i  LỜI CAM ĐOAN Tôi  xin  cam  đoan:  Luận  án  “Nghiên cứu tham số nhiệt động cumulant số vật liệu phương pháp XAFS phi điều hịa” là cơng trình  nghiên  cứu  của  riêng  tơi.  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 hồn thành luận án này, tơi đã nhận được rất nhiều sự giúp đỡ và tạo điều  kiện cũng như tình cảm động viên của Lãnh đạo cơ quan cơng tác, các thầy hướng  dẫn, các thầy cơ 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 Cơng nghệ - Viện Hàn  lâm Khoa học và Cơng 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, ngồi việc hướng dẫn, chỉ bảo về chun mơn, thầy đã dạy tơi  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, tơi cảm nhận được tính nghiêm khắc, tinh thần  trách  nhiệm  và  lịng  bao  dung  của  thầy  với  học  trò.  Những  điều  mà  tơi ln  cảm  phục và kính trọng.   Tơi xin gửi lời cảm ơn chân thành tới GS.TS. Nguyễn Quang Liêm đã quan  tâm, tạo điều kiện cho tơi trong suốt thời gian tơi học tập tại Viện Khoa học Vật liệu  và Học viện Khoa học và Cơng nghệ.  Để  hồn  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  tơi  được thực hiện đề tài thuộc Chương trình độc lập trẻ - Viện Hàn lâm Khoa học và  Cơng  nghệ  Việt  Nam  với  mã  số  VAST.  ĐLT.08/13-14.  Đó  là  tiền  đề  để  tơi  tiến  hành  nghiên  cứu  và  hồn  thành  luận  án.  Bên  cạnh  đó,  được  tiếp  cận  và  sử  dụng  nguồn  dữ  liệu  quốc  tế  rất  q từ  Trung  tâm  thơng tin tư  liệu  đã giúp tơi rất  nhiều  trong q trình thực hiện luận án. Tơi xin gửi lời cảm ơn sâu sắc nhất tới Chủ tịch  Viện và các cơ quan trực thuộc Viện.  Tơi 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 tơi trong thời gian tơi tiến hành thực nghiệm tại Thái Lan.  Khơng thể khơng nhắc tới gia đình, những người ln dành tất cả những điều  tốt đẹp nhất cho tơi và ln mong muốn tơi hồn thành nhiệm vụ học tập cũng như  trong cơng tác. Tơi cảm ơn mọi người rất nhiều.  iii  Cuối  cùng,  tôi  xin  gửi  lời  cảm  ơn  tới  Bộ  phận  đào  tạo,  các  phịng  ban  của  Học viện Khoa học và Cơng nghệ cũng như những người ln ủng hộ, động viên và  giúp đỡ tơi mà tơi đã vơ tình chưa nhắc tới ở đây. Tơi xin chân thành cảm ơn!  Hà Nội, ngày tháng Nghiên cứu sinh Cù Sỹ Thắng năm 2020 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 CHƯƠNG TỔNG QUAN VỀ HỆ SỐ DEBYE-WALLER PHỔ XAFS 1.1 Sơ lược phổ XAFS 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. Mơ 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 MƠ 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 mơ hình Einstein tương quan phi điều hịa 33 2.2 Thế tương tác cặp Morse 37 2.2.1. Áp dụng hàm thế Morse để tính tốn các tham số và thế hiệu dụng trong mơ  hình Einstein tương quan phi điều hịa với vật liệu cấu trúc fcc, hcp   41 2.2.2. Áp dụng hàm thế Morse để tính tốn các tham số và thế hiệu dụng trong mơ  hình Einstein tương quan phi điều hịa với vật liệu cấu trúc kim cương  . 45 2.3 Thế tương tác Stillinger-Weber 47 2.4 Tính tốn tham số nhiệt động phổ XAFS theo mơ hình Einstein tương quan phi điều hịa 49 2.4.1. Tính các cumulant trong mơ hình Einstein tương quan phi điều hịa   49 v  2.4.2.  Dẫn  giải  các  cumulant  thơng  qua  cumulant  bậc  2  trong  mơ  hình  Einstein  tương quan phi điều hòa   58 2.4.3. Tính hệ số giãn nở nhiệt của vật liệu trong mơ hình Einstein tương quan phi  điều hịa  . 60 2.4.4. Đánh giá kết quả tính cumulant bậc 2 của phổ XAFS sử dụng thế Morse và  thế  Stilinger-Weber  trong  mơ  hình  Einstein  tương  quan  phi  điều  hịa  và  phương  pháp mơ men với các kết quả khác đối với vật liệu bán dẫn cấu trúc kim cương   62 2.5 Các hiệu ứng lượng tử giới hạn nhiệt độ thấp gần cổ điển nhiệt độ cao 65 CHƯƠNG HỆ ĐO THỰC NGHIỆM VÀ ÁP DỤNG MƠ HÌNH EINSTEIN TƯƠNG QUAN PHI ĐIỀU HỊA TRONG NGHIÊN CỨU CÁC THAM SỐ NHIỆT ĐỘNG PHỔ XAFS VẬT LIỆU CẤU TRÚC HCP VÀ FCC 67 3.1 Hệ thống xạ synchrotron 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 thực nghiệm xác định hệ số Debye-Waller phổ XAFS vật liệu cấu trúc hcp 76 3.4 Xác định tham số nhiệt động phổ XAFS từ số liệu thực nghiệm hệ số Debye-Waller hay cumulant bậc hai theo mơ hình Einstein tương quan phi điều hịa vật liệu cấu trúc hcp 78 3.5 Kết thực nghiệm xác định hệ số Debye-Waller phổ XAFS vật liệu cấu trúc fcc 80 3.6 Xác định tham số nhiệt động phổ XAFS từ số liệu thực nghiệm hệ số Debye-Waller hay cumulant bậc hai theo mơ hình Einstein tương quan phi điều hịa vật liệu cấu trúc fcc (Cu) 82 CHƯƠNG MƠ 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 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 pha biên độ phổ XAFS vật liệu cấu trúc hcp (Zn) 90 4.5 Thành phần phi điều hòa pha 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 CƠNG 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  Mô  hình  Einstein  tương  quan  phi  Model  điều hịa  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  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  H2   Harmonic Second cumulant  Cumulant bậc 2 điều hòa   A2   Anharmonic Second cumulant  Cumulant bậc 2 phi điều hịa  T  Coefficient of Thermal Expansion  Hệ số giãn nở nhiệt  µ(E)  , D  Parameters of the Morse Potential  Các tham số thế Morse  ix  DANH MỤC CÁC BẢNG BIỂU   Bảng Các tham số thế Morse của đồng (Cu) từ các nguồn tài liệu[56]   38 Bảng 2. Các tham số thế Morse của đồng (Cu) và kẽm (Zn) tính tốn lý thuyết. 41 Bảng 4: Các tham số nhiệt động trong giới hạn nhiệt độ  66 -***** -  Bảng 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- Mơ hình điều hịa.   77 Bảng 2. Giá trị của các cumulant và tham số phi điều hịa 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 q trình hấp thụ tia X bởi điện tử lỗ trống và q trình hủy hấp  thụ tia X bởi tạo lỗ trống lớp lõi ngun 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 mơ tả hấp thụ tia X thơng qua hiệu ứng quang điện.   9 Hình 1.5: Giản đồ mơ 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 mơ hình tính tốn khác nhau   20 Hình 1.7: Sự phụ thuộc nhiệt độ của hệ số Debye-Waller với các phương pháp tính  tốn và các mơ hình khác nhau   21 -***** -  Hình 2.1: Dao động tử điều hịa[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 6: Sự phụ thuộc nhiệt độ của cumulant bậc 2 sử dụng thế Stillinger-Weber  theo phương pháp thống kê mơ men đối với Si.   64 Hình 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: Mơ hình một hệ synchrotron hiện đại [75].   68 Hình 3.2: Cấu hình một đầu ra đo phổ hấp thụ tia X hiện đại[75].   69 Hình 3.3: Các hệ synchrotron trên thế giới.   70 109  PHỤ LỤC   Tính yếu tố tốn tử ma trận: ˆ ˆ ˆ  aaa ˆ ˆ ˆ   aa ˆ ˆ  aˆ  aa ˆ ˆ  aˆ   aˆ  aa ˆ ˆ  aˆ  aa ˆ ˆ   aˆ  aˆ  aˆ  aˆ  aˆ  aˆ  ) n            n y n   ( )3 n (aaa Tính từng thành phần ta được:  ˆ ˆ ˆ n   n  n aa ˆ ˆ n  n  n aa ˆ ˆ n  n  n n aˆ n   n  n n  n n  2    n aaa ˆ ˆ ˆ  n   n  n aa ˆ ˆ n   n  n  n aˆ n   (n  2) n  n n  ( n  2) n    n aaa ˆ ˆ  aˆ n   n aˆ (n  1) n   (n  1) n aˆ n   (n  1) n  n n  (n  1) n    n aa ˆ ˆ  aˆ  n   n aa ˆ ˆ  n  n   n  n aa ˆ ˆ  n   n  n aˆ n  n   n  n  n aˆ n     n aa ˆ ˆ n   n aˆ  aˆ n  n  n  n aˆ  aˆ n  n n  n n  n n    n aˆ  aa ˆ ˆ  n   n aˆ  aˆ n  n   n  n aˆ  aˆ n   (n  2) n  n n  2    n aˆ  aa n aˆ  aˆ  aˆ n   n aˆ  (n  1) n   (n  1) n aˆ  n   (n  1) n n  n   ( n  1) n  n n  2    n aˆ  aˆ  aˆ  ) n   n aˆ  aˆ  n  n   n  n aˆ  aˆ  n     n  n aˆ  n  n   n  n  n aˆ  n   n  n  n n  n   n  n  n  n n  4    Vậy:  n y n   ( )3[(n  2) n   (n  1) n   n n  1]   3       ( ) n  1[(n  2)  (n  1)  n]=3( ) (n  1)   Tương tự đối với yếu tố ma trận:  ˆ ˆ ˆ  aaa ˆ ˆ ˆ   aa ˆ ˆ  aˆ  aa ˆ ˆ  aˆ   aˆ  aa ˆ ˆ  aˆ  aa ˆ ˆ   aˆ  aˆ  aˆ  aˆ  aˆ  aˆ  ) n    n y n   ( )3 n (aaa ˆ ˆ ˆ n   n aa ˆ ˆ n  n   n  n aa ˆ ˆ n   n  n aˆ n  n    n aaa  n  n  n aˆ n   n  n  n n  n  n  n  n  n n  n  n  n  ˆ ˆ ˆ  n   n aa ˆ ˆ n  n   n  n aa ˆ ˆ n   n  n aˆ n  n   (n  4) n aˆ n  n aaa  (n  4) n   n  n   (n  4) n  n n  2    110  ˆ ˆ  aˆ n   n aˆ (n  3) n   (n  3) n aˆ n   (n  3) n n aa n  n   (n  3) n  n n  3    ˆ ˆ  aˆ  n   n aa ˆ ˆ  n  n   n  n aa ˆ ˆ  n   n  n aˆ n  n   n  n  n aˆ n  n aa       n  n  n n  n   n  n  n  n n  4    ˆ ˆ n   n aˆ  aˆ n  n   n  n aˆ  aˆ n   n  n n  n   (n  2) n  n n  2    n aˆ  aa ˆ ˆ  n   n aˆ  aˆ n  n   n  n aˆ  aˆ n   (n  4) n  n n  4    n aˆ  aa n aˆ  aˆ  aˆ n   n aˆ  (n  3) n   (n  3) n aˆ  n   (n  3) n n  n   (n  3) n  n n  4    n aˆ  aˆ  aˆ  ) n   n aˆ  aˆ  n  n   n  n aˆ  aˆ  n   n  n aˆ  n  n     n  n  n aˆ  n   n  n  n n  n   n  n  n  n n  6    Vậy:  n y n   ( )3[(n+1)(n+2)(n+3)]2     Giá trị thực nghiệm Hệ số Debye-Waller nhiệt độ cao: 2  TN (T)   TN ( H ) (T) 1        Trong đó:    TN ( H ) (T) : giá trị đo thực nghiệm FEFF 1 : giá trị sai lệch thực nghiệm FEFF   : giá trị sai lệch FEFF và phương pháp lý thuyết khác.  Giá trị chấp nhận  1 ~ 5-10% tùy thuộc nhiệt độ và vật liệu nghiên cứu. Giá  trị    ~ 15-20% tùy thuộc nhiệt độ và vật liệu nghiên cứu. Ở đây, chúng tôi đánh giá  qua các phương pháp trong tài liệu[58,82,88].            111  Các số liệu đo phổ XAFS thực nghiệm  Đối với Cu: %rcu300=[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 46019424,0.49087385,0.52155347,0.55223308,0.5829127,0.61359232,0.64427193,0.67495155,0 70563116,0.73631078,0.76699039,0.79767001,0.82834963,0.85902924,0.88970886,0.92038847,0 95106809,0.9817477,1.0124273,1.0431069,1.0737866,1.1044662,1.1351458,1.1658254,1.196505 ,1.2271846,1.2578642,1.2885439,1.3192235,1.3499031,1.3805827,1.4112623,1.4419419,1.47262 16,1.5033012,1.5339808,1.5646604,1.59534,1.6260196,1.6566993,1.6873789,1.7180585,1.74873 81,1.7794177,1.8100973,1.8407769,1.8714566,1.9021362,1.9328158,1.9634954,1.994175,2.0248 546,2.0555343,2.0862139,2.1168935,2.1475731,2.1782527,2.2089323,2.239612,2.2702916,2.300 9712,2.3316508,2.3623304,2.39301,2.4236896,2.4543693,2.4850489,2.5157285,2.5464081,2.577 0877,2.6077673,2.638447,2.6691266,2.6998062,2.7304858,2.7611654,2.791845,2.8225246,2.853 2043,2.8838839,2.9145635,2.9452431,2.9759227,3.0066023,3.037282,3.0679616,3.0986412,3.12 93208,3.1600004,3.19068,3.2213597,3.2520393,3.2827189,3.3133985,3.3440781,3.3747577,3.40 54373,3.436117,3.4667966,3.4974762,3.5281558,3.5588354,3.589515,3.6201947,3.6508743,3.68 15539,3.7122335,3.7429131,3.7735927,3.8042724,3.834952,3.8656316,3.8963112,3.9269908,3.9 576704,3.98835,4.0190297,4.0497093,4.0803889,4.1110685,4.1417481,4.1724277,4.2031074,4.2 33787,4.2644666,4.2951462,4.3258258,4.3565054,4.3871851,4.4178647,4.4485443,4.4792239,4 5099035,4.5405831,4.5712627,4.6019424,4.632622,4.6633016,4.6939812,4.7246608,4.7553404,4 7860201,4.8166997,4.8473793,4.8780589,4.9087385,4.9394181,4.9700978,5.0007774,5.031457, 5.0621366,5.0928162,5.1234958,5.1541754,5.1848551,5.2155347,5.2462143,5.2768939,5.307573 5,5.3382531,5.3689328,5.3996124,5.430292,5.4609716,5.4916512,5.5223308,5.5530105,5.58369 01,5.6143697,5.6450493];  %thucnghiem300=[0.014634428,0.016019957,0.021275093,0.030457523,0.041108972,0.0 50152268,0.054970943,0.054228976,0.049330445,0.047175867,0.058211279,0.082397112,0.111 58706,0.13857507,0.15782675,0.16534714,0.15923054,0.14089414,0.1179126,0.10869843,0.131 59947,0.17779126,0.2283723,0.2701405,0.29427685,0.29502816,0.26964053,0.21874342,0.1475 2225,0.075357259,0.091631162,0.1799206,0.26843106,0.34002039,0.38718806,0.40897304,0.41 388136,0.4234648,0.46788306,0.56450512,0.70352305,0.85955563,1.0043341,1.1106079,1.1531 961,1.1101898,0.96479342,0.70843068,0.35453079,0.26507335,0.80000324,1.4464939,2.130915 9,2.8063396,3.4261964,3.9482337,4.3434877,4.6102028,4.7937789,5.008474,5.4368772,6.26704 93,7.5926343,9.3833232,11.534331,13.914502,16.386948,18.816158,21.072406,23.036576,24.60 5524,25.697311,26.255636,26.252915,25.69164,24.603833,23.048599,21.107987,18.881495,16.4 79721,14.017776,11.609109,9.3603996,7.3678754,5.7141444,4.4606187,3.6247333,3.14414,2.87 90288,2.6814512,2.4551578,2.1603505,1.7950301,1.3816014,0.97326708,0.71297241,0.8309983 8,1.2295862,1.7053699,2.1767585,2.6071038,2.9737438,3.2615339,3.4621252,3.5745001,3.6054 474,3.5694423,3.4876166,3.3855442,3.2896397,3.2224091,3.1978011,3.2188329,3.2790202,3.36 68204,3.4705872,3.5820013,3.6974507,3.8178175,3.9473251,4.0919608,4.2578352,4.4497704,4 6703457,4.9195261,5.1948241,5.4917893,5.8045429,6.1261104,6.4484344,6.7621045,7.055987,7 3170102,7.5303531,7.6801942,7.7510411,7.7295305,7.6065051,7.379149,7.0530001,6.6437204, 6.1785401,5.6971246,5.2509376,4.8986954,4.6944099,4.6685654,4.8140892,5.0910455,5.445789 7,5.8279436,6.1974778,6.5246891,6.7875721,6.9691506,7.0557513,7.0364173,6.9033108,6.6527 816,6.2867357,5.8139903,5.2514467,4.6251306,3.971425,3.3389869,2.7908583,2.4005178,2.224 1591,2.2510421,2.4005065,2.5808033,2.7285736,2.8107685,2.8157326,2.7456009,2.6110759,2.4 27667,2.2127501,1.9831862,1.7534694,1.5345002,1.3331264,1.1525388,0.99340836,0.85537204] ;      %rcu300=[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 46019424,0.49087385,0.52155347,0.55223308,0.5829127,0.61359232,0.64427193,0.67495155,0 70563116,0.73631078,0.76699039,0.79767001,0.82834963,0.85902924,0.88970886,0.92038847,0   112  95106809,0.9817477,1.0124273,1.0431069,1.0737866,1.1044662,1.1351458,1.1658254,1.196505 ,1.2271846,1.2578642,1.2885439,1.3192235,1.3499031,1.3805827,1.4112623,1.4419419,1.47262 16,1.5033012,1.5339808,1.5646604,1.59534,1.6260196,1.6566993,1.6873789,1.7180585,1.74873 81,1.7794177,1.8100973,1.8407769,1.8714566,1.9021362,1.9328158,1.9634954,1.994175,2.0248 546,2.0555343,2.0862139,2.1168935,2.1475731,2.1782527,2.2089323,2.239612,2.2702916,2.300 9712,2.3316508,2.3623304,2.39301,2.4236896,2.4543693,2.4850489,2.5157285,2.5464081,2.577 0877,2.6077673,2.638447,2.6691266,2.6998062,2.7304858,2.7611654,2.791845,2.8225246,2.853 2043,2.8838839,2.9145635,2.9452431,2.9759227,3.0066023,3.037282,3.0679616,3.0986412,3.12 93208,3.1600004,3.19068,3.2213597,3.2520393,3.2827189,3.3133985,3.3440781,3.3747577,3.40 54373,3.436117,3.4667966,3.4974762,3.5281558,3.5588354,3.589515,3.6201947,3.6508743,3.68 15539,3.7122335,3.7429131,3.7735927,3.8042724,3.834952,3.8656316,3.8963112,3.9269908,3.9 576704,3.98835,4.0190297,4.0497093,4.0803889,4.1110685,4.1417481,4.1724277,4.2031074,4.2 33787,4.2644666,4.2951462,4.3258258,4.3565054,4.3871851,4.4178647,4.4485443,4.4792239,4 5099035,4.5405831,4.5712627,4.6019424,4.632622,4.6633016,4.6939812,4.7246608,4.7553404,4 7860201,4.8166997,4.8473793,4.8780589,4.9087385,4.9394181,4.9700978,5.0007774,5.031457, 5.0621366,5.0928162,5.1234958,5.1541754,5.1848551,5.2155347,5.2462143,5.2768939,5.307573 5,5.3382531,5.3689328,5.3996124,5.430292,5.4609716,5.4916512,5.5223308,5.5530105,5.58369 01,5.6143697,5.6450493];  %fefffit300=[0.10995779,0.10996803,0.11140949,0.11715161,0.1282755,0.14214771,0.1 5378658,0.15825654,0.15227131,0.1353074,0.11127376,0.092310973,0.098124879,0.12984404,0 16933849,0.20266041,0.22152036,0.2212944,0.20088834,0.16399882,0.12390752,0.11403739,0 15627624,0.2213373,0.28347209,0.32910088,0.35004749,0.34185479,0.30364873,0.23820118,0 15199489,0.057725806,0.060642755,0.14654688,0.21399756,0.24916927,0.24370794,0.1931927 6,0.097701949,0.039039276,0.20523896,0.38896872,0.57293566,0.73854695,0.86764181,0.9453 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33787,4.2644666,4.2951462,4.3258258,4.3565054,4.3871851,4.4178647,4.4485443,4.4792239,4 5099035,4.5405831,4.5712627,4.6019424,4.632622,4.6633016,4.6939812,4.7246608,4.7553404,4 7860201,4.8166997,4.8473793,4.8780589,4.9087385,4.9394181,4.9700978,5.0007774,5.031457, 5.0621366,5.0928162,5.1234958,5.1541754,5.1848551,5.2155347,5.2462143,5.2768939,5.307573   114  5,5.3382531,5.3689328,5.3996124,5.430292,5.4609716,5.4916512,5.5223308,5.5530105,5.58369 01,5.6143697,5.6450493];                                                                                                                                                      %fefffit400=[0.098088747,0.10111836,0.10928672,0.1203101,0.13138709,0.13977325,0 1431624,0.14010441,0.13057569,0.11682043,0.10446947,0.10213741,0.11478165,0.13759257,0 16174875,0.18012501,0.18820396,0.18410221,0.16909612,0.14898507,0.13589549,0.14411099,0 17462795,0.21477491,0.25176555,0.27671333,0.2840478,0.2711162,0.23821854,0.18897507,0.1 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54373,3.436117,3.4667966,3.4974762,3.5281558,3.5588354,3.589515,3.6201947,3.6508743,3.68 15539,3.7122335,3.7429131,3.7735927,3.8042724,3.834952,3.8656316,3.8963112,3.9269908,3.9 576704,3.98835,4.0190297,4.0497093,4.0803889,4.1110685,4.1417481,4.1724277,4.2031074,4.2 33787,4.2644666,4.2951462,4.3258258,4.3565054,4.3871851,4.4178647,4.4485443,4.4792239,4 5099035,4.5405831,4.5712627,4.6019424,4.632622,4.6633016,4.6939812,4.7246608,4.7553404,4 7860201,4.8166997,4.8473793,4.8780589,4.9087385,4.9394181,4.9700978,5.0007774,5.031457, 5.0621366,5.0928162,5.1234958,5.1541754,5.1848551,5.2155347,5.2462143,5.2768939,5.307573 5,5.3382531,5.3689328,5.3996124,5.430292,5.4609716,5.4916512,5.5223308,5.5530105,5.58369 01,5.6143697,5.6450493];                                                                                                                                                      %thucnghiem500=[0.096422648,0.091653862,0.078215653,0.059099949,0.041733872,0.0 41286184,0.058747139,0.078858113,0.09338341,0.098559176,0.092685632,0.075743953,0.0498 77648,0.025480948,0.04184502,0.079385348,0.11561711,0.14384711,0.15946305,0.15908733,0 14114787,0.10802762,0.077384117,0.10305098,0.18419059,0.28732447,0.39872964,0.50953096, 0.6116213,0.69720326,0.7590232,0.79077344,0.78752478,0.74613349,0.66559748,0.54738247,0   115  3959377,0.22135646,0.089482933,0.23456683,0.44120604,0.64182245,0.82073168,0.96657099,1 0706981,1.1280222,1.1384678,1.1090895,1.0570501,1.0126209,1.0168089,1.1042785,1.281503, 1.5300796,1.8279403,2.1628095,2.5358343,2.9606819,3.4595511,4.0563974,4.7691536,5.603742 3,6.5515619,7.5901139,8.6854505,9.7953427,10.872635,11.868597,12.736196,13.433168,13.924 779,14.186095,14.203622,13.976203,13.515094,12.84322,11.993653,11.007441,9.9309212,8.812 7188,7.7006037,6.6383516,5.6627127,4.8005651,4.0664523,3.4610944,2.9719789,2.577038,2.25 09484,1.9716897,1.7248159,1.5047157,1.3138834,1.1613831,1.060301,1.0223719,1.0501528,1.1 334865,1.2544227,1.3941559,1.5362961,1.6673175,1.7763327,1.8550653,1.8981038,1.903325,1 8724011,1.8113319,1.7308989,1.6467066,1.5779865,1.5439288,1.5574033,1.6194182,1.7192248, 1.8400634,1.9657149,2.0845281,2.1908304,2.2845979,2.3699109,2.4524882,2.5368016,2.623676 3,2.7093547,2.7864731,2.8465962,2.8834574,2.8960365,2.8907479,2.881963,2.8898817,2.93504 98,3.0306042,3.1760299,3.3563773,3.5469895,3.7202503,3.851217,3.9211719,3.9194305,3.8439 566,3.7011552,3.5050337,3.275796,3.0378068,2.8167135,2.6355118,2.5099158,2.444723,2.4335 749,2.4626397,2.5156927,2.5776203,2.6355131,2.6783023,2.6961794,2.6805177,2.6244478,2.52 38974,2.378809,2.1943159,1.9817743,1.7595915,1.5533918,1.3935505,1.3060408,1.296962,1.34 57384,1.4177673,1.4813095,1.5147902,1.5068732,1.4544441,1.3605396,1.2325627,1.080733,0.9 167309,0.75254933,0.5995995,0.46806576,0.36622655,0.29882179,0.26397663,0.25255269];  %rcu500=[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 46019424,0.49087385,0.52155347,0.55223308,0.5829127,0.61359232,0.64427193,0.67495155,0 70563116,0.73631078,0.76699039,0.79767001,0.82834963,0.85902924,0.88970886,0.92038847,0 95106809,0.9817477,1.0124273,1.0431069,1.0737866,1.1044662,1.1351458,1.1658254,1.196505 ,1.2271846,1.2578642,1.2885439,1.3192235,1.3499031,1.3805827,1.4112623,1.4419419,1.47262 16,1.5033012,1.5339808,1.5646604,1.59534,1.6260196,1.6566993,1.6873789,1.7180585,1.74873 81,1.7794177,1.8100973,1.8407769,1.8714566,1.9021362,1.9328158,1.9634954,1.994175,2.0248 546,2.0555343,2.0862139,2.1168935,2.1475731,2.1782527,2.2089323,2.239612,2.2702916,2.300 9712,2.3316508,2.3623304,2.39301,2.4236896,2.4543693,2.4850489,2.5157285,2.5464081,2.577 0877,2.6077673,2.638447,2.6691266,2.6998062,2.7304858,2.7611654,2.791845,2.8225246,2.853 2043,2.8838839,2.9145635,2.9452431,2.9759227,3.0066023,3.037282,3.0679616,3.0986412,3.12 93208,3.1600004,3.19068,3.2213597,3.2520393,3.2827189,3.3133985,3.3440781,3.3747577,3.40 54373,3.436117,3.4667966,3.4974762,3.5281558,3.5588354,3.589515,3.6201947,3.6508743,3.68 15539,3.7122335,3.7429131,3.7735927,3.8042724,3.834952,3.8656316,3.8963112,3.9269908,3.9 576704,3.98835,4.0190297,4.0497093,4.0803889,4.1110685,4.1417481,4.1724277,4.2031074,4.2 33787,4.2644666,4.2951462,4.3258258,4.3565054,4.3871851,4.4178647,4.4485443,4.4792239,4 5099035,4.5405831,4.5712627,4.6019424,4.632622,4.6633016,4.6939812,4.7246608,4.7553404,4 7860201,4.8166997,4.8473793,4.8780589,4.9087385,4.9394181,4.9700978,5.0007774,5.031457, 5.0621366,5.0928162,5.1234958,5.1541754,5.1848551,5.2155347,5.2462143,5.2768939,5.307573 5,5.3382531,5.3689328,5.3996124,5.430292,5.4609716,5.4916512,5.5223308,5.5530105,5.58369 01,5.6143697,5.6450493];                                                                                                                                                      %fefffit500=[0.087104803,0.090009154,0.097372233,0.10623021,0.11370065,0.1177718, 0.11748515,0.11302151,0.10585436,0.098869165,0.095880637,0.099662012,0.10964026,0.12239 128,0.13401097,0.14158112,0.14365141,0.140485,0.13432318,0.12940304,0.1307237,0.1408831 4,0.1578538,0.17665046,0.19212025,0.20030798,0.19885146,0.18714372,0.16653298,0.1407050 3,0.11634097,0.10275828,0.1054138,0.11808253,0.12989112,0.13376725,0.12831205,0.1201014 2,0.12694246,0.1656511,0.23251652,0.31508882,0.40303231,0.48860609,0.56660701,0.6352835 6,0.69773493,0.76297565,0.84519912,0.95983109,1.1176076,1.3210127,1.5654681,1.8432529,2 1475387,2.4756675,2.8315574,3.2268337,3.6799067,4.2124742,4.8440145,5.5860842,6.4384167, 7.3876949,8.4085672,9.4659662,10.517988,11.518956,12.422496,13.184535,13.766115,14.13587 4,14.272076,14.164045,13.812898,13.231538,12.443885,11.483401,10.391025,9.2126525,7.9963 497,6.7894984,5.6360522,4.5740531,3.6334689,2.8342842,2.1846532,1.6790935,1.297728,1.009 2346,0.77925126,0.58055782,0.39852629,0.23011021,0.079549187,0.046537174,0.14102454,0.2 0046045,0.22437359,0.21610275,0.18260393,0.13482971,0.091678021,0.085759461,0.11707606, 0.1513983,0.17280065,0.17675034,0.1639707,0.1393141,0.11263898,0.099879598,0.11175019,0 13793471,0.16333018,0.17935076,0.18229563,0.17156674,0.14886551,0.11781629,0.084135345,   116  0.057539921,0.052505708,0.066197347,0.080980809,0.088460475,0.086423029,0.075447169,0.0 58108,0.039799241,0.032404672,0.043397642,0.059799374,0.07268357,0.078861815,0.0774014 16,0.068746113,0.054490487,0.037584185,0.024326084,0.026090559,0.03821499,0.049553065,0 056243522,0.057163797,0.052439576,0.043143263,0.03138419,0.021376543,0.020700779,0.028 674556,0.037294962,0.042928378,0.044413464,0.041722845,0.03570369,0.028223966,0.022759 632,0.023430446,0.0292949,0.036006951,0.040839767,0.042583459,0.040888904,0.035998133,0 028620526,0.019911984,0.011909831,0.009511507,0.014044722,0.019156781,0.022359189,0.02 3069455,0.021332926,0.017574487,0.012539808,0.007511954,0.005681285,0.008614785,0.0120 74224,0.014311531,0.014933183,0.014014416,0.011984873,0.009700992];   Đối với Zn: rzn300=[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];  thucnghiem300=[0.088857472,0.091611443,0.098357367,0.10579762,0.11081234,0.1113 896,0.10685508,0.097986196,0.08722676,0.078784303,0.077240239,0.083612442,0.093915115,0 1027361,0.10592542,0.10132637,0.089784713,0.07864584,0.086015874,0.12326358,0.1816179, 0.25119218,0.32527265,0.39833841,0.46529513,0.52140772,0.56246527,0.58501108,0.58657108 ,0.56584803,0.52286667,0.45907385,0.37744157,0.28278832,0.18349102,0.1036263,0.11635856, 0.19746386,0.28124901,0.35010974,0.39656982,0.41587013,0.40488965,0.36198859,0.28709837 ,0.1823745,0.063006856,0.13184067,0.30818026,0.50267769,0.70486182,0.90600845,1.0971184, 1.2690629,1.4131708,1.5222107,1.5919409,1.6235464,1.6273806,1.6279531,1.6674164,1.799140 9,2.0654859,2.4774361,3.0179928,3.6577331,4.3645795,5.1067349,5.8531095,6.5734932,7.2390 31,7.8229922,8.3016979,8.655472,8.8695027,8.9345239,8.8472509,8.6105253,8.233151,7.72942 26,7.1183723,6.4227816,5.6680207,4.8807944,4.0878855,3.3150041,2.5858896,1.9219244,1.342 9272,0.87130956,0.54614361,0.43172742,0.48905248,0.57498559,0.62456749,0.62587266,0.583 10065,0.50546648,0.40378552,0.28987208,0.18056739,0.12347394,0.17977855,0.28377821,0.39 394192,0.50178141,0.60547793,0.70467978,0.79910107,0.88797921,0.96989335,1.0428083,1.10 42717,1.1517077,1.1827602,1.195646,1.189481,1.1645454,1.1224484,1.0661504,0.99979485,0.9 2829924,0.85668046,0.78917609,0.72841303,0.67509669,0.62871879,0.58941497,0.56045482,0 54997012,0.56936867,0.62699176,0.72204717,0.84536721,0.98421545,1.1257097,1.2581915,1.3 717559,1.4586208,1.513494,1.5339179,1.5205438,1.4772977,1.4113864,1.3330454,1.2547895,1 1897583,1.148867,1.1374596,1.1535835,1.1895504,1.2356911,1.2837369,1.3284968,1.3680109,1 4027799,1.4345388,1.4649227,1.4943594,1.5214776,1.5431559,1.5551088,1.552744,1.5320223, 1.4901387,1.425961,1.3402376,1.2356315,1.1166583,0.98962487,0.86266267,0.74587415,0.6512   117  1691,0.59075867,0.57164418,0.59069382,0.63603468,0.69431532,0.75535007,0.81265321,0.862 43822,0.90261108,0.93209227,0.95042227];  rzn300=[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 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0.020364872,0.021500719,0.021291217,0.019743298,0.017144575,0.014077494,0.011509587,0.0 10662536,0.01186295,0.014018371,0.015983979,0.017128408,0.017192872,0.016166021,0.0142 32643,0.011771145,0.009409996,0.008070842,0.008409979,0.009890375,0.011518886,0.012677 278,0.013092574,0.012704281,0.011599855,0.009988199,0.008197698,0.00669033,0.005978737, 0.006204938,0.006913889,0.007567502];  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   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 12973451,0.15315779,0.17881377,0.20700446,0.23820916,0.27305716,0.31227332,0.35660919,0 40677881,0.46341686,0.52706835,0.59820699,0.67726988,0.76469066,0.8609133,0.96637266,1 0814351,1.2063014,1.3408839,1.4846756,1.6366327,1.7950907,1.9577263,2.1215761,2.283108,2 4383449,2.583028,2.7128106,2.8234683,2.9111126,2.9723954,3.0046903,3.0062415,2.9762704, 2.9150335,2.8238269,2.7049384,2.5615484,2.3975852,2.2175434,2.0262759,1.8287702,1.629923 6,1.4343283,1.2460803,1.0686215,0.90462551,0.75593366,0.62354794,0.50768284,0.40787732,0 32316219,0.25227283,0.1938909,0.14689505,0.11059003,0.084801034,0.069434534,0.06313467 4,0.062590252,0.064222726,0.06581283,0.066521324,0.066356312,0.065728031,0.065127257,0 0648904,0.0650741,0.065471267,0.065737994,0.065547369,0.064700522,0.063172366,0.061099 858,0.058727739,0.056326845,0.054105039,0.052140172,0.050364499,0.048608586,0.04668138 7,0.044449045,0.041885682,0.03908771,0.036253245,0.033629669,0.031435016,0.029773921,0 028590783,0.027696798,0.026857484,0.025886484,0.024703954,0.023351952,0.021974755,0.02 0769107,0.019908442,0.019463129,0.019363993,0.019439588,0.019497833,0.019396879,0.0190 7925,0.018573188,0.017971408,0.017393704,0.016940373,0.016651368,0.016491673,0.0163717 31,0.016189182,0.015868582,0.015384977,0.014769139,0.014096893,0.013464757,0.012955628, 0.012605185,0.012386573,0.012224152,0.012027491,0.011725699,0.011289077,0.010736159,0.0 10128621,0.009555134,0.009103916,0.008828622,0.008723838,0.008728725,0.008756887,0.008   123  730575,0.00860208,0.008360209,0.008026497,0.007645114,0.007268484,0.006940723,0.006683 469,0.006490574,0.006335015,0.006183893];      ... nghiên? ?cứu? ?phát triển mơ hình Einstein tương quan? ?phi? ?điều? ?hịa thành? ?phương? ?pháp? ? hồn chỉnh, thuận tiện? ?và? ?bao qt đối với phổ? ?XAFS.  Vì vậy,? ?nghiên? ?cứu? ?sinh lựa    3  chọn đề tài? ?nghiên? ?cứu? ?là: ? ?Nghiên cứu tham số nhiệt động cumulant số vật liệu phương pháp XAFS. .. Bảng 2.1 đưa ra  một? ?số? ?giá trị? ?của? ?các? ?tham? ? số? ?thế Morse từ? ?các? ?nguồn tài  liệu? ?khác nhau.? ?Trong? ?q trình tính tốn? ?các? ?tham? ?số? ?nhiệt? ?động? ?của? ?phổ? ?XAFS,  ta  có thể sử dụng? ?các? ?tham? ?số? ?thu được từ? ?các? ?giá trị thực nghiệm hay? ?các? ?giá trị tính ... XAFS phi điều hòa? ?? Mục đích nghiên cứu luận án - Xây dựng? ?một? ?phương? ?pháp? ?mà nó có thể đơn giản hóa việc tính? ?các? ?tham? ?số? ? nhiệt? ?động,  phổ? ?XAFS? ?và? ?ảnh Fourier? ?của? ?chúng chỉ thơng qua? ?một? ?tham? ?số? ?