∆
2
⁄
ℎ = 4 3
4
= (∆ ℎ + ∆ ℎ + ∆ ℎ ) + 2 + 4
2
2
3 ℎ
ℎ
∆ ℎ =
∆ ℎ =
∆ ℎ =
=
=
∆ ℎ
ℎ
ℎ
∆ ̅ ℎ ∆ ̅
̅ −
̅ −
∆ ̅ ℎ ∆ ̅ ℎ
ℎ
∆ = ̅ ∆ ̅ ℎ
−
∆ ̅ ℎ
∆ ℎ = ̅
−
ℎ
∆ ̅
̅ −
ℎ
∆ ̅ = −
=
=
=
∆ ℎ = −
≪ 1
⁄
ℎ
∆
1
ℎ
2
2
2
∆ = 1 − ∆ + 1 − 2 [Δ ∙ + 4(1 + ) + 1 (2 − ) ]
8 (1 + )
=
=
Δ =
=
=
, , 3 3
2
1
11
22 12
33
11 = 22 = Δ
33 = Δ + ξ
12 = = 2
21
α
〈0 0 0 1〉 −
11 = ≡ <1 1 2 ̅ 0> = <1 1 ̅ 0 0> ≡ Δ = 0.0458
22
≡ <0 0 0 1> ≡ Δ + ξ = 0.072; hence (ξ = 0.0262)
33
12 = ≡ 2 ≅ 0.18
21
̅
〈1 0 17〉 −
11 = 22 ≡ <1 1 2 ̅ 0> = <1 1 ̅ 0 0> = Δ ≅ 0
33 ≡ ≡ Δ + ξ = 0.172;hence (ξ = 0.172)
<1 0 1 ̅ 7>
12 = ≡ 2 ≅ 0.18
21
/
α
α
(∆ + )
∆ ℎ = − 11
Δg ℎ
ℎ
0
, () (1 − , ())
( + )/
Δg ℎ () = V ̅ { ln ( ) − (1 − ( + )/ ) ln [ (1 − ) ]}
ℎ
−
( + )/
=
=
=
̅ −
V =
, () =
=
=
( + )/
= H/Zr ℎ
= / ℎ ℎ
ℎ
ZrH, ZrH and ZrH 2 ℎ =
1.5
ℎ =
(α + )/
(α + )/
=
⁄ ℎ ℎ ≡ − = 1
− = 1
, ()
−
− () = + ln () + Δ ̅ ()
=
−
() =
Δ ̅ () =
− ()
= 0
− ( = 0) = + ln − ( = 0)
Δ ̅
−
−
() = ( = 0) ∙ (− )
− ( = 0) = ,
,
, () = (− Δ ̅ )
∆ ℎ
ℎ
≅ 1
ℎ
∆ ℎ = V ̅ ( , () )
−
Δ ̅
=
1/
1 1
1
2
= 2 ( + )
1
= 3
1 3 3
Δ
Δ = Ω − ( + + )
1
3
2
m 3 ̅
atom H
̅ −
= Δ ≡ |
, ,
=
=
=
|
, ,
̅ −
Δ ̅ = −V
⁄
1
Δ ̅
Δ = V ̅ = −
−
3
̅ −
∆ ̅ ( ) = −
ℎ
ℎ =
̅ −
=
̅ −
ℎ
, () = , exp [− ]
ℎ
∆ ℎ ( ) = ∆ ′ℎ − V ̅ ̅ −
ℎ
ℎ
−
,
∆ ′ℎ = V ̅ ( )
ℎ
−
Δ ̅
∆ ℎ ( ) = ∆ ′ℎ + Δ ̅
−
ℎ ℎ V ̅
′ℎ
∆ ℎ
∆ ′ℎ > ,
ℎ
∆
⁄
=
Δ ℎ ( ) = (1 − ) Δ 2
1
ℎ
2
Δ ( ) = (1 − ) 2 [Δ ∙ + 4(1 + ) ]
Δ ℎ ( )
ℎ
ℎ
Δ ( ) = Δ ℎ ( ) + Δ ( )
4
2
2
∆ = (∆ ′ℎ + [∆ ℎ ( ) + εΔ ℎ ( )] − ∆ + ∆ ℎ ) + 2 + 4
3 ℎ
∆ ℎ ( )
⁄
= 0 = ≪ 1.
Δ Δ
( ) = 0 and ( ) = 0
∗ ∗
3
∗
=
ℎ
′ℎ
(−∆ ℎ − Δ ℎ ( ) − ∆ + ∆ )
3
∗
=
ℎ
(−∆ ′ℎ − Δ ( ) − ∆ ℎ + ∆ )
ℎ
∗
∗
∗
⁄
= =
⁄
∗
Δ
( ) = 0
̅
∗
=
ℎ
ℎ
∗
(−∆ ′ℎ − Δ ( ) − ∆ + ∆ )
ℎ
∗
̅ = + 2
2 ̅ 3
∗
∆ =
3 [ (−∆ ′ℎ − Δ ( ) − ∆ + ∆ )] 2
ℎ
ℎ
∗
ℎ
≡
⁄
2 ̅ 3
∗
∆ =
3 [ (−∆ ′ℎ − Δ ℎ ( ) − Δ ℎ ( ) − ∆ ℎ + ∆ )] 2
∗
∗
ℎ
Δ ℎ ( )
∗
|−∆ ℎ + ∆ | ≪ |−∆ ′ − Δ ℎ ( ) − Δ ℎ ( )| ∆ ∗
ℎ
2 ̅ 3
∗
∆ =
3 [ (−∆ ′ℎ − Δ ℎ ( ) − Δ ℎ ( ))] 2
∗
∗
ℎ
∗
4 [−∆ ℎ + ∆ ] ̅ 3
− { }
3 [ (−∆ ′ − Δ ( ) − Δ ℎ ( ))] 3
ℎ
∗
∗
ℎ
4
∗ 3
∗
∗
= 3 ( )
∗
̅
=
∗
′ℎ
ℎ
∗
(−∆ ℎ − Δ ℎ ( ) − Δ ( ))
∗
∗
ℎ
∗
∗
∆ = ∆ − [−∆ + ∆ ]
∗
∆ ∗
2 ̅ 3
∗
∆ = 2
3
∗
[ (−∆ ′ℎ − Δ ℎ ( ) − Δ ℎ ( ))]
∗
ℎ
∆ ∗ ∗
∗
[−∆ ℎ + ∆ ]
∗
, = ∗ , { }
∗
,
∆ ∗
∗ = ∗ (− )
,
∗
∗2
= 2
= =
= =
α
( )
( ) ( )
( )
( ) = (25°C) × (25°C)
[H]
( )
[H]
( ) ( )
[H] − [H]
[H] =
1 −
[H] [H]
= +
= α
=
= +
α
= Ω [Zr] = Ω (1 − [H] )
= Ω [Zr] = Ω (1 − [H] )
Ω
Ω α
[Zr] [Z ]
α
[ r] = +
[ r] = +
α [H] [H]
[H] = +
[H] =
+
αZr phase and similarly for the
: [Zr] ℎ + [H] ℎ = 1 pha α
[Zr] ℎ 1 − [H] ℎ i α
Ω (1 − [H] )
=
Ω (1 − [H] )(1 − ) + Ω (1 − [H] )
(1 − )
+ = 1 (25°)
[H] − [H]
( ) = [H] − [H]
= 25°C [H] ≅ 0
[H]
(25°C) =
[H]
[H]
[H] =
0.0412 [H] = 0.625 (25°C) = 0.0659
[H] ≅ 0 Ω ⁄ Ω = 1.172
1.172 × 0.0659 × (1 − 0.625)
(25°C) = 0.934 + 1.172 × 0.0659 × (1 − 0.625) = 0.0301 (≅ 3%)
[H] ( )
( ) ( )
= +
+ (1− )
+ +
α
α α
[H]
= ( 1 − [H] )
[H]
= ( 1 − [H] )
[H] = 1.66
[H]
[H]
+ = 1 − [H]
+ =
1 − [H]
= 1−[H]
)
1−[H] + (1 − 1−[H]
′(1 − [H] )
=
′(1 − [H] ) + (1 − [H] )
′
=
(1 − )
(1 − [H] )[H] = { (1 − [H] ) + (1 − [H] )}[H] − ′(1 − [H] )[H]
′
′([H] − [H] ) + (1 − [H] )[H]
[ ] = (1 − [H] ) + ′([H] − [H] )
+ [H]
[H] = 1 +
′([H] − [H] )
=
δ
(1 − [H] )
at
′
=
(1 − )
(25°C)
2([H] − [H] )
=
(1 − )(1 − [H] )
46.6 Å 3 108.5 Å 3
Copyright © Advanced Nuclear Technology International Europe AB, ANT International, 2019.
∗ *
∗
ℎ
ℎ = 1, 1, 1.5, 2 ℎ = α
= ⁄ ℎ
∆ ∗
∗
∆
∗
α (≡ / αZr = )
αZr = 1
∗
α
α ≈
Copyright © Advanced Nuclear Technology International Europe AB, ANT International, 2019.
Δg ℎ ()
ℎ
α
∆ ℎ
ℎ
∆ ̅ ℎ ∆
∆
∆ ̅ ∆
∗
∗
∗
∗ = ⁄ ∗
∆ ′
ℎ
̅ −
α
̅ − = Δ ≡ |
, ,
̅ −ℎ
−
() α
− () α
Δ α
̅ −
α
Copyright © Advanced Nuclear Technology International Europe AB, ANT International, 2019.
∆
∆
∆ 1
∆ 2
,
()
,
∗
α
∗
∗
∗
∗ = ⁄ ∗
∗
Δ
ξ
̇
̇ ̇
( )
Copyright © Advanced Nuclear Technology International Europe AB, ANT International, 2019.
( )
( )
⁄
= ( ) ( )
(0)
(0)
(0) = (0) (0)
⁄
(0)
= 0°) = ± °
( )
= 0°) = ± °
ℎ ,
,
α −∆ + ∆
ℎ ,
α = −∆ +
∆ ,
∆ ℎ , ∆ ℎ
∆ , ∆
∆ ℎ , ∆ ℎ
∆ , ∆
∆ = −
( )
( )
∆ ( ) ∆
∆ ( ) ∆
⊥
∥
Copyright © Advanced Nuclear Technology International Europe AB, ANT International, 2019.
(α + )/
⁄
α (α + )
(α + )/
= ⁄ H
α
α
,
( ℎ )
,
α
̅
( )
ℎ
ℎ
∆
̅
∆ ( ),
( )
1
2
and
( ) − (0)
∗
,
∗
,
Copyright © Advanced Nuclear Technology International Europe AB, ANT International, 2019.
∆
( ) ≡
( ) ≡
( ) ≡
, , , ,
ℎ
( )
= 0
ℎ
⁄
= (1 − ) ≡ 1/ = (0) 1/ (
=
≡ = (σ = 0) = 1 =
2 ( , ), = 1 ≡
= 2 ≡ = 90° 1/ (0) = = =90° (0)/ = (0)
=
(0)
= 90° (0)
∗
Ω ∗ Ω ≡ ∗
∆
2
∝ ℓ ⁄ D ℓ
α
Copyright © Advanced Nuclear Technology International Europe AB, ANT International, 2019.
ℓ
Δ ∗ ( )
Δ ∗ ( )
Δ ∗ ( )
( )
( )
( )
= −1 ( ) ( ) ( ) ( )
2
= −1 ( ) ( ) ( ) ( )
α
∗
,( )
⁄
,( ) ⁄ = 3 Λ
,( ) ⁄
,( )
∆
= −( )
≡
Copyright © Advanced Nuclear Technology International Europe AB, ANT International, 2019.
, (40) (40)
′
, ,
∆
[H]
,100%
,0%
,
,0%
,0%
,0%
,0%
,0%
,0%
( ) α = TSSD
≡
( , )
1
2
⁄
2
1
⁄
ℎ = 1 3 ( + )
1
2
_ (≡ )
_
( _ , _ ) _ _
Copyright © Advanced Nuclear Technology International Europe AB, ANT International, 2019.
(40) ≡ = ±40°
(45)
0 °
≡ )
(40)
(45)
(40) (40)
(40) (40)
2
2
2
ℎ = ℎ √(ℎ + + )
(ℎ ) ℎ, ,
α
α
− α
− α
[H]
[H]
( )
(30°C)
1
α
α
= 0°
Copyright © Advanced Nuclear Technology International Europe AB, ANT International, 2019.
(≡ )
1
= 90°
(≡ )
1
∆ = −
( ) > 25°C
(25°C) = 25°C
[H]
[H]
( )
α
[H]
[Z ] α
[Zr]
α
α
α
α
Copyright © Advanced Nuclear Technology International Europe AB, ANT International, 2019.
Ω α
Ω
⁄
2
= (√3 4) α
∆
∆ ̅̅̅ = ̅ − ̅
̅ α
̅ α
̅ α
α
̅ α
α
− ( (K)) = − ( (K))+3.23118 {10.1}
2
( (K))−3.23118)
∆ − = − ( (K))
{10.1}
−
{10.1}
− ( (K)) = − ( (K))+5.14634 {00.2}
2
( (K))−5.14634)
∆ − = − ( (K))
{00.2}
−
{00.2}
α
, −ℎ α
, −ℎ α
Copyright © Advanced Nuclear Technology International Europe AB, ANT International, 2019.
α
α
̅ −ℎ
̅ − α
= 1, 2, 3
⊥
(≡ )
33
‖
(≡ 11 = )
22
(= ( + 2 )/3)
⊥
∥
≡ = 1, 2, 3
≡ = 1, 2, 3
⊥
(≡ )
33
∥
(≡ 11 = )
22
, , ( ) ( ) ( )
∆ 111 = ( − )
⁄
(1 1 1) = 0°
ℎ = 70°
Copyright © Advanced Nuclear Technology International Europe AB, ANT International, 2019.
ℎ (1 1 1)
= 0°
(1 1 1)
= 70°
í
ℎ
ℎ
α = −
⁄
, 2 , , 1 ( + )
2 1
⁄
, ( + )
∆ ̅ ℎ
, 2
í
∆ ̅ ℎ
, 1
∆ ̅ ℎ
,
, 1 ( ) 1
, 1 (0)
1 ≡ TSSP1
Δ , 1 ( )
1 = , 1 ( ) −
TSSP1
∆ , 2 ( )
2 =
, 2 ( ) − 2
∆ ( )
,
′
( )
Copyright © Advanced Nuclear Technology International Europe AB, ANT International, 2019.
(∇ ) 2
( )
̃
⁄
̅
,
,
( )
,
, ( )
,
′
,
′
,
′ ( , ) = ′ , ( )
( )
( , )
( , ) ( , )
Copyright © Advanced Nuclear Technology International Europe AB, ANT International, 2019.
( , )
=
,
= ,
4 ℎ 2
Ω ( ) Ω −1 =
̃ ( ) = ̃ ( ) = ∫ ( ) (− )
3
̃ ( )
⁄
= )
̃
̃
{Δ ( )} Δ ( )
{Δ ̃ ( )} ∗ {Δ ̃ ( )}
( ) (= ( )Ω ( ) ( ) )
ℎ
ℎ
12 44 14
,
Copyright © Advanced Nuclear Technology International Europe AB, ANT International, 2019.
TEMPERATURE MASS
°C + 273.15 = K °C × 1.8 + 32 = °F kg lbs
T(K) T(°C) T(°F) 0.454 1
273 0 32 1 2.20
289 16 61
298 25 77 DISTANCE
373 100 212 x (µm) x (mils)
473 200 392 0.6 0.02
573 300 572 1 0.04
633 360 680 5 0.20
673 400 752 10 0.39
773 500 932 20 0.79
783 510 950 25 0.98
793 520 968 25.4 1.00
823 550 1022 100 3.94
833 560 1040
873 600 1112 PRESSURE
878 605 1121 bar MPa psi
893 620 1148 1 0.1 14
923 650 1202 10 1 142
973 700 1292 70 7 995
1023 750 1382 70.4 7.04 1000
1053 780 1436 100 10 1421
1073 800 1472 130 13 1847
1136 863 1585 155 15.5 2203
1143 870 1598 704 70.4 10000
1173 900 1652 1000 100 14211
1273 1000 1832
1343 1070 1958 STRESS INTENSITY FACTOR
1478 1204 2200 MPa√m ksi√inch
0.91 1
Radioactivity 1 1.10
1 Sv = 100 Rem
1 Ci = 3.7 × 10 Bq = 37 GBq
10
-1
1 Bq = 1 s
Copyright © Advanced Nuclear Technology International Europe AB, ANT International, 2019.
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