Luận án Nghiên cứu các tham số nhiệt động và các cumulant của một số vật liệu trong phương pháp XAFS phi điều hòa

i 
LỜI CAM ĐOAN 
Tôi  xin  cam  đoan:  Luận  án  “Nghiên cứu các tham số nhiệt động và các 
cumulant của một số vật liệu trong phương pháp XAFS phi điều hòa” là công trình 
nghiên cứu của  riêng  tôi.  Các  số  liệu và kết  quả  trình  bày  trong  luận án  là  trung 
thực, đã được các đồng tác giả cho phép sử dụng và chưa từng được công bố trong 
các tài liệu nào khác. 
 Hà Nội, ngày tháng năm 2020 
                                         Tác giả Luận án 
                                            Cù Sỹ Thắng 
ii 
LỜI CẢM ƠN 
Để hoàn thành luận án này, tôi đã nhận được rất nhiều sự giúp đỡ và tạo điều 
kiện cũng như tình cảm động viên của Lãnh đạo cơ quan công tác, các thầy hướng 
dẫn, các thầy cô thuộc Bộ phận đào tạo - Viện Khoa học Vật liệu (Nay thuộc Khoa 
Khoa học Vật liệu và Năng lượng - Học viện Khoa học và Công nghệ - Viện Hàn 
lâm Khoa học và Công nghệ Việt Nam), các đồng nghiệp, gia đình và bạn bè. 
Trước  tiên,  tôi xin gửi  lời  cảm ơn  sâu  sắc  tới  thầy giáo NGƯT.GS.TSKH. 
Nguyễn Văn Hùng, ngoài việc hướng dẫn, chỉ bảo về chuyên môn, thầy đã dạy tôi 
về đức tính tự lực,  tinh thần hợp tác, niềm say mê và nghiêm túc trong khoa học. 
Được học tập và làm việc với thầy, tôi cảm nhận được tính nghiêm khắc, tinh thần 
trách nhiệm và  lòng bao dung của  thầy với học  trò. Những điều mà  tôi  luôn cảm 
phục và kính trọng.  
Tôi xin gửi lời cảm ơn chân thành tới GS.TS. Nguyễn Quang Liêm đã quan 
tâm, tạo điều kiện cho tôi trong suốt thời gian tôi học tập tại Viện Khoa học Vật liệu 
và Học viện Khoa học và Công nghệ. 
Để  hoàn  thành  bản  luận  án  này,  tôi  đã nhận được  sự ủng  hộ  của Chủ  tịch 
Viện Hàn  lâm, Ban Kế hoạch  tài  chính,  lãnh đạo Viện Địa  chất,  đã cho phép  tôi 
được thực hiện đề tài thuộc Chương trình độc lập trẻ - Viện Hàn lâm Khoa học và 
Công  nghệ  Việt  Nam  với  mã  số  VAST.  ĐLT.08/13-14.  Đó  là  tiền  đề  để  tôi  tiến 
hành nghiên cứu  và hoàn  thành  luận  án. Bên  cạnh  đó,  được  tiếp  cận  và  sử  dụng 
nguồn dữ  liệu quốc  tế  rất quí  từ Trung  tâm thông tin  tư  liệu đã giúp  tôi rất nhiều 
trong quá trình thực hiện luận án. Tôi xin gửi lời cảm ơn sâu sắc nhất tới Chủ tịch 
Viện và các cơ quan trực thuộc Viện. 
Tôi xin gửi lời cảm ơn tới TS. Wantana Klysubun, TS. Nirawat Thammajak  
và  các đồng nghiệp Viện Nghiên  cứu bức  xạ Synchrotron-Thái Lan đã nhiệt  tình 
giúp đỡ tôi trong thời gian tôi tiến hành thực nghiệm tại Thái Lan. 
Không thể không nhắc tới gia đình, những người luôn dành tất cả những điều 
tốt đẹp nhất cho tôi và luôn mong muốn tôi hoàn thành nhiệm vụ học tập cũng như 
trong công tác. Tôi cảm ơn mọi người rất nhiều. 
iii 
Cuối cùng,  tôi xin gửi  lời cảm ơn  tới Bộ phận đào  tạo,  các phòng ban của 
Học viện Khoa học và Công nghệ cũng như những người luôn ủng hộ, động viên và 
giúp đỡ tôi mà tôi đã vô tình chưa nhắc tới ở đây. Tôi xin chân thành cảm ơn! 
Hà Nội, ngày tháng năm 2020 
Nghiên cứu sinh 
 Cù Sỹ Thắng 
iv 
MỤC LỤC 
LỜI CAM ĐOAN ................................................................................................... i 
LỜI CẢM ƠN ........................................................................................................ii 
DANH MỤC CÁC TỪ VIẾT TẮT ..................................................................... vii 
DANH MỤC KÝ HIỆU CÁC ĐẠI LƯỢNG VẬT LÝ .....................................viii 
DANH MỤC CÁC BẢNG BIỂU ......................................................................... ix 
MỞ ĐẦU ................................................................................................................ 1 
CHƯƠNG 1. TỔNG QUAN VỀ HỆ SỐ DEBYE-WALLER PHỔ XAFS ......... 7 
1.1 Sơ lược về phổ XAFS ....................................................................................... 7 
1.1.1. Bản chất vật lý của phổ XAFS[30]: .................................................................. 9 
1.1.2. Phương trình phổ XAFS .............................................................................. 11 
1.1.3. Hệ số Debye-Waller của phổ XAFS ............................................................. 15 
1.1.4. Các cumulant của phổ XAFS ....................................................................... 17 
1.2. Phương pháp nghiên cứu hệ số Debye-Waller phổ XAFS .......................... 19 
1.2.1. Mô hình Einstein tương quan ....................................................................... 19 
1.2.2. Phương pháp phương trình chuyển động ...................................................... 21 
1.2.3. Phương pháp thống kê mô men .................................................................... 25 
CHƯƠNG 2. MÔ HÌNH EINSTEIN TƯƠNG QUAN PHI ĐIỀU HÒA 
TRONG NGHIÊN CỨU CÁC THAM SỐ NHIỆT ĐỘNG PHỔ XAFS ........... 33 
2.1. Thế tương tác hiệu dụng trong mô hình Einstein tương quan phi điều hòa ...... 33 
2.2. Thế tương tác cặp Morse .............................................................................. 37 
2.2.1. Áp dụng hàm thế Morse để tính toán các tham số và thế hiệu dụng trong mô 
hình Einstein tương quan phi điều hòa với vật liệu cấu trúc fcc, hcp ...................... 41 
2.2.2. Áp dụng hàm thế Morse để tính toán các tham số và thế hiệu dụng trong mô 
hình Einstein tương quan phi điều hòa với vật liệu cấu trúc kim cương ................. 45 
2.3. Thế tương tác Stillinger-Weber ................................................................... 47 
2.4. Tính toán các tham số nhiệt động phổ XAFS theo mô hình Einstein tương 
quan phi điều hòa ................................................................................................ 49 
2.4.1. Tính các cumulant trong mô hình Einstein tương quan phi điều hòa ............ 49 
v 
2.4.2.  Dẫn  giải  các  cumulant  thông  qua  cumulant  bậc  2  trong  mô  hình  Einstein 
tương quan phi điều hòa ........................................................................................ 58 
2.4.3. Tính hệ số giãn nở nhiệt của vật liệu trong mô hình Einstein tương quan phi 
điều hòa ................................................................................................................. 60 
2.4.4. Đánh giá kết quả tính cumulant bậc 2 của phổ XAFS sử dụng thế Morse và 
thế  Stilinger-Weber  trong  mô  hình  Einstein  tương  quan  phi  điều  hòa  và  phương 
pháp mô men với các kết quả khác đối với vật liệu bán dẫn cấu trúc kim cương .... 62 
2.5. Các hiệu ứng lượng tử ở giới hạn nhiệt độ thấp và gần đúng cổ điển ở nhiệt 
độ cao ................................................................................................................... 65 
CHƯƠNG 3. HỆ ĐO THỰC NGHIỆM VÀ ÁP DỤNG MÔ HÌNH EINSTEIN 
TƯƠNG QUAN PHI ĐIỀU HÒA TRONG NGHIÊN CỨU CÁC THAM SỐ 
NHIỆT ĐỘNG PHỔ XAFS VẬT LIỆU CẤU TRÚC HCP VÀ FCC ............... 67 
3.1. Hệ thống bức xạ synchrotron và hệ đo phổ XAFS ...................................... 67 
3.1.1. Khái quát chung về hệ đo phổ XAFS ........................................................... 68 
3.1.2. Quá trình chuẩn bị mẫu đo thực nghiệm phổ XAFS phụ thuộc nhiệt độ ....... 72 
3.2. Chương trình xử lý phổ cấu trúc tinh tế hấp thụ tia X (XAFS) ................. 74 
3.3. Kết quả thực nghiệm xác định hệ số Debye-Waller phổ XAFS của vật liệu 
cấu trúc hcp ......................................................................................................... 76 
3.4. Xác định các tham số nhiệt động phổ XAFS từ số liệu thực nghiệm hệ số 
Debye-Waller hay cumulant bậc hai theo mô hình Einstein tương quan phi 
điều hòa vật liệu cấu trúc hcp ............................................................................. 78 
3.5. Kết quả thực nghiệm xác định hệ số Debye-Waller phổ XAFS của vật liệu 
cấu trúc fcc ........................................................................................................... 80 
3.6. Xác định các tham số nhiệt động phổ XAFS từ số liệu thực nghiệm hệ số 
Debye-Waller hay cumulant bậc hai theo mô hình Einstein tương quan phi 
điều hòa của vật liệu cấu trúc fcc (Cu) ............................................................... 82 
CHƯƠNG 4. MÔ HÌNH EINSTEIN TƯƠNG QUAN PHI ĐIỀU HÒA 
TRONG NGHIÊN CỨU THÀNH PHẦN PHA VÀ BIÊN ĐỘ PHỔ XAFS VẬT 
LIỆU CẤU TRÚC HCP VÀ FCC ....................................................................... 85 
4.1. Khái quát về phổ XAFS phi điều hòa .......................................................... 85 
4.2. Hệ số Debye-Waller phổ XAFS với đóng góp phi điều hòa ........................ 86 
4.2.1. Xác định hệ số Grüneisen  G  ....................................................................... 86 
vi 
4.2.2. Xác định hệ số phi điều hòa (T)  ................................................................. 88 
4.3. Phổ XAFS với đóng góp phi điều hòa .......................................................... 89 
4.4. Thành phần phi điều hòa của pha và biên độ phổ XAFS vật liệu cấu trúc 
hcp (Zn) ................................................................................................................ 90 
4.5. Thành phần phi điều hòa của pha và biên độ phổ XAFS vật liệu cấu trúc 
fcc (Cu) ................................................................................................................. 92 
4.5.1.Thành phần phi điều hòa của cumulant bậc 2 và hệ số phi điều hòa  (T)  ..... 92 
4.5.2.Thành phần phi điều hòa của pha và biên độ phổ XAFS ............................... 93 
KẾT LUẬN VÀ KIẾN NGHỊ ............................................................................. 96 
DANH MỤC CÁC CÔNG TRÌNH CÔNG BỐ CỦA TÁC GIẢ ....................... 97 
TÀI LIỆU THAM KHẢO ................................................................................... 98 
PHỤ LỤC ........................................................................................................... 109 
vii 
DANH MỤC CÁC TỪ VIẾT TẮT 
Từ viết tắt Tiếng Anh Tiếng Việt 
ACEM 
Anharmonic Correlated Einstein 
Model 
Mô  hình  Einstein  tương  quan  phi 
điều hòa 
DCF 
Displacement Correlation 
Function 
Hàm dịch chuyển tương quan 
DFP  Density Function Theory  Lý thuyết hàm mật độ 
EM  Equation of Motion  Phương trình chuyển động 
EXAFS  Extended- XAFS 
Cấu trúc tinh tế hấp thụ tia X vùng 
mở rộng. 
FCC  Face-Centered Cubic  Lập phương tâm mặt 
FEFF  Force Effective 
Tên phần mềm xử lý phổ (viết tắt 
của Lực hiệu dụng) 
GGA 
Generalized Gradient 
Appoximation 
Gần đúng gradien mở rộng 
HCP  Hexagonal Close Packed  Lục giác xếp chặt 
h-GGA  Hybrid GGA  Phương pháp GGA lai 
LDA  Local Density Approximation  Gần đúng mật độ địa phương 
MSRD 
Mean Square Relative 
Displacement 
Độ dịch chuyển tương đối bình 
phương trung bình 
PES  Photo-Electron Spectroscopy  Phổ quang điện tử 
SLRI 
Synchrotron Light Research 
Instite 
Viện Nghiên cứu bức xạ synchrotron 
(Thái Lan) 
TM  Transmission Mode  Chế độ truyền qua 
VDOS  Vibrational Density of state  Mật độ trạng thái dao động 
XAFS  X-ray Absorption Fine Structure  Cấu trúc tinh tế hấp thụ tia X 
XANES 
X ray Absorption Near - Edge 
Structure 
Cấu trúc gần cận hấp thụ tia X  
XRF  X ray Fluorescence  Huỳnh quang tia X 
viii 
DANH MỤC KÝ HIỆU CÁC ĐẠI LƯỢNG VẬT LÝ 
Ký hiệu Tiếng Anh Tiếng Việt 
a  Lattice Expansion Coefficient  Hệ số giãn nở mạng 
µ  Effective Mass  Khối lượng hiệu dụng 
µ(E)  Absorption Coefficient   Hệ số hấp thụ 
E  Einstein Frequency  Tần số Einstein 
D  Debye Frequency  Tần số Debye 
E  Einstein Temperature  Nhiệt độ Einstein 
R  Interatomic Distance  Khoảng cách liên kết nguyên tử 
k3  Anharmonic Coefficients  Hệ số phi điều hòa 
keff  Effective Elastic Coefficients  Hệ số đàn hồi hiệu dụng 
 eff  Effective Potential  Thế tương tác hiệu dụng  
(1)  First-order cumulant  Cumulant bậc 1 
(2) Second-order cumulant Cumulant bậc 2 
(3) Third-order cumulant Cumulant bậc 3 
2
H
  Harmonic Second cumulant  Cumulant bậc 2 điều hòa 
2
A   Anharmonic Second cumulant  Cumulant bậc 2 phi điều hòa 
 T  Coefficient of Thermal Expansion  Hệ số giãn nở nhiệt 
 , D  Parameters of the Morse Potential  Các tham số thế Morse 
ix 
DANH MỤC CÁC BẢNG BIỂU 
Bảng 2. 1. Các tham số thế Morse của đồng (Cu) từ các nguồn tài liệu[56] ............. 38 
Bảng 2. 2. Các tham số thế Morse của đồng (Cu) và kẽm (Zn) tính toán lý thuyết. 41 
Bảng 2. 4: Các tham số nhiệt động trong giới hạn nhiệt độ.................................... 66 
---------------------------------*****------------------------------- 
Bảng 3. 1. Giá  trị của các cumulant và hệ số giãn nở nhiệt của Zn giữa  lý  thuyết 
(LT) và thực nghiệm (TN) tại các nhiệt độ. Ký hiệu: MHĐH- Mô hình điều hòa. .. 77 
Bảng 3. 2. Giá trị của các cumulant và tham số phi điều hòa của Cu giữa lý thuyết 
(LT) và thực nghiệm (TN) tại các nhiệt độ. ............................................................ 81 
x 
DANH MỤC CÁC HÌNH VẼ-ĐỒ THỊ 
Hình 1.1: Giản đồ quá trình hấp thụ tia X bởi điện tử lỗ trống và quá trình hủy hấp 
thụ tia X bởi tạo lỗ trống lớp lõi nguyên tử. ............................................................. 8 
Hình 1.2: Phổ XAFS tại cận hấp thụ K ở các nhiệt độ khác nhau của phoi Cu. ....... 8 
Hình 1.3: Sự hấp thụ tia X của vật liệu. .................................................................. 9 
Hình 1.4: Giản đồ mô tả hấp thụ tia X thông qua hiệu ứng quang điện. ................... 9 
Hình 1.5: Giản đồ mô tả cấu trúc tinh tế hấp thụ tia X. ......................................... 10 
Hình 1.6: Độ dịch chuyển bình phương trung bình và hệ số Debye-Waller đối với 
lớp thứ nhất của Cu phụ thuộc nhiệt độ từ các mô hình tính toán khác nhau .......... 20 
Hình 1.7: Sự phụ thuộc nhiệt độ của hệ số Debye-Waller với các phương pháp tính 
toán và các mô hình khác nhau .............................................................................. 21 
---------------------------------*****------------------------------- 
Hình 2.1: Dao động tử điều hòa[47]. ....................................................................... 33 
Hình 2.2: Hàm thế tương tác đơn cặp của Cu[47]. ................................................... 34 
Hình 2.3: Tinh thể cấu trúc lập phương tâm mặt fcc[47] ......................................... 41 
Hình 2.4: Tinh thể cấu trúc lục giác xếp chặt hcp[47]. ............................................ 44 
Hình 2.5: Tinh thể cấu trúc kim cương[47]. ............................................................ 45 
Hình 2. 6: Sự phụ thuộc nhiệt độ của cumulant bậc 2 sử dụng thế Stillinger-Weber 
theo phương pháp thống kê mô men đối với Si. ..................................................... 64 
Hình 2. 7:  Sự phụ thuộc nhiệt độ của cumulant bậc 2 sử dụng thế Stillinger-Weber 
theo phương pháp thống kê mô men đối với Ge. .................................................... 64 
---------------------------------*****------------------------------- 
Hình 3.1: Mô hình một hệ synchrotron hiện đại [75]. ............... ... 5
4373,3.436117,3.4667966,3.4974762,3.5281558,3.5588354,3.589515,3.6201947,3.6508743,3.681
5539,3.7122335,3.7429131,3.7735927,3.8042724,3.834952,3.8656316,3.8963112,3.9269908,3.95
76704,3.98835,4.0190297,4.0497093,4.0803889,4.1110685,4.1417481,4.1724277,4.2031074,4.23
3787,4.2644666,4.2951462,4.3258258,4.3565054,4.3871851,4.4178647,4.4485443,4.4792239,4.5
099035,4.5405831,4.5712627,4.6019424,4.632622,4.6633016,4.6939812,4.7246608,4.7553404,4.
7860201,4.8166997,4.8473793,4.8780589,4.9087385,4.9394181,4.9700978,5.0007774,5.031457,5
120 
.0621366,5.0928162,5.1234958,5.1541754,5.1848551,5.2155347,5.2462143,5.2768939,5.3075735
,5.3382531,5.3689328,5.3996124,5.430292,5.4609716,5.4916512,5.5223308,5.5530105];                                            
thucnghiem500=[0.13292272,0.12770161,0.11265876,0.089783252,0.063263487,0.04364
1836,0.049773712,0.074161174,0.099441496,0.11859377,0.12844434,0.1274786,0.11546004,0.0
93476307,0.064615333,0.039013143,0.047214337,0.082690725,0.1215669,0.15659319,0.184481
5,0.20348119,0.21318911,0.21470622,0.21085218,0.20621102,0.20644442,0.21622148,0.236696
46,0.26515035,0.29696659,0.32754964,0.35314995,0.37100828,0.37926604,0.37681772,0.36315
594,0.33823416,0.30238734,0.2564071,0.20208786,0.14468315,0.10424591,0.12649779,0.20489
736,0.30713414,0.4216879,0.54374692,0.66973987,0.79607645,0.91883706,1.0337676,1.13645,1
.2226381,1.2887961,1.3328995,1.3555863,1.3617275,1.3622965,1.375734,1.4266598,1.539431,1.
7284449,1.9929494,2.3200395,2.6907646,3.0844023,3.4804179,3.8592891,4.2030203,4.4956419,
4.7237366,4.876945,4.9483918,4.9349768,4.8374948,4.6605648,4.412367,4.1042053,3.7499296,
3.3652635,2.9670922,2.5727604,2.1993912,1.8631395,1.57808,1.3541885,1.1941978,1.0909081,
1.0283203,0.98730321,0.9515876,0.91042409,0.85823927,0.79314537,0.71547805,0.62673688,0.
52894071,0.42430786,0.31517066,0.20413329,0.095477568,0.041127848,0.13190751,0.2289690
3,0.31866546,0.39836103,0.46646404,0.52191799,0.56412795,0.59295304,0.60873416,0.612364
61,0.60540689,0.59023674,0.57015375,0.54932919,0.53238534,0.52342839,0.52469309,0.53552
046,0.55245503,0.57042384,0.58422509,0.58970984,0.58455495,0.56877912,0.54513027,0.5192
8725,0.49943758,0.49433952,0.50957719,0.54435367,0.59202644,0.64349106,0.6901314,0.7251
8121,0.74409265,0.74453878,0.72631362,0.69119839,0.64280176,0.58635801,0.52841362,0.476
19411,0.43626833,0.41237075,0.4035069,0.40435608,0.4079601,0.40837779,0.4019188,0.38729
37,0.36535327,0.33874864,0.31152805,0.28844167,0.27359823,0.26859405,0.27141913,0.27735
81,0.28100035,0.2777229,0.26426331,0.23882134,0.20112706,0.15297968,0.10143761,0.076271
591,0.11869129,0.19426769,0.27805354,0.36189481,0.44116486,0.51238312,0.57283012,0.6205
2854,0.65428788,0.67373452,0.67930169,0.67217126,0.65416687]; 
rzn500=[0,0.030679616,0.061359232,0.092038847,0.12271846,0.15339808,0.18407769,0.
21475731,0.24543693,0.27611654,0.30679616,0.33747577,0.36815539,0.398835,0.42951462,0.4
6019424,0.49087385,0.52155347,0.55223308,0.5829127,0.61359232,0.64427193,0.67495155,0.7
0563116,0.73631078,0.76699039,0.79767001,0.82834963,0.85902924,0.88970886,0.92038847,0.
95106809,0.9817477,1.0124273,1.0431069,1.0737866,1.1044662,1.1351458,1.1658254,1.196505,
1.2271846,1.2578642,1.2885439,1.3192235,1.3499031,1.3805827,1.4112623,1.4419419,1.472621
6,1.5033012,1.5339808,1.5646604,1.59534,1.6260196,1.6566993,1.6873789,1.7180585,1.748738
1,1.7794177,1.8100973,1.8407769,1.8714566,1.9021362,1.9328158,1.9634954,1.994175,2.02485
46,2.0555343,2.0862139,2.1168935,2.1475731,2.1782527,2.2089323,2.239612,2.2702916,2.3009
712,2.3316508,2.3623304,2.39301,2.4236896,2.4543693,2.4850489,2.5157285,2.5464081,2.5770
877,2.6077673,2.638447,2.6691266,2.6998062,2.7304858,2.7611654,2.791845,2.8225246,2.8532
043,2.8838839,2.9145635,2.9452431,2.9759227,3.0066023,3.037282,3.0679616,3.0986412,3.129
3208,3.1600004,3.19068,3.2213597,3.2520393,3.2827189,3.3133985,3.3440781,3.3747577,3.405
4373,3.436117,3.4667966,3.4974762,3.5281558,3.5588354,3.589515,3.6201947,3.6508743,3.681
5539,3.7122335,3.7429131,3.7735927,3.8042724,3.834952,3.8656316,3.8963112,3.9269908,3.95
76704,3.98835,4.0190297,4.0497093,4.0803889,4.1110685,4.1417481,4.1724277,4.2031074,4.23
3787,4.2644666,4.2951462,4.3258258,4.3565054,4.3871851,4.4178647,4.4485443,4.4792239,4.5
099035,4.5405831,4.5712627,4.6019424,4.632622,4.6633016,4.6939812,4.7246608,4.7553404,4.
7860201,4.8166997,4.8473793,4.8780589,4.9087385,4.9394181,4.9700978,5.0007774,5.031457,5
.0621366,5.0928162,5.1234958,5.1541754,5.1848551,5.2155347,5.2462143,5.2768939,5.3075735
,5.3382531,5.3689328,5.3996124,5.430292,5.4609716,5.4916512,5.5223308,5.5530105]; 
fefffit500=[0.020796983,0.020485252,0.019596283,0.018282009,0.016837165,0.0157335
97,0.015545335,0.016636736,0.018864299,0.02171238,0.024611082,0.027091735,0.028823612,0
.029631238,0.029524097,0.028739697,0.027780855,0.027377269,0.02824326,0.030660786,0.034
289995,0.03841291,0.042266352,0.045218415,0.046830018,0.046878378,0.04537139,0.0425551
52,0.038905024,0.035074746,0.031752379,0.029385171,0.027907771,0.026814418,0.025706137,
0.02510893,0.027134393,0.034408117,0.047597265,0.065738282,0.087664025,0.1123681,0.1390
17,0.16700471,0.19606561,0.2264015,0.25876872,0.29446683,0.33518639,0.38272807,0.438681
121 
48,0.50419151,0.5799005,0.66606889,0.76281115,0.87036555,0.98932488,1.1207692,1.2662552,
1.4276394,1.606747,1.8049397,2.0226668,2.259087,2.5118267,2.7769048,3.0488172,3.3207577,
3.584942,3.833003,4.0564264,4.2470014,4.3972604,4.5008841,4.5530506,4.5507085,4.4927601,
4.3801425,4.2158014,4.0045604,3.7528912,3.4685991,3.1604406,2.8376967,2.5097256,2.185518
2,1.8732839,1.5800833,1.3115286,1.0715629,0.86232974,0.68414704,0.53560885,0.41385294,0.
31503104,0.23497715,0.1699922,0.1176532,0.077815091,0.054211705,0.051295776,0.06081826
2,0.071183823,0.077772751,0.079744358,0.077875927,0.073857612,0.069873232,0.067937497,0
.068941401,0.072192164,0.076056513,0.078947202,0.079851293,0.078434647,0.074974885,0.07
0235889,0.065283714,0.061193644,0.058643472,0.057585735,0.057301974,0.056819364,0.0553
3574,0.052437612,0.048147383,0.042894879,0.037460502,0.032858774,0.030021989,0.0292284
92,0.02981605,0.030679234,0.030917555,0.030075365,0.028125711,0.025408202,0.022573857,0
.020469022,0.019780619,0.020514848,0.021983978,0.023363937,0.02408371,0.023893266,0.022
82378,0.021141312,0.01929773,0.017834481,0.017172975,0.01735501,0.018016014,0.01864935
1,0.018857027,0.018441726,0.017409481,0.015949951,0.014408766,0.013220428,0.012735691,0
.012985863,0.013653083,0.014306557,0.014612711,0.01440009,0.013653665,0.012496989,0.011
176158,0.01003039,0.009395781,0.009409851,0.009894677,0.010505331,0.010940558,0.011024
172,0.010702202,0.01002166,0.009110367,0.008155688,0.007367848,0.006906721,0.006791312]
;       
rzn600=[0,0.030679616,0.061359232,0.092038847,0.12271846,0.15339808,0.18407769,0.
21475731,0.24543693,0.27611654,0.30679616,0.33747577,0.36815539,0.398835,0.42951462,0.4
6019424,0.49087385,0.52155347,0.55223308,0.5829127,0.61359232,0.64427193,0.67495155,0.7
0563116,0.73631078,0.76699039,0.79767001,0.82834963,0.85902924,0.88970886,0.92038847,0.
95106809,0.9817477,1.0124273,1.0431069,1.0737866,1.1044662,1.1351458,1.1658254,1.196505,
1.2271846,1.2578642,1.2885439,1.3192235,1.3499031,1.3805827,1.4112623,1.4419419,1.472621
6,1.5033012,1.5339808,1.5646604,1.59534,1.6260196,1.6566993,1.6873789,1.7180585,1.748738
1,1.7794177,1.8100973,1.8407769,1.8714566,1.9021362,1.9328158,1.9634954,1.994175,2.02485
46,2.0555343,2.0862139,2.1168935,2.1475731,2.1782527,2.2089323,2.239612,2.2702916,2.3009
712,2.3316508,2.3623304,2.39301,2.4236896,2.4543693,2.4850489,2.5157285,2.5464081,2.5770
877,2.6077673,2.638447,2.6691266,2.6998062,2.7304858,2.7611654,2.791845,2.8225246,2.8532
043,2.8838839,2.9145635,2.9452431,2.9759227,3.0066023,3.037282,3.0679616,3.0986412,3.129
3208,3.1600004,3.19068,3.2213597,3.2520393,3.2827189,3.3133985,3.3440781,3.3747577,3.405
4373,3.436117,3.4667966,3.4974762,3.5281558,3.5588354,3.589515,3.6201947,3.6508743,3.681
5539,3.7122335,3.7429131,3.7735927,3.8042724,3.834952,3.8656316,3.8963112,3.9269908,3.95
76704,3.98835,4.0190297,4.0497093,4.0803889,4.1110685,4.1417481,4.1724277,4.2031074,4.23
3787,4.2644666,4.2951462,4.3258258,4.3565054,4.3871851,4.4178647,4.4485443,4.4792239,4.5
099035,4.5405831,4.5712627,4.6019424,4.632622,4.6633016,4.6939812,4.7246608,4.7553404,4.
7860201,4.8166997,4.8473793,4.8780589,4.9087385,4.9394181,4.9700978,5.0007774,5.031457,5
.0621366,5.0928162,5.1234958,5.1541754,5.1848551,5.2155347,5.2462143,5.2768939,5.3075735
,5.3382531,5.3689328,5.3996124,5.430292,5.4609716,5.4916512,5.5223308,5.5530105,5.583690
1,5.6143697];                                                                                                                                                                                       
thucnghiem600=[0.12793751,0.12265847,0.10741094,0.084067484,0.0565579,0.0359283
32,0.044955078,0.071672628,0.097618601,0.11664572,0.12589336,0.1239565,0.11065213,0.087
109526,0.056507524,0.031063234,0.047542907,0.085837526,0.12375595,0.15520889,0.1767309
7,0.18615884,0.18277413,0.16790021,0.14631695,0.1292169,0.13432326,0.16940519,0.2240067,
0.28570038,0.34599097,0.39894682,0.44018177,0.46653144,0.47600124,0.46779393,0.44236165
,0.4015093,0.34868266,0.28981284,0.23554156,0.20455902,0.21653807,0.2684614,0.34143804,0
.42161095,0.50175519,0.57821707,0.6492986,0.7146029,0.77476163,0.83129387,0.88648033,0.9
431853,1.0045884,1.0738288,1.153618,1.2459106,1.3517187,1.4710943,1.6032389,1.7466636,1.
8993266,2.058709,2.2218244,2.3851844,2.5447569,2.6959554,2.8336923,2.9525166,3.0468404,3
.1112453,3.1408443,3.1316717,3.0810644,2.988004,2.853392,2.680238,2.4737571,2.2413828,1.9
927211,1.7394765,1.4953473,1.2757045,1.0963507,0.96990748,0.89939235,0.87382089,0.87255
284,0.87488988,0.86612667,0.83845789,0.78965712,0.7214987,0.63847521,0.54683135,0.45384
347,0.36725402,0.29460556,0.24174119,0.20971819,0.19250183,0.18014937,0.16470616,0.1430
1411,0.11762516,0.09980327,0.10929846,0.15044101,0.21002771,0.27837244,0.3504532,0.4231
122 
6213,0.49411293,0.56118492,0.62235545,0.67567902,0.71935699,0.7518599,0.77206816,0.7794
0065,0.77390842,0.75632075,0.72804262,0.69111296,0.6481393,0.60222248,0.55686511,0.5158
124,0.4827109,0.46046495,0.45036699,0.45145656,0.46063826,0.47352998,0.48547695,0.49228
555,0.4906271,0.47824961,0.45411954,0.41856156,0.37344745,0.32251902,0.27196913,0.23109
633,0.2108845,0.21642843,0.24042864,0.27009928,0.29540548,0.31039999,0.31223669,0.30039
876,0.27633505,0.24338374,0.20697768,0.17503285,0.1570895,0.15860255,0.17467174,0.19500
588,0.21147215,0.21964922,0.21812318,0.20803724,0.19318998,0.18038918,0.17860429,0.1944
128,0.22707275,0.27069221,0.31917717,0.36810506,0.4146273,0.45702434,0.49432246,0.52599
103,0.55170629,0.57118619,0.58410693,0.59010185,0.58882751,0.58006859,0.56384814]; 
rzn600=[0,0.030679616,0.061359232,0.092038847,0.12271846,0.15339808,0.18407769,0.
21475731,0.24543693,0.27611654,0.30679616,0.33747577,0.36815539,0.398835,0.42951462,0.4
6019424,0.49087385,0.52155347,0.55223308,0.5829127,0.61359232,0.64427193,0.67495155,0.7
0563116,0.73631078,0.76699039,0.79767001,0.82834963,0.85902924,0.88970886,0.92038847,0.
95106809,0.9817477,1.0124273,1.0431069,1.0737866,1.1044662,1.1351458,1.1658254,1.196505,
1.2271846,1.2578642,1.2885439,1.3192235,1.3499031,1.3805827,1.4112623,1.4419419,1.472621
6,1.5033012,1.5339808,1.5646604,1.59534,1.6260196,1.6566993,1.6873789,1.7180585,1.748738
1,1.7794177,1.8100973,1.8407769,1.8714566,1.9021362,1.9328158,1.9634954,1.994175,2.02485
46,2.0555343,2.0862139,2.1168935,2.1475731,2.1782527,2.2089323,2.239612,2.2702916,2.3009
712,2.3316508,2.3623304,2.39301,2.4236896,2.4543693,2.4850489,2.5157285,2.5464081,2.5770
877,2.6077673,2.638447,2.6691266,2.6998062,2.7304858,2.7611654,2.791845,2.8225246,2.8532
043,2.8838839,2.9145635,2.9452431,2.9759227,3.0066023,3.037282,3.0679616,3.0986412,3.129
3208,3.1600004,3.19068,3.2213597,3.2520393,3.2827189,3.3133985,3.3440781,3.3747577,3.405
4373,3.436117,3.4667966,3.4974762,3.5281558,3.5588354,3.589515,3.6201947,3.6508743,3.681
5539,3.7122335,3.7429131,3.7735927,3.8042724,3.834952,3.8656316,3.8963112,3.9269908,3.95
76704,3.98835,4.0190297,4.0497093,4.0803889,4.1110685,4.1417481,4.1724277,4.2031074,4.23
3787,4.2644666,4.2951462,4.3258258,4.3565054,4.3871851,4.4178647,4.4485443,4.4792239,4.5
099035,4.5405831,4.5712627,4.6019424,4.632622,4.6633016,4.6939812,4.7246608,4.7553404,4.
7860201,4.8166997,4.8473793,4.8780589,4.9087385,4.9394181,4.9700978,5.0007774,5.031457,5
.0621366,5.0928162,5.1234958,5.1541754,5.1848551,5.2155347,5.2462143,5.2768939,5.3075735
,5.3382531,5.3689328,5.3996124,5.430292,5.4609716,5.4916512,5.5223308,5.5530105,5.583690
1,5.6143697]; 
fefffit600=[0.009701051,0.00973577,0.009841024,0.010025546,0.010317055,0.01076752
9,0.011441106,0.012384477,0.013596382,0.01501718,0.016543699,0.018058077,0.019458005,0.
020682125,0.021727762,0.022657316,0.023587472,0.024656437,0.02597343,0.027569696,0.029
376359,0.031239435,0.032960037,0.034339825,0.035218642,0.035499946,0.035163769,0.03426
7508,0.032935039,0.031336502,0.029666557,0.028138161,0.027016128,0.026700518,0.0278021
43,0.031058939,0.037049235,0.045987975,0.05780036,0.072286792,0.089224146,0.10841644,0.
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