http://www.periodictable.com/Properties/A/LatticeConstants.sp.wt.html Precise lattice parameter determination 80 60 40 20 0 20 40 60 80 100 Atomic Number
Precise lattice parameter determination http://www.periodictable.com/Properties/A/LatticeConstants.sp.wt.html
Lattice parameter matters in: 1.thermal expansion coefficient 2.residual stress measurement 3.study phase transformation 4.substitution vs interstitial solid solution
Lattice parameter matters in : 1. thermal expansion coefficient 2. residual stress measurement 3. study phase transformation 4. substitution vs interstitial solid solution ……
Using lattice parameter change to identify phase transformation in NigAl Experiment data -sum of peak 1 and peak 2 二 peak 1-y' peak 2-y 分峰条件: 峰形Voigt Accelerating Voltage Camera Length Magnificatior 200kV 10000x 500nm 置信度99% 采集条件: Misfit:0.15~0.35% 0.01/step 4s/step 72 73 74 75 76 77 78 20
’ 采集条件: 0.01o/step 4s/step 分峰条件: 峰形 Voigt 置信度 99% Using lattice parameter change to identify phase transformation in Ni3Al Misfit: 0.15~0.35% (220)
Identify the thermal expansion coefficient from in situ high-T XRD-TisSig 2242 (3251) An accuracy of at least 0.06%is required. Asuejul 200 *L.T.Zhang and J.S.Wu,Scripta 400 59 Temperature Materialia,38(1998)307 60 600 0.755 61 800 28 64 TigSia 65 1000 66 0750 0.525 0.745 0.520 ● 0.740 ● 0.515 ● a-axis ●c-ais 0.735 0.510 0 200 400 600 800 1000 200 400 600 800 1000 Temperature(C) Temperature(c)
*L.T. Zhang and J.S. Wu, Scripta Materialia, 38(1998)307 Identify the thermal expansion coefficient from in situ high-T XRD-Ti5Si3 An accuracy of at least 0.06% is required
(110 Strongest 3 peaks Si no.peak 2Theta d I/I1 FWHM no. (deg) (A) (deg) 28.3699 3.14332 100 0.11470 2 2 47.2380 1.92256 55 0.10980 56.0600 1.63912 6 0.10770 4000 Peak Data List peak 2Theta d I/I1 FWHM no. (deg) (A) (deg) 义 28.3699 3,14332 100 0.11470 23 47.2380 1.92256 55 0.10980 56.0600 1.63912 36 0.10770 4 69.0791 1.35858 8 0.11400 56 76.3222 1.24666 14 0.11000 E 87.9814 1.10905 17 0.12150 7 94.9030 1.04557 0.12970 2000 106.6626 0.96033 5 0.15280 18 114.0568 0.91816 10 0.14960 127.5153 0.85879 8 0.17250 1 136.8696 0.82826 4 0.18340 (400 3311) (61) 120
(111) (220) (311) (400) (331) (422) (511) (440) (531) (620) (533) Si
Principle of lattice parameter determination a 2dsin0=元 d= VH2+K2+D 几 a= VH2+K2+2 2sine △a △d a d
Principle of lattice parameter determination 2 2 2 2sin a H K L 2 d sin 2 2 2 H K L a d d d a a
The error in peak position determination 九 d 2sin 0 △兄 λ△0cosB △d= 2sin0 2sin20 △d △元△0cos0 d 元 sinθ
The error in peak position determination 2 2sin cos 2sin d 2sin d sin cos d d
1.0 业 不 △sin0 0.8 0 uls 0.6 △0→ 0.4- 0.2- 0.0 0 20 40 60 80 0(degrees) △d △元 △0cos0 The fractional error approaches d λ sinO zero as 0 approaches 90o
sin cos d d The fractional error approaches zero as approaches 90 o
Use peaks with large 20 0.030 0.025 0.05°-9 0.01°-A9 8 0.020 0.015 0.005°-9 p/pV 0.010 0.005 0.001°-A9 0.000 30405060708090 0() 点阵参数测量精度与和△的关系
30 40 50 60 70 80 90 0.000 0.005 0.010 0.015 0.020 0.025 0.030 d/d , % 0.010 ~ 0.050 ~ 0.0050 ~ 0.0010 ~ 点阵参数测量精度与 θ 和Δθ的关系 Use peaks with large 2