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Local structure and kinetics of paramagnetic defects, induced by γ-irradiation of the erbium doped Ag5Ga5Ge95S200 glasses

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Defects induced by γ-irradiation in Er-free and Er-doped glasses Ag5Ga5Ge95S200 were studied using the Raman and EPR spectroscopies. It is shown that γ-irradiation causes an increase in the intensity of Raman bands related with formation of S3Ge-GeS3 structural groups. During the low-temperature annealing at temperatures of 95–145 °C, the concentration Ns of γ-induced paramagnetic centres (PC), having the axial symmetry of the g-tensor with gz = 2.0180 and gx = gy = 2.0088, is being strongly reduced and the symmetry of the environment of these centres becomes lower. Subsequent storage of annealed samples in the air for about 15 days leads to a gradual restoration of the Ns concentration. The kinetics of these processes is described taking into account both the high mobility of sulfur vacancy and the long-time relaxation of the glass structure. A correlation between the intensity of 257 cm⁻¹ Raman band belonging to the S3Ge(Ga)-(Ga)GeS3 complex and PC characteristics is discussed.
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UNCORRECTED PROOF
)=NH>86)=NH>8HD;DC9:CH:9&6II:G MMM MMMM MMMMMM
DCI:CIHA>HIH6K6>A67A:6I,8>:C8:>G:8I
)=NH>86)=NH>8HD;DC9:CH:9&6II:G
?DJGC6A=DB:E6<:=IIE::H:AH:K>:G8DB
%D86A HIGJ8IJG: 6C9 @>C:I>8H D; E6G6B6<C:I>8 9:;:8IH >C9J8:9 7N γ>GG69>6I>DC D; I=:
:G7>JB 9DE:9 < 6 :, <A6HH:H
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6V. Lashkaryov Institute of Semiconductor Physics, NAS of Ukraine, Kyiv, Ukraine
7Eastern European National University Named By Lesya Ukrainka, Lutsk, Ukraine
8National University for Water Economy and Nature Management, Rivne, Ukraine
9Lutsk National Technical University, Lutsk, Ukraine
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Keywords
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:;:8IH >C9J8:9 7N γ>GG69>6I>DC >C G;G:: 6C9 G9DE:9 <A6HH:H < 6 :, L:G: HIJ9>:9 JH>C< I=: +6B6C
6C9 )+ HE:8IGDH8DE>:H "I >H H=DLC I=6I γ>GG69>6I>DC 86JH:H 6C >C8G:6H: >C I=: >CI:CH>IN D; +6B6C 76C9H G:
A6I:9 L>I= ;DGB6I>DC D; , : :,HIGJ8IJG6A <GDJEH JG>C< I=: ADLI:BE:G6IJG: 6CC:6A>C< 6I I:BE:G6IJG:H D;
 R I=: 8DC8:CIG6I>DC 'HD; γ>C9J8:9 E6G6B6<C:I>8 8:CIG:H ) =6K>C< I=: 6M>6A HNBB:IGN D; I=: <I:C
HDG L>I= <O  6C9 <M <N  >H 7:>C< HIGDC<AN G:9J8:9 6C9 I=: HNBB:IGN D; I=: :CK>GDCB:CI
D; I=:H: 8:CIG:H 7:8DB:H ADL:G ,J7H:FJ:CI HIDG6<: D; 6CC:6A:9 H6BEA:H >C I=: 6>G ;DG 67DJI  96NH A:69H ID 6
<G69J6A G:HIDG6I>DC D; I=: 'H8DC8:CIG6I>DC -=: @>C:I>8H D; I=:H: EGD8:HH:H >H 9:H8G>7:9 I6@>C< >CID 688DJCI 7DI=
I=: =><= BD7>A>IN D; HJA;JG K686C8N 6C9 I=: ADC<I>B: G:A6M6I>DC D; I=: <A6HH HIGJ8IJG: 8DGG:A6I>DC 7:IL::C I=:
>CI:CH>IN D;  8B+6B6C 76C9 7:ADC<>C< ID I=: , : 6 6 :,8DBEA:M 6C9 ) 8=6G68I:G>HI>8H >H 9>H
8JHH:9
1. Introduction
-=: JC>FJ: ;:6IJG: D; 8=6A8D<:C>9: <A6HH:H =  9DE:9 L>I= :G
7>JB >H I=: 8DB7>C6I>DC D; >CI:CH: E=DIDAJB>C:H8:C8: )% L>I= =><=
IG6CHE6G:C8N >C I=: K>H>7A: 6C9 C:6G>C;G6G:9 G:<>DCH 45 L=>8= B6@:H
I=:B EGDB>H>C< ;DG JH: >C I:A:8DBBJC>86I>DC 9:K>8:H >C E6GI>8JA6G >C
HE68: -=: G69>6I>DC HI67>A>IN D; I=:H: B6I:G>6AH >H >BEDGI6CI 7:86JH: ;DG
B6I>DC D; 9:;:8IH 7N γ>GG69>6I>DC 6;;:8IH I=: HIGJ8IJG: 6C9 )% EGDE:GI>:H
D; =  +:6AAN >I L6H ;DJC9 >C B6CN HIJ9>:H I=6I G69>6I>DC>C9J8:9 9:
;:8IH D88JG >C I=: 8GNHI6AA>C: 6C9 <A6HH 8=6A8D<:C>9:H JC9:G I=: 68I>DC
D; I=: γG6NH 45 -=: AD86A HIGJ8IJG: >H IG6CH;DGB:9 45 699>I>DC6A
G69>6I>DC>C9J8:9 67HDGEI>DC 76C9H B6N D88JG >C I=: DEI>86A 67HDGE
I>DC HE:8IG6 45 6C9 CDCA>C:6G E>:ODDEI>86A 6C9 )% EGDE:GI>:H 8=6C<:
45 .C9:G A6G<: 9DH:H D; G69>6I>DC I=: 76C9 <6E 9:8G:6H:H 45
-=: 67>A>IN D; G69>6I>DC ID 6;;:8I DEI>86A EGDE:GI>:H D; HJ8= H:B>8DC9J8
IDGH 86C 7: JH:9 ;DG 9:H><C D; 8DCI68IA:HH H:CHDGH (C I=: DI=:G =6C9
I=: IG6CHE6G:C8N >C I=: K>H>7A: 6C9 >C;G6G:9 HE:8IG6A 76C9H I=: 67>A>IN D;
= ID IG6CHB>HH>DC D; DEI>86A 96I6 6H L:AA 6H 6 G:A6I>K:AN A6G<: >C9:M
D; G:;G68I>DC 6C9 I=: FJ6CIJB N>:A9 D; )% 6AADLH I=:>G JH6<: 6H 68I>K:
B:9>6 >C A6H:G I:8=CDAD<N 45 DEI>86A I=:GBDB:I:GH 45 A><=I 8DC
K:GI:GH 45 6C9 X7:G DEI>8H 45
"I >H E6GI>8JA6GAN >BEDGI6CI ID >CK:HI><6I: I=: D88JGG:C8: 6C9 IG6CH
;DGB6I>DC 9NC6B>8H D; I=: 9:;:8I HJ7HNHI:B 6;I:G γ>GG69>6I>DC >C 8=6A8D
<:C>9: <A6HH:H 9DE:9 L>I= A6CI=6C>9:H G )G J '9 :I8 L=>8= 8DC
HI>IJI: 6 76H>H ;DG I=: BD9:GC DEID:A:8IGDC>8 9:K>8:H -=: :;;:8I D; γ>G
G69>6I>DC DC I=: IG6CH;DGB6I>DC D; I=: 9:;:8I HJ7HNHI:B >C = 6C
C:6A:9 6I ADL I:BE:G6IJG:H >H HD ;6G CDI HJ;X8>:CIAN HIJ9>:9 -=: B:I=D9
D; B6<C:I>8 G:HDC6C8: >H I=: BDHI HJ>I67A: ;DG >CK:HI><6I>DCH >C I=>H
X:A9 88DG9>C< ID +:; 45 I=: 9:;:8I HJ7HNHI:B >C I=: < 6 :,
<A6HH:H 9>G:8IAN 6;;:8IH I=: DEI>86A EGDE:GI>:H G 8AJHI:G>C< 6C9 :K:CIJ
6AAN I=: )A EGDE:GI>:H H L>AA 7: H=DLC >C I=: EG:H:CI LDG@ I=: HIJ9>:9
=:G: E6G6B6<C:I>8 9:;:8IH =6K: 6 ADL 9>H>CI:<G6I>DC I=G:H=DA9 6C9 86C
7: IG6CH;DGB:9 ID I=: CDCB6<C:I>8 HI6I: 6I I=: ADL I:BE:G6IJG: 6CC:6A
>C< -=>H IG6CH;DGB6I>DC >H G:K:GH>7A: 6I GDDB I:BE:G6IJG: -=: HIJ9N D;
I=:H: EGD8:HH:H 9NC6B>8H L>AA H=:9 A><=I DC I=: 9:;:8I C6IJG: I=:>G E6G
I>8>E6I>DC >C I=: 9:;:8I 8AJHI:G>C< 6C9 EG:9>8I>DC D; DEI>86A EGDE:GI>:H >C
I=: HNHI:B JC9:G γ >GG69>6I>DC
AI=DJ<= I=: :,<A6HH =6H 7::C HIJ9>:9 ;DG 6 ADC< I>B: C:L EGDE
:GI>:H D; HDA>9 :A:8IGDANI:H 6G: ;DGB:9 >; H>AK:G >H 699:9 6H I=: < 6IDBH
=6K: 6 =><= BD7>A>IN >C = 45 -=>H XC9>C< 86JH:9 B6CN 6EEA>86
I>DCH A>@: H:CHDGH 76II:G>:H 6C9 B:BDGN 9:K>8:H 45 -=: H>AK:G
9>;;JH>DC 86C 7: 688:A:G6I:9 7N I=: G69>6I>DC 6C9 6H 6 G:HJAI 6 H><C>;>
DGG:HEDC9>C< 6JI=DG
E-mail address: =6AN6CKJ@GC:I // !6AN6C
=IIEH9D>DG<?E=NH7
+:8:>K:9  ,:EI:B7:G +:8:>K:9>CG:K>H:9;DGB  #6CJ6GN 88:EI:9  #6CJ6GN 
K6>A67A:DCA>C: MMM
S 
UNCORRECTED PROOF
A.A. Konchits et al. Physica B: Physics of Condensed Matter xxx (xxxx) xxx-xxx
86CI 8=6C<: >C I=: :A:8IG>86A EGDE:GI>:H D; I=: =DHI>C< <A6HH K:C
 6I < >CIGD9J8:9 >C I=: 8=6A8D<:C>9: B6IG>M 86JH:H I=: 8=6C<:
D; I=: = 8DC9J8I>K>IN 7N 67DJI DC: DG9:G D; B6<C>IJ9: 45 H 6 G:
HJAI D; I=: G69>6I>DC >C9J8:9 :;;:8IH >C I=: =  I=: G:B6G@67A: < 9>;;J
H>DC 6C9 I=: <GDLI= D; <8DCI6>C>C< 8AJHI:GH 86C D88JG -=: 699>C< D; 6
HB6AA ;G68I>DC D; 6 ID I=: <A6HH 6AADLH I=: :G7>JB >DCH ID 7: JC>;DGBAN
9>HIG>7JI:9 I=GDJ<=DJI I=: KDAJB: D; I=: B6IG>M 45 -=>H >H 9J: ID I=:
;68I I=6I I=: IG>K6A:CI G 6C9 6 86I>DCH 6G: G:EA68:67A: >C I=: 76H:
<A6HH:H 45
H HIJ9>:9 >C 9:I6>A >C +:;H 45 I=: HIGJ8IJG: D; I=: :,
<A6HH >H I=: 76H: ;DG < 6 :, <A6HH:H >CK:HI><6I:9 >C I=>H LDG@
"I >H 9:H8G>7:9 7N I=: 9>HDG9:G:9 C:I D; I:IG6=:9GDCH 45 -=: DEI>86A
EGDE:GI>:H D; < 6 :, <A6HH:H L:G: HIJ9>:9 >C +:;H 45 6C9
6AHD >C +:;H 45 L=:G: I=: H6B: H6BEA:H L:G: JH:9
"I L6H H=DLC >C +:; 45 I=6I HJ8= H6BEA:H :;;:8I>K:AN AJB>C:H8:C8:
>C I=: K>H>7A: 6C9 C:6G>C;G6G:9 G:<>DCH 6C9 I=: G69>6I>DC :;X8>:C8N 6C9
G69>6I>DC G:H>HI6C8: D; I=: <A6HH H><C>;>86CIAN 9:E:C9 DC I=: :G7>JB 8DC
I:CI
"C I=>H E6E:G I=: AD86A HIGJ8IJG: D; γ>GG69>6I:9 <A6HH:H 6C9 I=: @>
C:I>8H D; E6G6B6<C:I>8 9:;:8IH >C 8DC9>I>DCH D; I=: ADL I:BE:G6IJG: 6C
C:6A>C<  ]V L:G: >CK:HI><6I:9 JH>C< +6B6C HE:8IGDH8DEN 6C9
:A:8IGDC E6G6B6<C:I>8 G:HDC6C8: )+ -=: H6BEA:H D; I=: H6B: INE:H
6H >C +:; 45 C6B:AN I=: :G7>JB;G:: H6BEA: < 6 :, HD 6H
H6BEA:H 6C9 L>I= 6 8DC8:CIG6I>DC D; :G7>JB D;  6C9  6I 
G:HE:8I>K:AN L:G: >CK:HI><6I:9 -=: >GG69>6I>DC D; <A6HH:H ;GDB I=: D
HDJG8: L6H E:G;DGB:9 >C I=: 6>G 6I GDDB I:BE:G6IJG: AA I=: H6BEA:H
L:G: γ>GG69>6I:9 L>I= 6 9DH: D;  N -=: B:6C :C:G<N D; γG6NH
L6H 8ADH: ID  &:/
)+ B:6HJG:B:CIH L:G: 86GG>:9 DJI JH>C< 6 8B HE:8IGDB:I:G +6
9>DE6C,1 -D 9:I:GB>C: I=: 8DC8:CIG6I>DC D; E6G6B6<C:I>8
8:CIG:H ) 6 G:;:G:C8: H6BEA: &<( G L>I= I=: CJB7:G D; HE>CH
'G  L6H JH:9 -=: +6B6C HE:8IG6 L:G: :M8>I:9 7N I=:
HDA>9 HI6I: A6H:G L>I= I=: L6K:A:C<I= D;  CB 6C9 68FJ>G:9 JH>C< H>C
<A: HI6<: BDCD8=GDB6IDG :FJ>EE:9 L>I= C9DG  9:I:8IDG
2. Results and discussion
2.1. Raman spectroscopy characterization of glasses
-=: +6B6C HE:8IGDH8DEN >H 6C :;;:8I>K: B:I=D9 ;DG 6C6ANO>C< I=:
HIGJ8IJG6A DG9:G>C< >C I=: :,,: INE: <A6HH:H >C8AJ9>C< I=: :;;:8I D;
K6G>DJH >BEJG>I>:H 6C9 I:8=CDAD<>86A IG:6IB:CIH DC I=:>G HIGJ8IJG: &6C
>;:HI6I>DCH D; I=: DH8>AA6I>DCH 8DGG:HEDC9>C< ID 8:GI6>C HIGJ8IJG6A JC>IH
>C I=: HE:8IG6 D; I=: 76C9H 8=6C<: >C I=:>G >CI:CH>IN =6A; L>9I= 6C9 >C
;G:FJ:C8N EDH>I>DC EGDK>9: ;DG I=: 8DCIGDA D; I=: EGD8:HH:H D; HNCI=:
H>H 9DE>C< I:8=CDAD<>86A IG:6IB:CIH 6C9 :MI:GC6A >CYJ:C8: -=: +6B6C
HE:8IG6 D; G;G:: 6C9 G9DE:9 <A6HH H6BEA:H CDC>GG69>6I:9 6C9 γ>GG6
9>6I:9 L>I= 6 9DH: D;  N 6G: H=DLC >C >< -=: 6C6ANH>H D; +6
B6C HE:8IG6 L6H E:G;DGB:9 DC I=: 76H>H D; 6 9>HDG9:G:9 <G>9 BD9:A 45
L=>8= 8DCH>HIH D; 8DGC:G H=6G>C< :, I:IG6=:9GDCH 6C9 :9<:H=6G>C<
:, I:IG6=:9GDCH
-=: BDHI >CI:CH>K: 76C9 L>I= I=: ;G:FJ:C8N D;  8B 8DGG:HEDC9H
ID HNBB:IG>8 HIG:I8=>C< K>7G6I>DCH D; I=: HNBB:IGN  D; 8DGC:GH=6G>C<
: 6,I:IG6=:9GDCH L=>8= >H I=: B6>C HIGJ8IJG6A JC>I >C I=: : 6,
<A6HH:H 45 88DG9>C< ID I=: 8DBEDC:CI 8DBEDH>I>DC D; I=: HIJ9>:9
8DBEDJC9 I=: 6, I:IG6=:9GDCH 6G: 6EEGDM>B6I:AN 7N DG9:GH D;
B6<C>IJ9: HB6AA:G "C 699>I>DC I=: :A:B:CIH D; : 6C9 6 =6K: 8ADH:
B6HH:H 6C9 ;DG I=>H G:6HDC I=: ;G:FJ:C8>:H D; I=: 8DGG:HEDC9>C< 76C9H
L=>8= 6G: B6C>;:HI:9 >C I=: +6B6C HE:8IG6 6G: FJ>I: 8ADH: "I B:6CH I=6I
>I >H >BEDHH>7A: ID H:E6G6I: I=: 76C9H >C I=: HE:8IGJB G:HEDCH>7A: ;DG
6, K>7G6I>DCH
-=: 76C9 L>I= 6 ;G:FJ:C8N D;  8B86AA:9 I=: 876C9 >H 6H
H><C:9 ID I=: K>7G6I>DC6A BD9: D; I=: :9<:H=6G>C< :,I:IG6=:9GDCH
45 -=: BDHI 8DCIGDK:GH>6A ID96N >H I=: C6IJG: D; I=: DH8>AA6I>C<
BD9: L=>8= 86JH:H 6 76C9 L>I= 6 ;G:FJ:C8N D; Q 8B>C I=: +6
Fig. 1. +6B6C HE:8IG6 CDGB6A>O:9 ID I=: >CI:CH>IN D; I=: 76C9  8B 6 CDC>GG69>6I:9 H6BEA:H   6C9 L>I= 9>;;:G:CI E:G8:CI6<:H D; :G7>JB   6C9  6I  7 H6BEA:
7:;DG: 6C9 6;I:G >GG69>6I>DC 8 H6BEA: 7:;DG: 6C9 6;I:G >GG69>6I>DC 9 H6BEA: 7:;DG: 6C9 6;I:G >GG69>6I>DC 6H L:AA 6H 6;I:G 6CC:6A>C< -=: >CH:I ID >< H=DLH I=: HE:8IGJB D; I=:
>C>I>6A H6BEA: 6C9 >IH 9:8DBEDH>I>DC >CID 8DBEDC:CIH
UNCORRECTED PROOF
A.A. Konchits et al. Physica B: Physics of Condensed Matter xxx (xxxx) xxx-xxx
B6C HE:8IGJB .CA>@: I=: DI=:GH I=>H 76C9 >H CDI 8A:6GAN B6C>;:HI:9
>C I=: HE:8IGJB CDI K>H>7A: >C I=: B6M>BJB D; I=: 76C9 !DL:K:G >I
>H 9:I:8I:9 DCAN 6H 6 G:HJAI D; I=: :ME6CH>DC D; I=: 8DBEA:M HE:8IGJB
DC H:E6G6I: 8DBEDC:CIH >< 6 >CH:GI 88DG9>C< ID +:; 45 I=:
HJ776C9 L>I= 6 B6M>BJB 6I  8B>H 86JH:9 7N K>7G6I>DCH D; I=:
8DGC:GH=6G:9 <GDJEH :, "C 6CDI=:G LDG@ 45 I=: 76C9 L>I= 6
;G:FJ:C8N D; Q 8B>H 6HHD8>6I:9 L>I= I=: EG:H:C8: D; 9:;:8I>K:
B:B7:G:9 G>C< 8AJHI:GH >C I=: HIGJ8IJG: D; :,<A6HH
7GD69 76C9 L>I= 6 ;G:FJ:C8N D; Q 8B>H 6HHD8>6I:9 L>I= YJ8
IJ6I>DCH D; ILD I:IG6=:9GDCH L=>8= 6G: 8DCC:8I:9 7N K:GI>8:H I=GDJ<= 6
7G>9<: 6C 6IDB D; HJA;JG >C , :, :,45 88DG9>C< ID +:; 45
I=: 8DCIG>7JI>DC ID I=>H 76C9 86C 6AHD 7: <>K:C 7N I=: DH8>AA6I>DCH D;
H=DGI ,, 8=6>CH 7:IL::C :,I:IG6=:9GDCH
76C9 L>I= 6 ;G:FJ:C8N D; Q 8B>H 6HHD8>6I:9 L>I= YJ8IJ6
I>DCH D; I=: HIGJ8IJG6A JC>IH D; , : 6 6 :,45 H 86C 7: H::C
;GDB >< 6 6C >C8G:6H: D; CDC8AJHI:G:9 :G7>JB 8DCI:CI >C I=: <A6HH
A:69H ID 6C >C8G:6H: >C I=: >CI:CH>IN D; DCAN ILD 76C9H L>I= ;G:FJ:C
8>:H D;  6C9  8B6I I=:>G 8DCHI6CI L>9I= ,>B>A6G 8=6C<:H D8
8JG 6AHD L>I= I=: γ>GG69>6I>DC H 6 G:HJAI I=: γ>GG69>6I>DC A:69H ID
I=: ;DGB6I>DC D; , : :,HIGJ8IJG6A JC>IH 6C9 8DGC:GH=6G:9 <GDJEH
:, (C I=: DI=:G =6C9 I=>H ;68I :K>9:C8:H I=: 9:HIGJ8I>DC D; DI=:G
7DC9 INE:H B:CI>DC:9 67DK: -=: >CI:CH>IN D; I=: 76C9 L>I= 6 ;G:
FJ:C8N D;  8B6I I=: γ>GG69>6I>DC >C8G:6H:H 9:HE>I: I=: ;68I I=6I
I=: 7>C9>C< :C:G<N : :  :/ >H I=: HB6AA:HI >C 8DBE6G>HDC L>I=
:,  :/ 6C9 ,,  :/ "C I=>H G:A6I>DC >I >H :ME:8I:9 I=6I
I=: CJB7:G D; , : :,HIGJ8IJG6A JC>IH L>AA 9:8G:6H: >C I=: γ>GG6
9>6I>DC EGD8:HH !DL:K:G 6C6ANO>C< +6B6C HE:8IG6 >I >H C:8:HH6GN ID
I6@: >CID 688DJCI I=: ;68I I=6I I=: >CI:CH>IN D; I=: 76C9 L>I= 6 ;G:
FJ:C8N D;  8BH><C>;>86CIAN >C8G:6H:H L>I= γ>GG69>6I>DC DCAN >C
I=: <A6HH:H 9DE:9 L>I= H>AK:G 46C955 -=: A6II:G B6N 7: 9J:
ID I=: ;68I I=6I 9JG>C< I=: γ>GG69>6I>DC I=: HJA;JG 96C<A>C< 7DC9H 6G:
;DGB:9 L=:G:6H I=: >CI:CH>K: < 9>;;JH>DC HJEEDGIH ;DGB6I>DC D; <,
6C9 < :,8DBEDJC9H HD I=6I I=: G6I>D D; I=: : ID , 6IDBH CJB
7:G >C I=: =DHI>C< 768@7DC: >C8G:6H:H C 699>I>DC6A ADLI:BE:G6IJG:
6CC:6A>C<  R D; I=: γ>GG69>6I:9 H6BEA:H >C K68JJB L>I= 6 HJ7H:
FJ:CI =DA9>C< >C I=: 6>G ;DG  = 9D:H CDI EG68I>86AAN 8=6C<: I=: >CI:C
H>IN G6I>D 7:IL::C I=: 76C9H D;  8B6C9  8B I I=: H6B:
I>B: I=: >CI:CH>IN G6I>D 7:IL::C I=: 76C9H D;  8B6C9  8B
9:8G:6H:H H:: I=: HE:8IGJB D; I=: 6CC:6A:9 6C9 γ>GG69>6I:9 H6BEA: 
>C >< 9
2.2. Kinetics of γ-induced paramagnetic defects during low-temperature
annealing
-=: )+ H><C6AH L:G: CDI 9:I:8I:9 >C I=: CDC>GG69>6I:9 H6BEA:H >:
I=: 8DC8:CIG6I>DC D; E6G6B6<C:I>8 9:;:8IH 'H>H HB6AA:G I=6C I=: G:<>H
IG6I>DC I=G:H=DA9 -=: )+ HE:8IG6 ;DG γ>GG69>6I:9 L>I= 9DH:  N
H6BEA:H 7:;DG: 6CC:6A>C< 6G: <>K:C >C ><
=6G68I:G>HI>8 E6G6B:I:GH D; E6G6B6<C:I>8 8:CIG:H ;DGB>C< HE:8IG6 >C
>< 9D CDI 9>;;:G ;GDB I=DH: EG:K>DJHAN HIJ9>:9 >C DJG LDG@ 45 H
H=DLC >C +:; 45 ) G:HEDCH>7A: ;DG I=: )+ H><C6A =6K: I=: 6C>HDIGDE>8
<I:CHDG L>I= I=: 6M>6A HNBB:IGN <O  6C9 <M <N  "C
I=>H HIJ9N I=: 67DK: B:CI>DC:9 H6BEA:H L:G: HJ7?:8I:9 ID I=: ADLI:B
E:G6IJG: 6CC:6A>C< >C K68JJB L>I=>C I=: I:BE:G6IJG: G6C<: D;
 R R HIGDC< :;;:8I D; ADL I:BE:G6IJG: 6CC:6A>C< DC I=: )+
H><C6A D; EG:K>DJHAN ;DGB:9 7N γ>GG69>6I>DC E6G6B6<C:I>8 9:;:8IH =6H
7::C I=: XGHI I>B: G:K:6A:9
-=: 9:E:C9:C8: D; I=: 8DC8:CIG6I>DC D; ) DC I=: 9JG6I>DC D; K68
JJB 6CC:6A>C< D; H6BEA: 6I -  R >H H=DLC >C ><
H ;DAADLH ;GDB >< 'H9:8G:6H:H 9JG>C< I=: 6CC:6A>C< 7N 67DJI
 I>B:H -=: IG6CH;DGB6I>DC D; HE:8IG6 9JG>C< 6CC:6A>C< D; H6BEA:H
6I I:BE:G6IJG:H D;   6C9 RV 6H L:AA 6H I=:>G G:8DK:GN 9JG
>C< HJ7H:FJ:CI =DA9>C< >C I=: 6>G >H CDI IG>K>6A -=:G: EGD8::9H CDI DCAN
Fig. 2. )+ HE:8IG6 D; I=: γ>GG69>6I:9 <A6HH H6BEA:H   6C9 8DCI6>C>C< I=: :G7>JB
L>I=   6C9  6I G:HE:8I>K:AN 7:;DG: I=: 6CC:6A>C< -=: >GG69>6I>DC 9DH: L6H
:FJ6A ID  N
Fig. 3. DC8:CIG6I>DC D; E6G6B6<C:I>8 9:;:8IH 'H >C H6BEA: 6H ;JC8I>DC D; K68JJB 6C
C:6A>C< I>B: 6I -  R ,NB7DAH :ME:G>B:CI HDA>9 A>C: I=:DGN
6 9:8G:6H: >C I=: 8DC8:CIG6I>DC D; I=: ) G:HEDCH>7A: ;DG H><C6AH EG:
H:CI:9 >C >< 7JI I=: HE:8IGJB 8=6C<:H 6H >I >H 9:BDCHIG6I:9 >C ><
6 6C9 7
0: 7:A>:K: I=6I I=: K686C8N BDI>DC 6C9 <A6HH B6IG>M G:A6M6I>DC 9JG
>C< I=: ADL I:BE:G6IJG: 6CC:6A>C< 86JH: I=: G:DG>:CI6I>DC D; ) 6C9 G:
9J8I>DC D; I=:>G HNBB:IGN HD I=6I I=G:: B6>C 8DBEDC:CIH D; I=: <I:C
HDG 6G: H=>;I:9 ID <O  TU <N  TU 6C9
<M  TU >C I=: G;G:: H6BEA:  ;I:G I=: ADC<I:GB
=DA9>C< D; I=: 6CC:6A:9 H6BEA: >C I=: 6>G I=: 8=6G68I:G>HI>8 E6G6B:I:GH
D; I=: )+ H><C6A <G69J6AAN G:IJGC ID I=: K6AJ:H D7H:GK:9 7:;DG: I=: 6C
C:6A>C< -=: )+ H><C6A D; ) >C H6BEA: L>I=  6I G G:B6>CH >C
I=: H6B: G:HDC6C8: B6<C:I>8 X:A9 8DGG:HEDC9>C< ID I=: 6K:G6<:9 HE:8
IGJB L>I= <PP  6C9 <  7JI >I >H HEA>I 9J: ID I=: 9:
8G:6H: D; I=: A>C: L>9I=
>< 6 H=DLH I=: 9:86N D; I=: B6>C H><C6A >CI:CH>IN >C I=: G;G::
H6BEA:  6C9 I=: G:HJAIH ;DG G 8DCI6>C>C< H6BEA:H 6C9 6G: <>K:C
>C >< 7 'DI: I=6I 6I I6CC  B>C I=: >CI:CH>IN D; I=: )+ A>C: 6H
L:AA 6H >IH <;68IDG >C >< 6 >C8G:6H: 67CDGB6AAN -=>H ;68I =6H HD ;6G
CD :MEA6C6I>DC
UNCORRECTED PROOF
A.A. Konchits et al. Physica B: Physics of Condensed Matter xxx (xxxx) xxx-xxx
Fig. 4. 6 -=: )+ HE:8IGJB ;DG H6BEA: G ;G:: 6;I:G  B>C 6CC:6A>C< 6I  R -=:
HE:8IGJB 7:;DG: 6CC:6A>C< >H H=DLC >C >< 8JGK:  b -=: )+ HE:8IGJB ;DG H6BEA:
 6I G 6;I:G  B>C 6CC:6A>C< 6I  R 6C9 HJ7H:FJ:CI :MEDHJG: ID 6>G ;DG  =
-=: HE:8IGJB 7:;DG: 6CC:6A>C< >H H=DLC >C >< 8JGK: 
AA I=: G:HJAIH >C >< 6 6C9 7 6G: 9:H8G>7:9 7N ILD :MEDC:CI>6A
;JC8I>DCH I6CC caU:ME Iτ 7U:ME Iτ L>I= 8DCHI6CIH a,
b, τ1,τ29>;;:G:CI ;DG 9>;;:G:CI H6BEA:H 6H >I >H H::C ;GDB -67A:
-=: 8DBBDC EGDE:GIN D; 6AA H6BEA:H >H I=: EG:H:C8: D; ;6HI :MEDC:C
I>6A ;JC8I>DC L>I= τ B>C L=>8= >C9>86I:H ID I=: BDI>DC D; K686C
8>:H &DG:DK:G DC: 86C HJEEDH: I=6I I=: ) 8DCI6>CH I=: K686C8N D; HJA
;JG +:6AAN I=: HJA;JG =6H 6 B6M>BJB 9>;;JH>DC G6I: 6C9 I=: B>C>BJB
68I>K6I>DC :C:G<N ;DG 9>;;JH>DC 45 -=: 6CC:6A>C< 68I>K6I:H I=: BDI>DC
D; 6 HJA;JG 6IDB ID >IH K686C8N /H L=>8= >H >C I=: H:8DC9 H=:AA D; I=:
C:6G:HI :CK>GDCB:CI H 6 G:HJAI I=: ) 9>H6EE:6GH 7:86JH: 6 >C 67
H:C8: D; /,9D:H CDI G:K:6A E6G6B6<C:I>HB
-=: H:8DC9 :MEDC:CI>6A ;JC8I>DC 9:E:C9H DC I=: 6BDJCI D; G >C
H6BEA:H C6B:AN τ>H ADC<:G >C H6BEA:H L>I= A6G<:G G 6BDJCI :H>9:
I=>H G >C8G:6H:H I=: 8DCIG>7JI>DC D; I=: H:8DC9 :MEDC:CI -=>H ;68I H6NH
67DJI I=: HADL>C< 9DLC D; I=: A6II>8: G:A6M6I>DC >C EG:H:C8: D; G
"; 6;I:G I=: ADL I:BE:G6IJG: 6CC:6A>C< H6BEA: G:B6>CH DE:C >C I=:
6>G ;DG 6 ADC< I>B: 67DJI  96NH I=: )+ H><C6A >H 6ABDHI 8DBEA:I:AN
G:HIDG:9 7JI >I EGD8::9H HADLAN >< H=DLH I=: G:8DK:GN D; I=: )+
H><C6A >C H6BEA:  6I G
(C: 86C H:: >C >< I=6I 6C >C8G:6H: D; 6CC:6A>C< I:BE:G6IJG:
G:HJAIH >C 6 A>IIA: A6G<:G 9:86N D; H><C6A 7JI I=: G:8DK:GN EGD8:HH
Fig. 5. 6 =6C<: D; I=: ) 8DC8:CIG6I>DC 'HK:GHJH I=: 6CC:6A>C< I>B: >C H6BEA: G
;G:: ^6CC RV HFJ6G:H 6G: I=: :ME:G>B:CI6A ED>CIH 6C9 HDA>9 8JGK: >H I=: 86A8JA6I:9
I>B: ;JC8I>DC "CH:GI 9:BDCHIG6I:H 67CDGB6A 7:=6K>DG D; I=: )+ H><C6A 6I I6CC  B>C
b. =6C<: D; I=: ) 8DC8:CIG6I>DC K:GHJH I=: 6CC:6A>C< I>B: -6CC  ;DG  8>G
8A:H 6C9 ^6CC RV ;DG  HFJ6G:H %>C:H 6G: 86A8JA6I:9 I>B: ;JC8I>DCH IG>6C<A:H 6G:
I=: :ME:G>B:CI6A ED>CIH ;DG C:L H><C6A "HEA>I DZ ;GDB I=: B6>C H><C6A
Table 1
DCHI6CIH D; I=: ;JC8I>DC 9:86N
,6BEA: 'G6I c a b τ1B>C τ2B>C
   
    
    
<D:H BJ8= ;6HI:G ;I:G 6CC:6A>C< 6I -6CC  R I=: ) 8DC8:CIG6
I>DC >C8G:6H:H ;DAADL>C< I=: ;JC8I>DC D; :ME I L=:G:6H 6;I:G
6CC:6A>C< 6I -6CC  R I=: ) 8DC8:CIG6I>DC >C8G:6H:H 6H ;JC8I>DC
D; :ME I
"I >H LDGI= CDI>C< I=6I 7DI= I=: +6B6C 6C9 I=: )+ HE:8IGDH8DE>:H
8:GI6>CAN >C9>86I: I=6I G HJEEDGIH I=: HI67>A>IN D; I=: <A6HH B6IG>M %:I
JH B6@: HDB: HI6I:B:CIH 8DC8:GC>C< I=: C6IJG: D; I=: HIJ9>:9 E6G6
B6<C:I>8 8:CIG:H -=: 6M>6A HNBB:IGN D; <I:CHDG :K>9:C8:H I=6I ) >H 6
8DBEA:M -=: ;6HI :MEDC:CI>6A ;JC8I>DC D; I=: 8DC8:CIG6I>DC 9:86N ?JH
I>X:H I=6I I=: K686C8N >H DC: D; I=: 8DBEDC:CIH -=: 67H:C8: D; =NE:G
UNCORRECTED PROOF
A.A. Konchits et al. Physica B: Physics of Condensed Matter xxx (xxxx) xxx-xxx
Fig. 6. +:8DK:GN D; I=: )+ H><C6A >C I=: H6BEA: 9JG>C< >IH =DA9>C< >C I=: 6>G 6 6;I:G
6CC:6A>C<  B>C 6I  R 7 6;I:G G:6CC:6A>C< ;DG  B>C 6I  R
XC: HIGJ8IJG: >C I=: )+ HE:8IGJB >C9>86I:H ID I=: 67H:C8: D; I=: DLC
CJ8A:> HE>C >C I=: ) (CAN DC: 6IDB >C <A6HHN 6AADNH =6H CDC8DBE:C
H6I:9 :A:8IGDC HE>C L=>8= >H 6 L>I= 8DCX<JG6I>DC D; 4G59HE
-=: 6 6IDB =6H I=: CJ8A:> HE>C "  :;DG: I=: >GG69>6I>DC D; H6B
EA:H 6 9D:H CDI G:K:6A 6 E6G6B6<C:I>8 H><C6A !DL:K:G I=: K686C8N
8DC8:CIG6I>DC >H <GDL>C< JE 6;I:G I=: >GG69>6I>DC "; I=: 6 E:A:8IGDC
=6K>C< 6 CDC8DBE:CH6I:9 HE>C 7DJC9H I=: 6 6IDB L>I= I=: HJA;JG K6
86C8N /, I=: :A:8IGDC HE>C 9:CH>IN DC I=: 6 CJ8A:> L>AA 7: 67DJI O:GD
6C9 8DCH:FJ:CIAN I=: =NE:GXC: HIGJ8IJG: >H 67H:CI -=: 9:;:8I 6/,>H
I=: BDHI EDHH>7A: 86C9>96I: ID 7: I=: ) HIJ9>:9 >C DJG H6BEA:H >C6AAN
I=: HI6I:B:CI 6I I=: :C9 D; E6G6<G6E=  67DJI I=: 76C9 D;  8B>C
I=: +6B6C HE:8IGJB 7:ADC<H ID 6 8DBEA:M D; , : 6 8DGG:A6I:H L>I=
I=>H >9:6 67DJI I=: C6IJG: D; )
3. Summary
H ;DAADLH ;GDB I=: +6B6C HE:8IG6 I=: γ>GG69>6I>DC >C8G:6H:H I=:
6BDJCI D; :I=NA:C:A>@: , : :,HIGJ8IJG6A <GDJEH 9J: ID I=: <GDL>C<
G6I>D D; I=: CJB7:G D; : ID I=6I D; , 6IDBH -=: A6II:G >H 9J: ID I=: EG:
9DB>C6CI ;DGB6I>DC D; H>AK:GHJA;JG HIGJ8IJG6A JC>IH D; <, 6C9 < :,
>C I=: JCHIGJ8IJG:9 <G>9 D; I=: <A6HH
DG I=: XGHI I>B: >I >H 9:I:8I:9 I=6I I=: ADL I:BE:G6IJG:  R
6CC:6A>C< D; γ>GG69>6I:9 H6BEA:H 86JH:H 6 H><C>;>86CI JE ID ;DA9 9:
8G:6H: >C I=: CJB7:G D; E6G6B6<C:I>8 8:CIG:H 6C9 >C I=: ADL:G HNB
B:IGN D; I=: ) :CK>GDCB:CI HD I=6I <I:CHDG =6K>C< 7:;DG: I=: 6M
>6A HNBB:IGN <O  <M <N  7:8DB:H BDCD8A>C>8 L>I=
<O  <N  6C9 <M 
-=: 9:86N D; I=: ) 8DC8:CIG6I>DC L>I= I=: 6CC:6A>C< I>B: >H 9:
H8G>7:9 7N I=: HJB D; ILD :MEDC:CI>6A ;JC8I>DCH I=: ;6HI 9:86N L>I=
τ B>C >H G:A6I:9 L>I= BDI>DC D; K686C8N 6C9 I=: ADC<I>B: DC:
L>I= τ    B>C 9:E:C9>C< DC I=: G 8DC8:CIG6I>DC 8DGG:
HEDC9H ID I=: A6II>8: G:A6M6I>DC -=: 9:E:C9:C8: D; I=: ADC< G:A6M6I>DC
I>B: DC I=: G 8DC8:CIG6I>DC >C9>86I:H ID G HI67>A>O6I>DC D; I=: A6II>8:
HIGJ8IJG:
-=: G:8DK:GN D; E6G6B6<C:I>8 8:CIG:H >C I=: 6B7>:CI 6IBDHE=:G: 6;
I:G 6CC:6A>C< >C8G:6H:H I=: ) 8DC8:CIG6I>DC JE ID K6AJ:H L=>8= L:G:
G:8DG9:9 7:;DG: 6CC:6A>C< -=>H G:K:GH>7>A>IN >H I=: >BEDGI6CI @:N ;DG JC
9:GHI6C9>C< I=: ) C6IJG: -=: 9:;:8I 6/,>H I=: BDHI EGD767A: BD9:A
;DG I=: E6G6B6<C:I>8 8:CI:G HIJ9>:9 =:G:
>C6AAN I=: 76C9 D;  8B>C I=: +6B6C HE:8IGJB 7:ADC<>C< ID
I=: 8DBEA:M , : 6 6 :,8DGG:A6I:H L>I= I=: EGDEDH:9 C6IJG: D;
I=: )
-=:G:;DG: I=: G:HJAIH D; I=>H HIJ9N H=:9 I=: A><=I DC I=: C6IJG: 6C9
7:=6K>DG D; 9:;:8IH >C I=: γ>GG69>6I:9 8=6A8D<:C>9: <A6HH:H :ME6C9>C<
EDHH>7>A>IN ID 8DCIGDA I=:>G EGDE:GI>:H
H I=: = <A6HH:H 6G: 8DCH>9:G:9 ID 7: HJ>I67A: B6I:G>6AH ;DG 6EEA>
86I>DC >C I:A:8DBBJC>86I>DC 9:K>8:H E6GI>8JA6GAN >C I=: HE68: L>I= 6C
>C8G:6H:9 G69>6I>DC 768@<GDJC9 I=: @CDLA:9<: D; C6IJG: 6C9 7:=6K>DG
D; I=: 9:;:8I HNHI:B >C I=: <A6HH:H B6@:H >I EDHH>7A: ID EG:9>8I 6 8=6C<:
>C I=:>G AJB>C:H8:CI EGDE:GI>:H JC9:G G69>6I>DC 8DC9>I>DCH
-=: D7I6>C:9 G:HJAIH =6K: H=DLC I=6I I=: HNHI:B D; E6G6B6<C:I>8
9:;:8IH >H 6 EGD7: ;DG HIGJ8IJG6A IG6CH;DGB6I>DCH D88JGG>C< >C I=: <A6HH
A:69>C< ID 6 8=6C<: >C I=: AD86A HNBB:IGN D; I=: :CK>GDCB:CI D; 9:;:8IH
;GDB I=: 6M>6A ID I=: BDCD8A>C>8 DC: -=: :HI67A>H=:9 :MIG:B:AN =><=
BD7>A>IN D; K686C8>:H 6C9 I=: EDHH>7>A>IN D; FJ:C8=>C<E6G6B6<C:I>8
9:;:8IH 9J: ID 6 HA><=I =:6I>C< D; <A6HH:H 8DCXGB 6 EDHH>7>A>IN ID 8DC
IGDA I=: EGD8:HH D; G69>6I>DC>C9J8:9 9:;:8I ;DGB6I>DC 6C9 ID EGDADC< I=:
LDG@ I:GB D; I=: 9:K>8:H 76H:9 DC < 6 :, <A6HH:H
CRediT authorship contribution statement
A.A. Konchits: DGB6A 6C6ANH>H V.O. Yukhymchuk: DGB6A 6C6AN
H>H S.V. Krasnovyd: 0G>I>C< G:K>:L :9>I>C<
Uncited Reference
45
Acknowledgments
-=>H LDG@ L6H E6GI>6AAN HJEEDGI:9 7N I=: )GD?:8I D; ', D; .@G6>C:
[
References
45 #% 96B 1 3=6C< 9H =6A8D<:C>9: A6HH:H )G:E6G6I>DC )GDE:GI>:H 6C9
EEA>86I>DCH 0DD9=:69 )J7A>H=>C< %>B>I:9  E 
45 // !6AN6C // ,IG:A8=J@ /( 2J@=NB8=J@ ! $:KH=NC 2 6KN9NJ@
&/ ,=:K8=J@ ,/ /DGDCNJ@ +DA: D; HIGJ8IJG6A DG9:G>C< DC DEI>86A EGDE:GI>:H D;
I=: <A6HH:H < 6 :,G, )=NH>86   
45  3=>A>CH@6N6 /' %6OJ@>C '$ /6A::K $ (7A6HDK :M,M <A6HH:H :;:8IH
9:CH>IN 6C9 HIGJ8IJG: # 'DCGNHI ,DA>9H   
45 % W:GK>C@6  !GJ7N >C # ,IJ@: G:CC>C< )GD8 I= "CI DC; (C BDGE=DJH
6C9 %>FJ>9 ,:B>8DC9J8IDGH  -6NADGG6C8>H %DC9DC 
45 // !6AN6C  $DC8=>IH  ,=6C>C6 ,/ $G6HCDKN9 (( %:7:9 !
$:KH=NC &/ ,=:K8=J@ / D9C6GJ@ /( 2J@=NB8=J@ )+ D; γ>C9J8:9 9:
;:8IH 6C9 I=:>G :;;:8IH DC I=: E=DIDAJB>C:H8:C8: >C I=: <A6HH:H D; I=:
< 6 :,G,HNHI:B +69>6I )=NH =:B   
45 (" ,=EDINJ@ # >A>E:8@>  $DO9G6H -, $6K:IH@NN +69>6I>DC>C9J8:9 9:;:8I
;DGB6I>DC >C 8=6A8D<:C>9: <A6HH:H # 'DCGNHI ,DA>9H   
45 ( ,=EDINJ@  $DK6AH@>N - $6K:IH@NN + DADK8=6@ & )DE:H8J =:B>86A >C
I:G68I>DC D; 8=6A8D<:C>9: K>IG:DJH H:B>8DC9J8IDGH L>I= 67HDG7:9 >BEJG>I>:H >C
9J8:9 7N γ>GG69>6I>DC # (EID:A:8IGDC 9K &6I:G  
45 // !6AN6C /( 2J@=NB8=J@ 2 JA: $ (O<6 $# #:9GN@6 " "K6H=8=:C@D
& ,@DGN@ ! $:KH=NC " (A:@H:NJ@ )/ ->H=8=:C@D &/ ,=:K8=J@ &
)>6H:8@> )=DIDAJB>C:H8:C8: ;:6IJG:H 6C9 CDCA>C:6GDEI>86A EGDE:GI>:H D; I=:
< 6 :,G,<A6HH:H (EI &6I:G   
45 "/ $>IN@ // !6AN6C ! $:KH=NC " "K6H=8=:C@D " (A:@H:NJ@ ((
%:7:9 %6@H=B>C6G6N6C6 & )>6H:8@> 6"CG, H>C<A: 8GNHI6A
CDK:A B6I:G>6A ;DG 9:I:8I>DC D; γG69>6I>DC 7N E=DID>C9J8:9 CDCA>C:6G DEI>86A
B:I=D9 # &6I:G ,8> &6I:G A:8IGDC   
45 \ $>IN@ /( 2J@=NB8=J@  :9DG8=J@ // !6AN6C " "K6H=8=:C@D "
(A:@H:NJ@ & ,@DGN@ %6@H=B>C6G6N6C6 & A'6<<6G  A76HH6B
(( %:7:9 & )>6H:8@> %6H:G HI>BJA6I:9 E>:ODDEI>8H D; γ>GG69>6I:9
 6"C, 6C9  6"CG, H>C<A: 8GNHI6AH # AADNH DBE9
  
45 "/ $>IN@ $ (O<6 / !6AN6C " "K6H=8=:C@D & )>6H:8@>  6"C,
C6CD8GNHI6AA>I:H 6H CDK:A B6I:G>6AH ;DG CDCA>C:6G DEI>86A 9:I:8I>DC D; <6BB6 G69>6
I>DC &+, 9K   
45  1>6 , 6886GD  3=6D & 6A8DC>:G> =:C 6BB6 G6N >GG69>6I>DC >C
9J8:9 DEI>86A 76C9 <6E K6G>6I>DCH >C 8=6A8D<:C>9: <A6HH:H 'J8A "CHIGJB &:I=D9H
)=NH +:H   
45 - ,8=L:>O:G ' ,6BHDC + &DDG: 0 !:L6@ ' )6NC: +6G::6GI=
9DE:9 8=6A8D<:C>9: <A6HH X7:G A6H:G A:8IDC %:II   
45 // !6AN6C "/ $>IN@ ! $:KH=NC " "K6H=8=:C@D %6@H=B>C6G6N6C6
&/ ,=:K8=J@  :9DG8=J@ & )>6H:8@> ;;:8I D; I:BE:G6IJG: DC I=: HIGJ8IJG:
6C9 AJB>C:H8:C8: EGDE:GI>:H D; < 6 :,G,<A6HH:H # %JB>C 
 
45 // !6AN6C (2 $=NO=JC " "K6H=8=:C@D ! $:KH=NC " (A:@H:NJ@ )
-NH=8=:C@D () /DK@ 2/ JA>@ A:8IGDC>8 HIGJ8IJG: 6C9 DEI>86A EGDE:GI>:H D;
 6%6, 6C9  6%6G, H>C<A: 8GNHI6AH CDK:A A><=I8DCK:GI
>C< B6I:G>6AH )=NH>86   
45 $ &6>G6? (EI>86A 06K:<J>9: 6C9 %6H:GH >C "BEGDK:9 6AA>JB %6CI=6CJB ,JA
E=>9: A6HH )= I=:H>H .C>K:GH>IN D; ,DJI=6BEIDC ,DJI=6BEIDC .$ 
UNCORRECTED PROOF
A.A. Konchits et al. Physica B: Physics of Condensed Matter xxx (xxxx) xxx-xxx
45 ) =:C & >A6K6?=6A6 & &>I@DK6  -:CC: " ,6C8=:O HFJ:96 ! 6GC67N
,IGJ8IJG6A HIJ9N D; < :, HDA>9 :A:8IGDANI: <A6HH HNHI:B ;DG G:H>HI>K: G69>6I>DC
H:CH>C< "  9D>0&
45   >I@:C 0 )DC69:G +, *J>B7N AJHI:G>C< D; G6G: :6GI=H >C :H HJAX9:
<A6HH + =>B>:  
45 ! -6@:J8=> ( &6IHJ96 $ &JG6H: +:K:GH>7A: B:HDH8DE>8 HIGJ8IJG6A IG6CH;DGB6
I>DCH >C K68JJB :K6EDG6I:9 6BDGE=DJH :,: XAB HIJ9>:9 7N +6B6C H86II:G
>C< # 'DCGNHI ,DA>9H   
45 2 ,6@6<J8=> - !6C6H=>B6 $ (=6G6  ,>BDC & &>I@DK6 ,IGJ8IJG6A
IG6CH;DGB6I>DC >C :x,x x C:ILDG@ <A6HH:H HIGJ8IJG6A K6G>:I>:H >C
H=DGIG6C<: B:9>JBG6C<: 6C9 C6CDH8DE>8 H86A: )=NH +:K &6I:G 

45 * &:> # ,6>:C<6 # ,8=GDDI:C  &:N:G , &6GI>C )G:E6G6I>DC 6C9 8=6G68I:G>
O6I>DC D; <A6HH:H >C I=: <,, :,HNHI:B # 'DCGNHI ,DA>9H 
 
45 / &>IH6 + !DADB7 %DK6H & /:G:H & "K6C96 - $DK68= ,E:8IGDH8DE>8 K>
9:C8: D; D:M>HI:C8: D; AJHI:GH 6H:9 DC %DL α 6C9 !><= -:BE:G6IJG: β :,
GNHI6AA>C: )=6H:H >C A6HHN :GB6C>JB >HJAX9: &6IG>M &")+(  (E6I>?6
GD6I>6
45 %J8DKH@N  6A::C:G + $::O:G + :>AH ! ,>M ,IGJ8IJG6A >CI:GEG:I6I>DC D;
I=: >C;G6G:9 6C9 +6B6C HE:8IG6 D; <A6HH:H >C I=: 6AADN HNHI:B :M,M )=NH +:K
  
45  !J6C< 0 !:L6@ #/ 699>C< :EDH>I>DC 6C9 8=6G68I:G>O6I>DC D; <:GB6
C>JB HJAE=>9: <A6HH EA6C6G L6K:<J>9:H (EI>8 MEG:HH   
45 1 06C< , J # 2J 1 3=6D ! -6D ,IGJ8IJG6A >CK:HI><6I>DCH D;
:, 6,9, 8=6A8D<:C>9: <A6HH:H JH>C< +6B6C HE:8IGDH8DEN ,DA>9 ,I6I:
DBBJC   
45 & G6:C@A  GJB6GDK6 / )D9O:BC6 , ,A6C< % :C:H & /A8:@ - 06<C:G
!DL H>AK:G >CYJ:C8:H I=: HIGJ8IJG: 6C9 E=NH>86A EGDE:GI>:H D; 8=6A8D<:C>9: <A6HH
 :,,7, # 'DCGNHI ,DA>9H   
45 & 6A6@G>H=C6C &' $DO>8@>  )DL:A:>I , =6<6I -% A;DG9 & &>I@DK6
GNHI6AA>O6I>DC :;;:8IH >C 6CC:6A:9 I=>C :,XABH E=DID9>;;JH:9 L>I= < #
'DCGNHI ,DA>9H   
... A number of publications reported the influence of γrays irradiation on optical absorption spectra of such materials [10][11][12]. However, only few works are devoted to the analysis of changes in the photoluminescence (PL) intensity under the action of γ-radiation, establishing the mechanism of the PL and the nature of radiation-induced defects at different radiation doses [13][14][15]. This especially applies to the analysis of crystal structures of chalcogenides doped with RE metals. ...
... Irradiation with γ-rays leads to the appearance of radiationinduced defects that interfere with the processes of energy exchange between erbium ions and, as a consequence, with an increase in the radiation dose, the PL intensity decreases. According to our previous investigation of similar systems, Ga-V S can be the γ-induced defect centers [15]. ...
Article
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An erbium-doped β-GaLaS3 crystal has been grown by the solution-melt method, and the effect of γ-irradiation on their vibrational and radiative properties has been investigated. Experiments have demonstrated that the crystal is transparent in the near and mid-IR regions (transparency ∼62% in the range of 350 – 7100 cm-1), which allows it to be used as an effective matrix for creating lasers in this spectral range. For the first time, the vibrational spectrum of the crystal and the density of phonon states have been calculated using the DFT method. Both the original and γ -irradiated β-GaLaS3:Er crystals were investigated by Raman and IR spectroscopy. It has been established that irradiation with a dose of up to 5000 Gray does not lead to structural changes in the crystals. The effect of the formed defects is more clearly manifested in the IR reflection spectra, compared to the Raman spectra. The mechanism of the occurrence of excited states and the emission of Er ions embedded in the lattice has been established, and the effect of γ-irradiation on the radiative properties of β-GaLaS3:Er due to the occurrence of radiation-induced defects has been analyzed. A model has been constructed that explains the Stokes and anti-Stokes radiation of the erbium ions in the crystal. It has been demonstrated that the grown crystal has good prospects for sensor and laser technology of the near and mid-IR ranges due to relatively high values of optical transparency and the intense radiative capacity of the erbium ions.
... 13−15 Some established experimental physical methods for the investigation of lattice defects have not been applied so far to these materials. In particular, electron paramagnetic resonance (EPR) spectroscopy has proved to be capable of providing the defect geometry and charge state in numerous solid-state 16 and molecular systems, 17 including those structurally related to CZTS ternaries like CuInS 2 , 18 CuInSe 2 , 19 and CIGS, 20 but was not applied to CZTS so far. Among different techniques used for the fabrication of CZTS thin films, colloidal synthesis of CZTS nanocrystals (NCs) in solution 21,22 is highly attractive because of the immense possibilities of varying the synthesis parameters, NC functionalization, and full compatibility of the process with printing, spraying, and other low-cost techniques of thin-film fabrication, including those on flexible substrates. ...
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Precise x-ray diffraction measurements using high-energy x rays of synchrotron radiation and systematic Raman scattering measurements were carried out for GexS100−x(10⩽x⩽40) network glasses. The structural models of the network glasses were proposed based on the results. In the stoichiometric composition Ge33S67, GeS4 tetrahedral units are connected forming either corner-sharing or edge-sharing structures. In the S-rich glasses, S atoms are inserted between two neighboring GeS4 tetrahedra, resulting in a flexible floppy network. In a much more S-rich region, some S8 ring molecules are isolated from the network, and assemble to form a crystal in nanoscopic scale. In this respect, Ge10S90 samples are regarded as crystallized glasses. In the Ge-rich region, the GeS4 tetrahedra are connected with bridging Ge atoms. The connection makes a new rigid network. The bridging Ge-S bond is weaker than the intratetrahedron bond, and this leads to drastic changes in the optical properties.
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It was shown a possibility to use the (Ga54.59In44.66Er0.75)2S300 single crystal as optoelectronics detectors of gamma-irradiation using photoinduced nonlinear optical methods and photoluminescence. The crystal was irradiated by a ⁶⁰Co source at ambient conditions. The average energy of the incident γ-rays was about 1.25 MeV. The luminescence excitation was carried out using a 150 mW cw laser with wavelength 532 nm. The best results sensitive to the gamma irradiation were obtained for the third harmonic generations (THG) of the materials treated by bicolor Er: glass laser two beams propagated at angles about 21°–24°. The photoinduced gratings profile also were explored and their correlation with the gamma radiation and nonlinear optical response were explored. Comparison of photoluminescence and photoinduced nonlinear optical sensitivity to radiations was performed.
Article
The presented study shows how the incorporation of silver changes the structure and physical properties of chalcogenide glass (GeS2)50(Sb2S3)50. Nine samples with silver content (0–25 at. %) were studied to give a detailed picture. The structure and its changes were analyzed by Raman spectroscopy. The medium range order of the (GeS2)50(Sb2S3)50 glass was identified. The structural motif of interconnected SbS3/2 pyramids is the doorway for the silver incorporation in the (GeS2)50(Sb2S3)50 glass. The material hardness is significantly increased by up to 26% due to silver addition. The ability of silver to fill cavities in a glass is responsible for the observed hardness increase. Electronic properties and silver ion mobility were examined by impedance spectroscopy and radioactive tracer diffusion. The purpose of the presented study is to give an instructive description of how silver change the structure of the studied chalcogenide glass and give a complex feeling of how the silver changes its physical properties.
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Electronic structure and optical properties were studied for novel (Ga70La30)2S300 and (Ga69.75La29.75Er0.5)2S300 single crystals synthesized by solution-melt technique. In particular, X-ray photoelectron spectroscopy (XPS) was used to measure core-level binding energies and valence-band spectra for as-synthesized and Ar⁺ ion-irradiated surfaces of these crystals. Presented XPS measurements show that the (Ga70La30)2S300 and (Ga69.75La29.75Er0.5)2S300 single crystals are rather stable in relation to Ar⁺ ion-irradiation. X-ray emission (XE) S Kβ1,3 and Ga Kβ2 bands were measured for the (Ga70La30)2S300 crystal giving information on the energy distribution of the S 3p and Ga 4p states, respectively. A comparison of these XE bands on a common energy scale with the XPS valence-band spectrum of (Ga70La30)2S300 indicates that the principal contribution of the S 3p and Ga 4p states occurs mainly at the top and in the central part of the valence band, respectively. In addition, optical absorption and photoluminescence spectra of the crystals were explored. Energy band gap values are estimated as 2.01 and 1.99 eV at room temperature for the (Ga70La30)2S300 and (Ga69.75La29.75Er0.5)2S300 crystals, respectively. Observed high-intensity green photoluminescence band when excited by a laser emitting at 810 nm suggests that the (Ga69.75La29.75Er0.5)2S300 crystal is a very attractive material for infrared to visible light conversion.
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(Ga 55 In 45 ) 2 S 300 and (Ga 54.59 In 44.66 Er 0.75 ) 2 S 300 single crystals were successfully grown with the aim of exploring their potential for laser induced third harmonic generation (THG) and piezo-optical applications. Their Raman and luminescence spectra in the 150-300 K temperature range were studied. Influence of different gamma ray doses on the nonlinear optical properties were also explored. The optical properties of these crystals exhibit strong variation with temperature. It is concluded that (Ga 54.59 In 44.66 Er 0.75 ) 2 S 300 may be applied as promising materials for dosimetry applications in γ - radiation and optical temperature sensors.
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Single crystals (Ga55In45)2S300 and (Ga54.59In44.66Er0.75)2S300 possessing space group P61 were successfully grown and explored with respect to laser induced piezooptics. Their structural properties were studied by Raman spectroscopy and additionally, dependence of different gamma ray doses on the photoinduced piezo-optical responses were also explored. Structural parameters were evaluated using the Rietveld methods following the X-ray diffraction data. The chemical composition of the synthesized samples was determined by EDS analysis. We discussed the influence of Er³⁺-doping on the crystal structure and piezo-optical properties. It was established that these crystals behavior is very sensitive to γ−irradiation dose and therefore they are promising for applications as elastooptical radiation sensors.
Thesis
A number of developmental stages are still required to advance and mature optical waveguide technology in non-silica glasses. The primary stage includes raw material purification and improving quality and thermal stability of an optical glass for waveguide fabrication processes. Further stages can include design, application and integration of these waveguides with other photonic devices. Gallium lanthanum sulphide (Ga:La:S) chalcogenide glass (ChG), first discovered in 1976, is a material proposed as an optical waveguide for use in the infrared (IR). Interest in this glass system has been maintained, over the years, primarily due to its exceptional and unusual optical properties. The aim of this project is to advance the current state of art for Ga:La:S glass by demonstrating working solutions for fibre and planar waveguides. Chapter 1 of this thesis provides a general overview of current glass technology and the motivations of this project. The optical glass system under study has yet to attain acceptable stability for fibre production and as such investigation into fundamental manufacturing steps is still required. Raw material purity is an important aspect, of fabricating practical optical glasses, and directly affects performance. Chapter 2 of this thesis describes the purification and synthesis processes performed to produce raw materials with purity far superior to similar products available commercially. Each powdered precursor synthesised in our labs and used in fabrication of Ga:La:S based optical glasses has a transition metal impurity content of less than 1 parts-per-million (ppm wt%). The water content, OH-, of these fabricated glasses has been reduced to < 2 ppm. The primary concern when fabricating Ga:La:S based optical fibre is crystallisation. Optimising the composition to obtain a glass suitable for fibre fabrication is significant in providing thermal stability for fibre drawing. Chapter 3 describes some of the steps taken towards the fabrication and improvement of Ga:La:S based glasses for waveguide technology. The invention of a new variant in the Ga:La:S family of glasses provides key enhancements over existing Ga:La:S and Ga:La:S:O glasses. The hybrid oxy-chalcohalide glass, Ga:La:S:O:F, contains compounds of sulphide, oxide and fluoride as constituents. This new glass type provides significant thermal stability, in the context of fibre drawing. Fibre drawn from a single piece of polished Ga:La:S:O:F glass had attenuation at 1.5 and 4.0 µm of 3.3 and 2.1 dB m-1 respectively. The reduction of the OH- absorption at 2.9 µm to < 1 ppm in Ga:La:S:O:F glass, can potentially allow development of planar waveguide devices for the mid-IR. A range of extremely stable compositions for Ga:La:S, Ga:La:S:O and Ga:La:S:O:F glasses was also identified. These glasses were amorphous upon slow cooling in the furnace (8 oC min-1) indicating danced thermal stability against crystallisation. In Chapter 4 and 5, the fabrication and characterisation of channel waveguides is discussed. Photoinduced changes were introduced by directly writing waveguides into Ga:La:S glass through exposure to short wavelength light (l = 244 nm). Focused fluence of 1.5 - 150 J/cm2 from a continuous wave laser operating at 244 mn was applied, inducing photocompaction and photochemical changes. These passive channel waveguides were spatially single-mode and bad Dn ~ +10-3. The first chalcogenide channel waveguide laser in Nd3+-Ga:La:S glass was also demonstrated. Maximum laser output (l = 1075 nm) of 8.6 mW for an absorbed laser pump power of 89 mW and slope efficiency of 17% was achieved with measured device attenuation of < 0.5 dB cm-1. Discussed in Chapter 6 is the first demonstration of the hotdip spin coating process used to fabricate thin films of a ChG (Ga:La:S). This promising technique is presented as an enhancement to waveguide development. In addition, buried (50 µm) channel waveguides were directly written into the spun thin film using a pulsed laser source (l = 830 nm). These buried channel waveguides had a measured attenuation of < 1 dB cm-1.
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The chemical interaction of chalcogenide vitreous semiconductors (ChVS) with absorbed impurities induced by high-energetic (E>1 MeV) gamma-irradiation has been investigated at the example of vitreous v-As2S3. Radiation-induced processes of oxidation, hydrogenization, hydratation, carbonization and hydrocarbonization have been observed in this material after prolonged gamma-irradiation and studied using IR spectroscopy (4000-400 cm(-1)), laser mass-spectroscopy methods and electron microprobe analysis.
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Clustering of rare-earth dopants in GeAs sulfide glasses was studied by fluorescence spectroscopy of Pr-doped glasses and by EPR measurements of Gd-doped samples. The linewidth of the g ∼ 2 resonance of Gd3+, as well as the relative intensity of emission from the 1D2 level of Pr3+, was used as a relative measure of rare-earth clustering. Rare earths were found to have low solubility in uncodoped GeAs sulfide glasses, which also displayed poor fluorescence efficiency due to severe clustering. Codoping such glasses with Ga greatly enhanced rare-earth solubility and dispersal, particularly for Ga:rare earth ratios ≥ 10:1, as evidenced by the narrower EPR resonances and more intense luminescence of Gd- and Pr-doped glasses, respectively. In, P and Sn were also observed to ‘decluster’ rare earths, although less efficiently than Ga, whereas codoping with I was found to have no effect on clustering. These phenomena are explained by a structural model in which (1) rare-earth dopants and codopants are spatially associated and (2) rare-earth dispersal is accomplished by a statistical distribution of codopants in tetrahedral network sites.
Article
Raman investigations were carried out for various compositions of chalcogenide glasses in the GeS2–Ga2S3–CdS system. Addition of Ga2S3 into GeS2 results in the formation of metal–metal bonds and edge-shared GaS4/2 tetrahedra. Ge2+ ions may surround [GaS4/2]1− tetrahedra acting as charge compensators. Upon the addition of CdS into the GeS2–Ga2S3 system, the number of the metal–metal bonds and edge-shared GaS4/2 tetrahedra decreases, resulting in the formation of corner-shared tetrahedra with non-bridging sulfurs (NBS). Cd2+ ions can be dissolved into the glass network as charge compensators for these NBS and exited few [GaS4/2]1− tetrahedra. The high solubility of CdS is ascribed to the dissociation of metal–metal bonds and edge-shared tetrahedra in these Ga-containing glasses.