\_jkby ^h hklZlhqghc dhgp_gljZ pbb fhghhdkb^Z m]e_jh^Z –0,5% [7, @ Ijb wlhf k mf_gvr_gb_f dhgp_gljZpbb KH gZ dhebq_kl\h ijh ^m\hqguo ]Zah\ kgb`Z_lky ijbf_jgh gZ Z ijhba\h ^bl_evghklv ih ZffbZdm m\_ebqb\Z_lky gZ 0,7—1% [7]. 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Ijhba\h^bl_evghklv `_e_ahojhfh\uo dZlZebaZlhjh\ fh`_l [ulv ih\ur_gZ iml_f \\_^_gby ijhfhlbjmxsbo ^h[Z\hd m\_ebqb\Zxsbo m^_evgmx ih\_joghklv dZlZebaZ lhjZ b khhl\_lkl\_ggh _]h dZlZeblbq_kdmx Zdlb\ghklv [19—22]. :dlb\ghc nZahc `_e_ahojhfh\h]h dZlZebaZlhjZ y\ey_lky l_ljZhdkb^ `_e_aZ )H3O4 < kljmdlmj_ dZlZeb aZlhjZ hg h[jZam_l l\_j^uc jZkl\hj ribg_evgh]h lbiZ 3+ )_AH4Kr2O3 — ijhbkoh^bl aZf_s_gb_ bhgh\ )H \ djb 3+ klZeebq_kdhc j_r_ld_ )_3H4 bhgZfb Kr Hdkb^ ojhfZ jZkkfZljb\Z_lky dZd klZ[bebaZlhj Zdlb\gh]h dhfihg_g lZ Ba[ulhd hdkb^Z ojhfZ \ \b^_ k\h[h^ghc nZau kgb `Z_l Zdlb\ghklv dZlZebaZlhjZ wlh \hafh`gh ijb kh ^_j`Zgbb Cr2O3 k\ur_ —15%) [16, 17]. Y^Zfb ^ey `_e_ahojhfh\uo dZlZebaZlhjh\ y\eyxlky kh_^bg_gby dj_fgby nhknhjZ [hjZ furvydZ g_ij_ ^_evgu_ m]e_\h^hjh^u Z lZd`_ k_jgbklu_ kh_^bg_gby Hj]Zgbq_kdb_ k_jgbklu_ kh_^bg_gby \ kemqZ_ bo ihiZ 85 ^Zgby \ ]Zah\mx kf_kv \ ijbkmlkl\bb \h^ygh]h iZjZ gZ dZlZebaZlhj_ dhg\_jlbjmxlky \ k_jh\h^hjh^ dhlhjuc j_Z]bjm_l k hdkb^gh-`_e_aguf dhfihg_glhf dZlZebaZ lhjZ k h[jZah\Zgb_f kmevnb^Z `_e_aZ )_3O4 G26 G2 = 3FeS + 4H2O; ∆G ° 298 = –79,5 d>`fhev J_Zdpby h[jZlbfZ b \ aZ\bkbfhklb hl khhlghr_gby \h^yghc iZjdhg\_jlbjm_fuc ]Za b l_fi_jZlmju \ha fh`gh dZd ih]ehs_gb_ k_ju lZd b \u^_e_gb_ jZg__ ih]ehs_gghc k_ju \ iZjh]Zah\mx kf_kv H[jZamxsbcky kmevnb^ `_e_aZ lZd `_ dZd b )_3O4 dZlZebabjm_l j_Zd pbx dhg\_jkbb KH gh ih kjZ\g_gbx k Fe3O4 hg ]hjZa^h f_g__ Zdlb\_g HljZ\e_gb_ dZlZebaZlhjZ k_jhc — h[jZ lbfuc ijhp_kk > 11]. GZ jZ[hlhkihkh[ghklb dZlZebaZlhjZ fh]ml g_]Zlb\gh kdZau\Zlvky kh^_j`Zsb_ky \ iZjh]Zah\hc kf_kb b g_ y^h\blu_ ijbf_kb lZdb_ dZd iuev kZ`Z kheb ba iZjZ b dhg^_gkZlZ hgb hldeZ^u\Zxlky gZ ih\_joghklb dZlZ ebaZlhjZ aZ[b\Zxl _]h ihju qlh ijb\h^bl d kgb`_gbx Zdlb\ghklb b f_oZgbq_kdhc ijhqghklb dZlZebaZlhjZ I_j_^ wdkiemZlZpb_c dZlZebaZlhj h[uqgh \hkklZgZ\ eb\Zxl j_Zdpbhgghc ]Zah\hc kf_kvx )_2O3 G2 )_3O4 G2O; (3) ∆G ° 298 = –9,6 d>`fhev _ KH )_3O4 KH2; ∆G ° 298 = –50,6 d>`fhev ) 2O3 <hkklZgh\e_gb_ `_e_ahojhfh\h]h dZlZebaZlhjZ gZqbgZ_lky ijb l_fi_jZlmj_ —180 K b ijhl_dZ_l kh agZqbl_evghc kdhjhklvx Ijhp_kk \hkklZgh\e_gby bf_ _l Z\lhdZlZeblbq_kdbc oZjZdl_j b khijh\h`^Z_lky \u ^_e_gb_f l_ieZ hkh[_ggh \ kemqZ_ bkihevah\Zgby ]Zah \uo kf_k_c kh^_j`Zsbo [hevrh_ dhebq_kl\h fhghhd kb^Z m]e_jh^Z > @ AgZqbl_evgh_ \ebygb_ gZ mkdhj_gb_ ijhp_kkZ \hk klZgh\e_gby hdZau\Z_l \\_^_gb_ \ dZlZebaZlhj hdkb^h\ dZeby b fZ]gby >@ ?keb \ dZq_kl\_ kujvy ^ey ihemq_gby dZlZebaZlhjZ [ue \ayl kmevnb^ `_e_aZ lh ijb \hkklZgh\e_gbb dZlZ ebaZlhjZ k_jZ [m^_l \u^_eylvky \ \b^_ k_jh\h^hjh^Z Gh [hevrZy qZklv kh^_j`Zs_cky \ dZlZebaZlhj_ k_ju k\yaZgZ \ kmevnZl )H624 j_Z]bjmxsbc k \h^hjh^hf b \h^yguf iZjhf FeSO4 G2 )H6 G2O (5) )H6 G22 )_3O4 + 3H26 G2; ∆G ° 298 = –75 d>`fhev Dhebq_kl\h k_ju \u^_ey_fhc \ ijhp_kk_ \hkklZgh\ e_gby dZlZebaZlhjZ b \ gZqZevguc i_jbh^ _]h wdkiemZ lZpbb lZdh\h qlh \hafh`gh kbevgh_ hljZ\e_gb_ gbadh l_fi_jZlmjgh]h dZlZebaZlhjZ Ihwlhfm ihke_ \hkklZ gh\e_gby dZlZebaZlhjZ ^he`gh [ulv ijh\_^_gh _]h h[_kk_jb\Zgb_ >@ AZljZlu gZ ijhp_kk ^_kmevnmjbaZpbb fh]ml khklZ \blv — klhbfhklb dZlZebaZlhjZ QZklbqguf j_ r_gb_f ijh[e_fu ^_kmevnmjbaZpbb fh`_l klZlv kgb 86 `_gb_ kh^_j`Zgby k_ju \ dZlZebaZlhj_ ^h \hafh`gh fbgbfZevgh]h mjh\gy ijb dhlhjhf hgZ hl]hgyeZkv [u aZ dhjhldh_ \j_fy beb klZ[bebaZpby k_ju ^h[Z\dZfb k l_f qlh[u ij_^hl\jZlblv __ hl]hgdm Ij_^eh`_g dZlZebaZlhj k ^h[Z\dZfb KZ FJ <Z MklZgh\e_gh qlh \\_^_gb_ wlbo ^h[Z\hd k^\b]Z_l ijh p_kk ^_kmevnmjbaZpbb \ h[eZklv [he__ \ukhdbo l_fi_ jZlmj > 25]. Iheguf j_r_gb_f ijh[e_fu wnn_dlb\gh]h b gZ ^_`gh]h dZlZebaZlhjZ ^ey ijhba\h^kl\Z ZffbZdZ y\ey _lky ijbf_g_gb_ [_kk_jgbklh]h hdkb^Z `_e_aZ Dbg_lbdZ ijhp_kkZ dhg\_jkbb fhghhdbkb m]e_jh^Z Hlf_lbf hkgh\gu_ jZ[hlu ih bkke_^h\Zgbx dbg_lb db dhg\_jkbb fhghhdkb^Z m]e_jh^Z gZ jZaebqguo `_e_ ahkh^_j`Zsbo dZlZebaZlhjZo BamqZeZkv dbg_lbdZ j_Zd pbb ijb l_fi_jZlmjZo \ur_ K gZ dZlZebaZlhj_ ba g_ijhfhlbjh\Zggh]h hdkb^Z `_e_aZ b gZ \ukhdhl_f i_jZlmjghf `_e_ahfZ]gb_\hf dZlZebaZlhj_ G< Dmevdh\Z b FB Lëfdbg Ijb \u\h^_ dbg_lbq_kdh]h mjZ\ g_gby bkke_^h\Zl_eb hkgh\u\Zebkv gZ f_oZgbaf_ ijh p_kkZ khklhys_]h \ ihi_j_f_gghf hdbke_gbb-\hkklZgh\e_gbb ih\_joghklgh]h fhghfhe_dmeyjgh]h kehy dZlZebaZlhjZ >@ D*—H KH D* KH2 (7) * * D + H22 D —H G2 (8) ]^_ D — Zdlb\guc mqZklhd p_glj ih\_joghklb dZlZ ebaZlhjZ IjbgbfZy \ dZq_kl\_ ebfblbjmxs_c klZ^bb hij_^_eyxs_c kdhjhklv kmffZjgh]h ijhp_kkZ j_Zdpbx Z\lhju ij_^eh`beb ke_^mxs__ dbg_lbq_kdh_ mjZ\g_gb_ S+ 2 ω = N S &2 S+ β S+ − N S &2 S+ 2 − β (9) ]^_ ω — kdhjhklv j_Zdpbb k1, k2 — dhgklZglu kdhjhklb ijyfhc b h[jZlghc j_Zdpbc jKH, jG2H, jG2, jKH2 — iZj pbZevgu_ ^Z\e_gby khhl\_lkl\mxsbo ]Zah\ β — dhwn nbpb_gl jZ\guc Ba ZgZebaZ mjZ\g_gby ke_^m_l qlh kdhjhklv j_Zd pbb aZ\bkbl hl dhgp_gljZpbb fhghhdkb^Z m]e_jh^Z \h^hjh^ \ h[eZklb l_fi_jZlmj —500 K lhjfhabl j_Zdpbx dhg\_jkbb ^bhdkb^ m]e_jh^Z g_ \eby_l gZ kdhjhklv j_Zdpbb ZgZeh]bqgh bg_jlghfm jZa[Z\bl_ex — Zahlm >bnnmabhggu_ nZdlhju ijb l_fi_jZlmjZo 400—500 K g_ \ebyxl gZ kdhjhklv ijhp_kkZ Bkke_^h\ZeZkv dbg_lbdZ dhg\_jkbb hdkb^Z m]e_jh^Z \h^yguf iZjhf gZ `_e_ahojhfh\hf b gbadhl_fi_jZlmj ghf pbgdojhff_^ghf dZlZebaZlhjZo == Sb[jy GF Fhjhah\ FB Lëfdbg Ihemq_ggu_ hiulgu_ ^Zggu_ \ dbg_lbq_kdhc h[eZklb hibku\Zxlky ke_^mx sbf mjZ\g_gb_f >@ ω=N S &2 S + 2 − .S + S &2 $S + 2 − S &2 (10) ! " ]^_ k — dhgklZglZ kdhjhklb ijyfhc j_Zdpbb D — dhg klZglZ jZ\gh\_kby : — dhwnnbpb_gl aZ\bkysbc hl l_fi_jZlmju < kemqZ_ `_e_ahojhfh\h]h dZlZebaZlhjZ OJ $ = − + 7 Ihemq_gh lZd`_ ke_^mxs__ dbg_lbq_kdh_ mjZ\g_gb_ dhg\_jkbb fhghhdkb^Z m]e_jh^Z iZjZfb \h^u gZ `_e_ ahojhfh\hf dZlZebaZlhj_ gZg_k_gghf gZ hdkb^ fZ]gby <B :ljhs_gdh ; ;b[j − GS &2 Gτ ′ S &2 − S &2 =N S+ ⋅ S+ 2 (11) ]^_ τ — \j_fy p′CO — jZ\gh\_kgh_ iZjpbZevgh_ ^Z\e_ gb_ fhghhdkb^Z m]e_jh^Z :\lhju mklZgh\beb aZ\bkbfhklv dhgklZglu kdhjhklb j_Zdpbb hl l_fi_jZlmju k = 4, 92 ⋅105 ⋅ e − 18460 RT Ijhba\h^bl_evghklv dZlZebaZlhjZ \ aZ\bkbfhklb hl ^Z\e_gby J jZ\gZ 3 ] = ] 3 >d]f q@ ]^_ z0 — ijhba\h^bl_evghklv dZlZebaZlhjZ ijb Zlfh kn_jghf ^Z\e_gbb Ih ^Zgguf ;G @b^dh\Z <B :ljhs_gdh b :I AZkhjbgZ kdhjhklv dhg\_jkbb fhghhdkb^Z m]e_jh ^Z iZjZfb \h^u gZ `_e_ahojhfh\hf dZlZebaZlhj_ hij_ ^_ey_lky mjZ\g_gb_f − GS &2 Gτ =N S &2 S &2 (12) BamqZebkv dbg_lbq_kdb_ aZdhghf_jghklb ijhp_kkZ gZ jZaebqguo Zdlb\guo kj_^g_l_fi_jZlmjguo dZlZebaZ lhjZo BI Dbjbeeh\ <N KZdkbg IhdZaZgh qlh baf_g_gb_ kh^_j`Zgby \h^hjh^Z \ bkoh^ghc ]Zah\hc kf_kb \ ij_^_eZo hl ^h g_ \eby_l gZ kdhjhklv j_Zdpbb Z ^bhdkb^ m]e_jh^Z lhjfhabl __ Ijbgy\ qlh lhjfhays_c klZ^b_c y\ey_lky hdbke_gb_ ih\_joghklb dZlZebaZlhjZ Z\lhju \u\_eb ke_^mxs__ ^bnn_j_gpb Zevgh_ mjZ\g_gb_ kdhjhklb dhg\_jkbb fhghhdkb^Z m]e_ jh^Z \h^yguf iZjhf S ω = N S + 2 &2 S &2 − N S+ S &2 S &2 (13) JZaebqb_ lhjfhaysbo nZdlhjh\ khhl\_lkl\mxsbo ^Zgguf BI Dbjbeeh\Z b <N KZdkbgZ \ebygb_ ^bhd kb^Z m]e_jh^Z b ^Zgguf G< Dmevdh\hc b FB LëfdbgZ \ebygb_ \h^hjh^Z ih-\b^bfhfm ke_^m _l h[tykgblv baf_g_gb_f ebfblbjmxs_c klZ^bb \ jZa ebqguo l_fi_jZlmjguo mkeh\byo ijh\_^_gby j_Zdpbb GZ hkgh\Zgbb nhjfmeu [ueh ihemq_gh mjZ\g_ gb_ ^ey hij_^_e_gby \j_f_gb dhg\_jkbb fhghhdkb^Z m]e_jh^Z iZjZfb \h^u τ= D N Q − D [ 0 [ (14) ]^_ τ — \j_fy dhg\_jkbb k Z0 — kh^_j`Zgb_ KH \ bkoh^ghf ]Za_ ^heb _^bgbpu k — dhgklZglZ kdhjhklb ijyfhc j_Zdpbb n — h[t_fgh_ khhlghr_gb_ \h^yghc iZjdhg\_jlbjm_fuc ]Za o — kl_i_gv dhg\_jkbb KH, ^heb _^bgbpu M(o) — fgh`bl_ev aZ\bkysbc hl o b khhlghr_gby \ bkoh^ghf ]Za_ KH2 : CO. Kujv_ ^ey ijhba\h^kl\Z dZlZebaZlhjh\ dhg\_jkbb fhghhdkb^Z m]e_jh^Z b ljZ^bpbhggu_ f_lh^u bo ijb]hlh\e_gby Ihbkd g_^_nbpblgh]h kujvy b ih\ur_gb_ wnn_d lb\ghklb _]h bkihevah\Zgby \ ijhba\h^kl\_ ijhfur e_gguo dZlZebaZlhjh\ y\ey_lky h^gbf ba \Z`g_crbo gZijZ\e_gbc \ mkh\_jr_gkl\h\Zgbb l_ogheh]bb ijb]h lh\e_gby dZlZebaZlhjh\ >—30]. Hdkb^ `_e_aZ — hkgh\ghc dhfihg_gl dZlZebaZlhjh\ ^ey dhg\_jkbb fhghhdkb^Z m]e_jh^Z fh`gh ihemqblv l_jfbq_kdbf jZaeh`_gb_f jZaebqguo kh_^bg_gbc `_e_ aZ ]b^jhdkb^Z gbljZlZ dZj[hgZlZ kmevnZlZ oehjb^Z Zedh]heylZ hdkZeZlZ b ^j L_ogbq_kdb_ hdkb^u `_e_aZ ihemq_ggu_ l_jfhebahf khe_c jZaebqZxlky fhjnheh ]b_c b ^_n_dlghklvx qZklbp qlh h[mkeh\eb\Z_l jZaebq gmx Zdlb\ghklv \ obfbq_kdbo j_Zdpbyo b qZklh h]jZgb qb\Z_l \hafh`ghklv bo bkihevah\Zgby ^ey ijb]hlh\e_ gby dZlZebaZlhjh\ >—33]. GZb[he__ jZkijhkljZg_gguc f_lh^ ihemq_gby Zd lb\gh]h hdkb^Z `_e_aZ [Zabjm_lky gZ kh\f_klghf hkZ` ^_gbb ba jZkl\hjh\ khe_c g_ jZkl\hjbfuo \ \h^_ kh_^b g_gbc `_e_aZ ]b^jhdkb^h\ dZj[hgZlh\ ]b^jhdkhdZj [hgZlh\ b ^j k ihke_^mxsbf l_jfbq_kdbf jZaeh`_gb _f wlbo ijh^mdlh\ < dZq_kl\_ hkZ^bl_e_c bkihevamxl jZkl\hju ZffbZdZ b dZj[hgZlZ Zffhgby >@ Ko_fZlb q_kdb l_ogheh]bx hkZ`^_gby fh`gh ij_^klZ\blv ke_^mxsbf h[jZahf >@ jZkl\hj khe_c `_e_aZ + hkZ^bl_ev → klZj_gb_ hkZ^dZ→ → ijhfu\dZ → kmrdZ → ijhdZeb\Zgb_ :\lhju jZ[hl > @ \ dZq_kl\_ bkoh^gh]h kujvy hl^Zxl ij_^ihql_gb_ gbljZlm `_e_aZ lZd dZd gbljZlbhgu g_ y\eyxlky y^hf ^ey dZlZebaZlhjZ b e_]dh m^Zey _lky ijb ijhdZeb\Zgbb < kemqZ_ kmevnZlZ `_e_aZ kmev nZl-bhgu ba hkZ`^_ggh]h ]b^jhdkb^Z ijb ijhfu\d_ m^Zeyxlky k ljm^hf b ^ey dZlZebaZlhjZ hgb y\eyxlky y^hf Wlb kheb ohjhrh ]b^jhebamxlky h[jZamy dbkeu_ jZkl\hju < ijZdlbd_ ijb]hlh\e_gby dZlZebaZlhjh\ bkihevamxlky jZkl\hju khe_c ih dhgp_gljZpbb [ebadb_ d gZkus_gguf > 30]. 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>@ >@ >@ (15) 89 k jãÒÓ s s väÒ¯Óºm k k jãÒÓ ah\Zgbb ik_\^hjZkieZ\h\ dh]^Z bgl_gkb\gh_ f_oZgbq_ kdh_ i_j_f_rb\Zgb_ kihkh[gh ^h\_klb ih^\b`ghklv fhe_dme ohly [u h^gh]h ba j_Z]_glh\ ^h mjh\gy bo ih^ \b`ghklb \ jZkieZ\_ Gh ^Z`_ _keb obfbq_kdh_ \aZbfh ^_ckl\b_ j_Z]_glh\ \ f_evgbp_ g_ ijhbkoh^bl f_oZgbq_ kdZy Zdlb\Zpby \k_ jZ\gh kms_kl\_ggh h[e_]qZ_l ijhl_ dZgb_ ihke_^mxsbo klZ^bc ijhp_kkZ ijb]hlh\e_gby dZ lZebaZlhjZ Wlh h[mkeh\e_gh baf_g_gb_f l_jfh^bgZfb q_kdbo ihl_gpbZeh\ \ke_^kl\b_ h[jZah\Zgby ^_n_dlh\ baf_g_gby we_dljhgguo k\hckl\ h[jZah\Zgby k\_`_c ih\_joghklb b l i DZd [ueh hlf_q_gh \ur_ kljmdlmjm n_jjblZ dZev pby [jZmgfbee_jbl h[uqgh jZkkfZljb\Zxl dZd Zgbhg^_nbpblguc i_jh\kdbl k mihjy^hq_ggufb dbkehjh^gu fb \ZdZgkbyfb hkgh\gufb kljmdlmjgufb we_f_glZfb dhlhjh]h y\eyxlky q_j_^mxsb_ky hdlZw^jbq_kdb_ b l_ljZw^jbq_kdb_ kehb Fh`gh h`b^Zlv qlh \ j_amevlZl_ f_oZghobfbq_kdh]h kbgl_aZ — mihjy^hq_gb_ Zgbhgguo \ZdZgkbc g_ ^hklb]Z_lky D mihjy^hq_gbx dbkehjh^guo \ZdZgkbc ijb\h^bl ihke_^mxsZy l_jfh h[jZ[hldZ Bamq_gb_ kljmdlmju n_jjblZ dZevpby Ca2Fe2O5 kbgl_abjh\Zggh]h f_oZghobfbq_kdbf f_lh ^hf \ ieZg_lZjghc f_evgbp_ \ khq_lZgbb k l_jfhebahf ijb jZaebqguo l_fi_jZlmjZo iha\hebeh mklZgh\blv qlh ihemqZ_fu_ gbadhl_fi_jZlmjgu_ h[jZapu y\eyxlky Zgbhggh-fh^bnbpbjh\Zggufb b ijhp_kku mihjy^hq_ gby dbkehjh^guo \ZdZgkbc \ gbo _s_ g_ aZ\_jr_gu ebaZ ihdZau\Zxl qlh ihemq_gguc n_jjbl f_^b y\ey_lky ribg_evx kf_rZggh]h lbiZ Ih ^Zgguf jZ[hl — kl_i_gv h[jZs_gghklb khklZ\ey_l GZihfgbf qlh ih kl_i_gb aZiheg_gby dZlbhgZfb F2+ b F3+ \ l_ljZw^jbq_kdbo maeZo b \k_o bhgh\ F3+ \ hdlZw^ jbq_kdbo maeZo jZaebqZxl ghjfZevgmx h[jZs_ggmx b kf_rZggmx ribg_eb GhjfZevghc ribg_eb khhl\_lkl \m_l jZkiheh`_gb_ \k_o bhgh\ F2+ \ l_ljZw^jbq_ kdbo b \k_o bhgh\ F3+ \ hdlZw^jbq_kdbo maeZo < kemqZ_ h[jZs_gghc ribg_eb dZlbhgh\ F3+ aZgbfZxl \k_ l_ljZw^jbq_kdbo ihabpbc Z hklZevgu_ dZlbhgh\ F3+ b dZlbhgh\ F2+ aZihegyxl hdlZw^jbq_kdbo ihabpbc jZkiheZ]Zykv \ gbo klZlbklbq_kdb [_kihjy^hq gh —52]. 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>_eh \ lhf qlh wnn_dlb\ghklv jZ [hlu dZlZebaZlhjh\ aZ\bkbl g_ lhevdh hl bo nbabdhobfbq_kdbo k\hckl\ gh b \h fgh]hf hij_^_ey_lky ]_h f_ljbq_kdhc nhjfhc bo ]jZgme Wlh klZgh\blky ihgyl guf _keb mq_klv qlh ]_hf_ljbq_kdZy nhjfZ dZlZebaZ lhjh\ b khj[_glh\ kms_kl\_ggh \eby_l gZ oZjZdl_j ijh p_kkh\ fZkkh- b l_iehh[f_gZ \ keh_ Z lZd`_ gZ ]Zah^b gZfbq_kdh_ khijhlb\e_gb_ B a^_kv k emqr_c klhjhgu aZj_dhf_g^h\Zeb k_[y dZlZebaZlhju b khj[_glu keh` ghc ]_hf_ljbq_kdhc nhjfu \ lhf qbke_ [ehdb khlh\hc kljmdlmju H[sZy ihjbklhklv wdkljm^bjh\Zgguo dZlZ ebaZlhjh\ gZ — \ur_ q_f m lZ[e_lbjh\Zgguo F_lh^ nhjfh\Zgby wdkljmab_c hlebqZ_lky hlghkbl_ev ghc ijhklhlhc b g_ lj_[m_l ijbf_g_gby ^hjh]hklhys_]h h[hjm^h\Zgby h[_ki_qb\Zy ihemq_gb_ dZlZebaZlhjh\ k ^hklZlhqgh \ukhdhc f_oZgbq_kdhc ijhqghklvx Kms_kl\_gguc g_^hklZlhd wdkljmab\ghc l_ogheh]bb k\yaZg k l_f qlh ih^[hj fZkk ^ey nhjfh\Zgby ]jZgme dZlZebaZlhjh\ ijh\h^blky dZd ijZ\beh wfibjbq_kdbf iml_f qlh aZqZklmx aZljm^gy_l \u[hj hilbfZevghc j_p_ilmju b kihkh[Z ihemq_gby nhjfh\hqghc fZkku GZ gZr \a]ey^ jZajZ[hldZ gh\uo b mkh\_jr_gkl\h\Zgb_ kms_kl\mxsbo kihkh[h\ ijb]hlh\e_gby dZlZebaZlhj guo fZkk g_\hafh`gu [_a ]em[hdh]h bamq_gby ijhp_k kh\ kljmdlmjhh[jZah\Zgby Lhevdh agZy k\hckl\Z dhZ]m eypbhgghc kljmdlmju fh`gh p_e_gZijZ\e_ggh mijZ\ eylv j_heh]bq_kdbfb k\hckl\Zfb fZkk gZ jZggbo klZ^b yo bo ijb]hlh\e_gby < jy^_ jZ[hl > @ ihdZaZgh qlh nhjfh\hqgu_ fZkku hlghkylky d l\_j^hh[jZaguf \yadhieZklbqguf kljmdlmjbjh\Zgguf kbkl_fZf l_ ^h ^hklb`_gby g_dh lhjh]h gZijy`_gby J1 hgb \_^ml k_[y dZd l\_j^u_ l_eZ b ebrv ihke_ ij_\ur_gby ih^ ^_ckl\b_f gZ]jmadb wlh]h ij_^_eZ bo ih\_^_gb_ klZgh\blky ih^h[guf l_q_gbx \yadhieZklbqguo `b^dhkl_c > @ >_nhjfZpbhggu_ b j_eZdkZpbhggu_ k\hckl\Z kljmdlmjbjh\Zgguo kbkl_f k ^hklZlhqghc lhqghklvx fh]ml [ulv hibkZgu fh^_evx FZdk\_eeZ—R\_^h\Z—D_ev\bgZ >@ ε′ = ! + ! τ − H[S − η + ! + ! τ η (16) ]^_ ε′ — hlghkbl_evgZy kmffZjgZy ^_nhjfZpby J — \g_rgyy gZ]jmadZ J1 — mkeh\guc klZlbq_kdbc ij_^_e l_dmq_klb ?1, ?2 — fh^mev [ukljhc b f_^e_gghc weZ klbq_kdbo ^_nhjfZpbc khhl\_lkl\_ggh η1 — gZb[hev rZy ieZklbq_kdZy \yadhklv η2 — \yadhklv mijm]h]h ihke_^_ckl\by τ — \j_fy ^_ckl\by gZ]jmadb < nhjfh\hqghc fZkk_ ijbkmlkl\mxl \k_ ljb \b^Z ^_nhjfZpbc [ukljZy weZklbq_kdZy mijm]Zy εmi f_^ e_ggZy weZklbq_kdZy εwe ieZklbq_kdZy εie DZ`^h_ keZ ]Z_fh_ \ mjZ\g_gbb khhl\_lkl\m_l i_j_qbke_gguf \b^Zf ^_nhjfZpbc l_ ε′ = εmi + εwe + εie Hlkx^Z fh` gh jZkkqblZlv ^hex dZ`^h]h \b^Z ^_nhjfZpbc \ h[s_f [ZeZgk_ ijbgbfZy \_ebqbgm ε′ aZ Fh^_ev fh`_l [ulv bkihevah\ZgZ ^ey bamq_gby kljmdlmjgh-f_oZgbq_kdbo k\hckl\ nhjfh\hqguo dZlZ ebaZlhjguo fZkk Z ih ihemq_gguf ba g__ ^Zgguf fh` gh ijh]ghabjh\Zlv ijb]h^gZ eb fZkkZ d wdkljmabhgghfm nhjfh\Zgbx >@ MklZgh\e_gh qlh fZkkZ `_e_ahojhfh\h]h dZlZebaZ lhjZ ijb]hlh\e_ggZy ih ljZ^bpbhgghc l_ogheh]bb im l_f kf_r_gby ojhfh\h]h Zg]b^jb^Z k hdkb^hf `_e_aZ b \h^hc hlghkblky d gme_\hfm kljmdlmjgh-f_oZgbq_kdhfm lbim k ij_h[eZ^Zgb_f [ukljuo weZklbq_kdbo ^_nhjfZ pbc jbk h[jZa_p H[jZ[hldZ wlhc `_ fZkku ih ^\mo klZ^bcghc l_ogheh]bb \ ^bki_j]bjmxsbo mkljhckl\Zo baf_evq_gb_ qZklb α-Fe2O3 \ ojhfh\hc dbkehl_ k ihke_ ^mxsbf ^h[Z\e_gb_f g_h[oh^bfh]h dhebq_kl\Z hdkb^Z `_e_aZ b jZkl\hjZ \h^hjZkl\hjbfh]h ihebf_jZ iha\hey_l kgbablv \_ebqbgm [ukljuo weZklbq_kdbo ^_nhjfZpbc k ^h jbk h[jZa_p Ijb wlhf f_^e_ggu_ weZklbq_ kdb_ b ieZklbq_kdb_ ^_nhjfZpbb \hajZklZxl khhl\_lkl\_g gh k ^h b k ^h >@ Hkgh\ghc ijbqbghc memqr_gby j_heh]bq_kdbo k\hckl\ gZjy^m k nZdlhjhf baf_evq_gby qZklbp hdkb^Z `_e_aZ y\ey_lky \hajZklZgb_ obfbq_kdh]h \aZbfh^_ckl \by dhfihg_glh\ Z lZd`_ \ha^_ckl\b_ \h^hjZkl\hjbfh ]h ihebf_jZ iheb\bgbeh\uc kibjl beb dZj[hdkbf_ lbep_eexehaZ MklZgh\e_gh qlh dZlZebaZlhjgZy fZkkZ ihemq_ggZy ba n_jjblh\ dZevpby b f_^b h[eZ^Z_l \u 91 k jãÒÓ s s väÒ¯Óºm k k jãÒÓ 4. FheqZgh\ εie < < ;mygh\ J : Mki_ob obfbb l k —492. 5. >abkvdh < : Hkgh\u f_lh^h\ ijb]hlh\e_gby dZlZebaZlh jh\ Gh\hkb[bjkd GZmdZ k 6. Ijhba\h^kl\h ZffbZdZ Ih^ j_^ < I K_f_gh\Z F Ob fby k 7. HqbkldZ l_ogheh]bq_kdbo ]Zah\ Ih^ j_^ L : K_f_gh\hc B E E_cl_kZ F Obfby k 8. K_f_gh\ < I K_f_gh\Z L : Ijhba\h^kl\h ZffbZdZ ih wg_j]h l_ogheh]bq_kdhc ko_f_ F GBBLWOBF k 9. H\kb_gdh H E b ^j DZlZeba \ ijhfure_gghklb k —45. 10. K_f_gh\Z L : b ^j DZlZebaZlhju ZffbZqgh]h ijhba\h^kl \Z F GBBLWOBF k 11. KijZ\hqgbd ZahlqbdZ F Obfby k 12. KijZ\hqgh_ jmdh\h^kl\h ih dZlZebaZlhjZf ^ey ijhba\h^kl \Z ZffbZdZ b \h^hjh^Z Ih^ j_^ < I K_f_gh\Z E Obfby k 13. L_ogheh]by dZlZebaZlhjh\ Ih^ j_^ B I Fmoe_gh\Z E Obfby k 14. :e_dk__\ : F FboZceh\Z G I ;_kdh\ < K Obf ijhf k —103. 15. Dhfh\Z A < DZlZeba \ ijhfure_gghklb k 16. FZjdbgZ F B b ^j Lj =B:I \ui k —84. 17. FZjdbgZ F B b ^j Dbg_lbdZ b dZlZeba l k —871. 18. Bevbg : I b ^j <hij dbg_lbdb b dZlZebaZ B\Zgh\h k —114. 19. Nmj_g W E b ^j Dbg_lbdZ b dZlZeba l k . 20. Nmj_g W E b ^j Obf ijhf-klv k —288. 21. Nmj_g W E b ^j Dbg_lbdZ b dZlZeba l k —456. 22. Rbjhdh\ X = Bevbg : I <hij dbg_lbdb b dZlZebaZ B\Zgh\h k —110. 23. :ljhs_gdh < B b ^j L_ogheh]by k\yaZggh]h ZahlZ OZjv dh\ k 24. Dhfh\Z A < b ^j MdjZbgkdZy gZmqgh-l_ogbq_kdZy dhgn ih dZlZebam k —69. 25. DZeZrgbd : < b ^j LZf `_ k —50. 26. Dmevdh\Z G < Lëfdbg F B @ nba obfbb l k 27. Sb[jy = = b ^j Dbg_lbdZ b dZlZeba l k —1068. 28. Dhfh\Z A < b ^j <hij dbg_lbdb b dZlZebaZ B\Zgh\h k 14—119. 29. >abkvdh < : Dbg_lbdZ b dZlZeba l k 30. Rbjhdh\ X = >bkk ^hdl l_og gZmd B\Zgh\h k 31. Kl_iZgh\ ? = Dhl_evgbdh\ = J DZlZeba \ ijhfure_ggh klb k —56. 32. Dhl_evgbdh\ = J @ ijbde obfbb l k —282. 33. Kl_iZgh\ ? = b ^j Dbg_lbdZ b dZlZeba l k —944. 34. Dmgbg : < b ^j Ba\ \ukr mq_[ aZ\_^_gbc Obfby b obfbq_kdZy l_ogheh]by k —89. 35. Djb\hjmqdh H I Ju`bd B : Dbg_lbdZ b dZlZeba l k —477. 36. ;mjqbgZ ? ; b ^j @ kljmdl obfbb l k —497. 37. QZeuc < I =b^jhhdbkb f_lZeeh\ Db_\ GZmdh\Z ^mfdZ k 38. :\\Zdmfh\ ? = F_oZgbq_kdb_ f_lh^u Zdlb\Zpbb obfbq_ kdbo ijhp_kkh\ Gh\hkb[bjkd GZmdZ k V 2 II 3 1 εwe I 0 >bZ]jZffZ jZa\blby ^_nhjfZpbc \ fZkk_ dZlZeb aZlhjZ dhg\_jkbb fhghhdkb^Z m]e_jh^Z gZ klZ^bb wdkljm abhggh]h nhjfh\Zgby DZlZebaZlhj b kihkh[ ijb]hlh\e_gby fZkku ^ey wdkljmabb 1 — `_e_ahojhfh\uc dZlZebaZlhj ijhfure_ggZy l_ogheh ]by 2 — `_e_ahojhfh\uc dZlZebaZlhj bkihevah\Zgb_ ^bk i_j]bjh\Zgby b \h^hjZkl\hjbfh]h ihebf_jZ 3 — gZ hkgh\_ n_jjblh\ dZevpby b f_^b 0, I,...,V — kljmdlmjgh-f_oZgbq_kdbc lbi fZkku khdbfb j_heh]bq_kdbfb oZjZdl_jbklbdZfb ^Z`_ [_a ^h[Z\hd ihebf_jh\ Ijb wlhf \_ebqbgu [ukljuo b f_^e_gguo weZklbq_kdbo ^_nhjfZpbc b ieZklbq_kdhc ^_nhjfZpbb khklZ\eyxl khhl\_lkl\_ggh jbk h[jZa_p 3). LZdbf h[jZahf jZ\ghf_jgh_ jZa\blb_ \k_o \b^h\ ^_nhjfZpbc h[_ki_qb\Z_l \hafh`ghklv wdkljmabhggh]h nhjfh\Zgby dZlZebaZlhjguo fZkk \ ]jZgmeu :gZeba ijhp_kkZ dhg\_jkbb fhghhdkb^Z m]e_jh^Z \h^yguf iZjhf \ ^_ckl\mxs_c l_ogheh]bq_kdhc ko_f_ ijhba\h^kl\Z ZffbZdZ b bkke_^h\Zgby ijh\h^bfu_ \ B\Zgh\kdhf ]hkm^Zjkl\_gghf obfbdh-l_ogheh]bq_kdhf mgb\_jkbl_l_ ^Zxl hkgh\Zgby kqblZlv qlh ^ey klZ^bb kj_^g_l_fi_jZlmjghc dhg\_jkbb fhghhdkb^Z m]e_jh^Z i_jki_dlb\gufb y\eyxlky dZlZebaZlhju gZ hkgh\_ n_j jblh\ dZevpby b f_^b ijb]hlZ\eb\Z_fu_ ih f_lh^m f_oZghobfbq_kdh]h kbgl_aZ Wlhl f_lh^ iha\hey_l ih emqZlv \ukhdh^bki_jkgu_ ihjhrdb n_jjblh\ dZevpby b f_^b Z lZd`_ kms_kl\_ggh kgbablv l_fi_jZlmjm ihke_ ^mxs_c l_jfhh[jZ[hldb N_jjbl dZevpby ijhy\ey_l \ukhdmx dZlZeblbq_kdmx Zdlb\ghklv \ h[eZklb l_fi_ jZlmj — K Z n_jjbl f_^b gZb[he__ Zdlb\_g \ [he__ gbadhl_fi_jZlmjghc h[eZklb — K DZlZ ebaZlhjgZy fZkkZ ihemq_ggZy ba n_jjblh\ dZevpby b f_^b h[eZ^Z_l \ukhdbfb j_heh]bq_kdbfb oZjZdl_jb klbdZfb b g_ gm`^Z_lky \ bkihevah\Zgbb ^h[Z\hd iheb f_jh\ N_jjblu dZevpby b f_^b fh]ml [ulv bkihevah \Zgu ^ey kha^Zgby dZlZebaZlhjh\ dhg\_jkbb KH gh\h]h ihdhe_gby EBL?J:LMJ: 1. I_ljh\ E : DZlZeba \ ijhfure_gghklb k 2. Imlbeh\ : < Obfby b jughd k —35. 3. IZjfhg < G Obfby \ bgl_j_kZo mklhcqb\h]h jZa\blby l k 92 Jbk εmi III IV 39. Eyoh\ G A ;he^uj_\ < < Ba\ KH :G KKKJ l k —8. 40. F_oZghobfbq_kdbc kbgl_a \ g_hj]Zgbq_kdhc obfbb K[ gZmqg lj Ih^ j_^ ?= :\\Zdmfh\Z Gh\hkb[bjkd GZmdZ k 41. Rbjhdh\ X = Bevbg : I Ba\ KH :G J:G KKKJ k —38. 42. ;mly]bg I X Mki_ob obfbb l k —1780. 43. ;he^uj_\ < < :\\Zdmfh\ ? = LZf `_ l k —1856. 44. ;mygh\ J : FheqZgh\ < < Obf ijhf k —158. 45. Rbjhdh\ X = F_oZghobfby \ l_ogheh]bb dZlZebaZlhjh\ B\Zgh\h k 46. :\\Zdmfh\ ? = Obf l_ogheh]by k —17. 47. :g^jbZgZkmem G L b ^j Ba\ \ukr mq_[ aZ\_^_gbc Obfby b obfbq_kdZy l_ogheh]by k —59. 48. Bevbg : I b ^j GZmqgu_ hkgh\u ijb]hlh\e_gby dZlZebaZ lhjh\ Gh\hkb[bjkd k —185. 49. <Zkbev_\Z G : Rbjhdh\ X = LZf `_ k —75. 50. E_\bg ; ? Lj_lvydh\ X > Nbabdh-obfbq_kdb_ hkgh\u ihemq_gby b ijbf_g_gb_ n_jjblh\ F F_lZeemj]by 51. ;eykk_ k @ DjbklZeehobfby n_jjhribg_e_c F F_lZeemj ]by k 52. E_lxd E F @mjZ\e_\ = B Obfby b l_ogheh]by n_jjblh\ E Obfby k 53. Dhkh\Z G < b ^j G_hj]Zg fZl l k —484. 54. Bkmih\Z E : b ^j Dbg_lbdZ b dZlZeba l k —139. 55. :[Zdmfh\ : F b ^j Mki_ob obfbb l k —139. 56. FheqZgh\ < < ;mygh\ J : Dbg_lbdZ b dZlZeba l k —1423. 57. IZ\exobg X L b ^j >hde :G KKKJ l k —864. 58. IZ\exobg XL b ^j Ba\ :G KH :G KKKJ l k —20. 59. Bkmih\Z E: b ^j Dbg_lbdZ b dZlZeba l k —320. 60. Bkmih\Z E: b ^j LZf `_ l k —480. 61. Hkljhmrdh :: Rm[_jl W @ ijbde obfbb l k —1320. 62. Lj_lvydh\ X> L\_j^hnZagu_ j_Zdpbb F Obfby k k 63. >_evfhg ; Dbg_lbdZ ]_l_jh]_gguo j_Zdpbc F Fbj 64. Ijh^Zg ? : G_hj]Zgbq_kdZy lhihobfby Fbgkd GZmdZ b l_ogbdZ k 65. He_cgbdh\ G G b ^j G_hj]Zg fZl l k —486. 66. Bevbg : I Kfbjgh\ G G Bevbg : : GZmqgu_ hkgh\u ijb]hlh\e_gby dZlZebaZlhjh\ Hfkd k 67. Bevbg : : Kfbjgh\ G G Bevbg : I Wg_j]hk[_j_]Zxsb_ l_ogheh]bb wdheh]bq_kdb [_ahiZkguo ijhba\h^kl\ B\Zgh \h k 68. IZjn_gh\ < < GZabih\ J : G_hj]Zg fZl l k —106. 69. Bevbg : : Kfbjgh\ G G Bevbg : I L_jfh^bgZfbdZ ih\_joghklguo y\e_gbc b Z^khj[pbb B\Zgh\h k —47. 70. IZl_gl JN 2005. 71. Bevbg : I Ijhdhnv_\ < X DZlZeba \ ijhfure_gghklb k —51. 72. Bevbg : I Rbjhdh\ X = <hijhku dbg_lbdb b dZlZebaZ B\Zgh\h BOLB k —55. 73. Djm]ebpdbc G G Hkgh\u nbabdh-obfbq_kdhc f_oZgbdb Db_\ <ukrZy rdheZ q k 74. Bevbg : I Ijhdhnv_\ < X Nbabdh-obfbq_kdZy f_oZgbdZ \ nhjfh\Zgbb dZlZebaZlhjh\ B\Zgh\h B=OLM k 75. :\l k\b^ KKKJ 93
