========================================================================================== TLT-002-PT: FULL PERIODIC TABLE SUITE — COMPREHENSIVE DATA ========================================================================================== Date: 2026-03-13 Test ID: TLT-002-PT (Periodic Table extension) Elements: 118 METHODOLOGY -------------------------------------------------- For each element: 1. Compton frequency: nu_C = m * c^2 / h 2. Compton wavelength: lambda_C = c / nu_C = h / (m * c) 3. Scale ratio: a / lambda_C (lattice constant / Compton wavelength) 4. N-wave interference: compute patterns for N=2,3,4,6 5. Crystal-to-N mapping: which N matches the element's structure 6. {2,3} cipher: factor coordination number into 2^a * 3^b CONSTANTS -------------------------------------------------- c (speed of light) = 299792458 m/s (exact) h (Planck constant) = 6.62607015e-34 J*s (exact) 1 amu = 1.66053906660e-27 kg 1 amu -> Compton freq = 2.252343e+23 Hz N-WAVE INTERFERENCE REFERENCE DATA -------------------------------------------------- (wavelength = 1.0, grid_extent = 5.0, resolution = 600) N=2: I_max=4.00, I_min=0.0000, peak_spacing=0.4999 lambda, maxima_on_axis=19 N=3: I_max=9.00, I_min=0.0000, peak_spacing=0.6666 lambda, maxima_on_axis=15 N=4: I_max=16.00, I_min=0.0000, peak_spacing=0.9996 lambda, maxima_on_axis=9 N=6: I_max=36.00, I_min=0.0000, peak_spacing=1.9992 lambda, maxima_on_axis=5 ========================================================================================== SECTION A: FULL ELEMENT TABLE ========================================================================================== Z Sym Mass(amu) Crystal a(A) Coord nu_C(Hz) lam_C(m) a/lam_C N_match 2,3 cipher ----------------------------------------------------------------------------------------------------------------------- 1 H 1.0080 HCP 3.7700 12 2.2704e+23 1.3205e-15 2.8551e+05 3 12 = 2^2 * 3 [mixed_ 2 He 4.0026 HCP 3.5700 12 9.0152e+23 3.3254e-16 1.0736e+06 3 12 = 2^2 * 3 [mixed_ 3 Li 6.9400 BCC 3.5100 8 1.5631e+24 1.9179e-16 1.8301e+06 4 8 = 2^3 [pure_2] 4 Be 9.0122 HCP 2.2866 12 2.0299e+24 1.4769e-16 1.5482e+06 3 12 = 2^2 * 3 [mixed_ 5 B 10.8100 rhombo 5.0600 6 2.4348e+24 1.2313e-16 4.1095e+06 3 6 = 2 * 3 [mixed_23] 6 C 12.0110 diamond 3.5668 4 2.7053e+24 1.1082e-16 3.2186e+06 3 4 = 2^2 [pure_2] 7 N 14.0070 SC 5.6610 12 3.1549e+24 9.5026e-17 5.9573e+06 4 12 = 2^2 * 3 [mixed_ 8 O 15.9990 mono 5.4030 2 3.6035e+24 8.3194e-17 6.4944e+06 None 2 = 2 [pure_2] 9 F 18.9980 mono 5.5000 2 4.2790e+24 7.0061e-17 7.8503e+06 None 2 = 2 [pure_2] 10 Ne 20.1800 FCC 4.4290 12 4.5452e+24 6.5958e-17 6.7149e+06 3 12 = 2^2 * 3 [mixed_ 11 Na 22.9900 BCC 4.2906 8 5.1781e+24 5.7896e-17 7.4109e+06 4 8 = 2^3 [pure_2] 12 Mg 24.3050 HCP 3.2094 12 5.4743e+24 5.4763e-17 5.8605e+06 3 12 = 2^2 * 3 [mixed_ 13 Al 26.9820 FCC 4.0495 12 6.0773e+24 4.9330e-17 8.2090e+06 3 12 = 2^2 * 3 [mixed_ 14 Si 28.0850 diamond 5.4310 4 6.3257e+24 4.7393e-17 1.1460e+07 3 4 = 2^2 [pure_2] 15 P 30.9740 ortho 3.3136 3 6.9764e+24 4.2972e-17 7.7110e+06 None 3 = 3 [pure_3] 16 S 32.0600 ortho 10.4650 2 7.2210e+24 4.1517e-17 2.5207e+07 None 2 = 2 [pure_2] 17 Cl 35.4500 ortho 6.2400 2 7.9846e+24 3.7547e-17 1.6619e+07 None 2 = 2 [pure_2] 18 Ar 39.9480 FCC 5.3111 12 8.9977e+24 3.3319e-17 1.5940e+07 3 12 = 2^2 * 3 [mixed_ 19 K 39.0980 BCC 5.3280 8 8.8062e+24 3.4043e-17 1.5651e+07 4 8 = 2^3 [pure_2] 20 Ca 40.0780 FCC 5.5884 12 9.0269e+24 3.3211e-17 1.6827e+07 3 12 = 2^2 * 3 [mixed_ 21 Sc 44.9560 HCP 3.3090 12 1.0126e+25 2.9607e-17 1.1176e+07 3 12 = 2^2 * 3 [mixed_ 22 Ti 47.8670 HCP 2.9508 12 1.0781e+25 2.7807e-17 1.0612e+07 3 12 = 2^2 * 3 [mixed_ 23 V 50.9420 BCC 3.0240 8 1.1474e+25 2.6128e-17 1.1574e+07 4 8 = 2^3 [pure_2] 24 Cr 51.9960 BCC 2.8839 8 1.1711e+25 2.5599e-17 1.1266e+07 4 8 = 2^3 [pure_2] 25 Mn 54.9380 BCC 8.9125 12 1.2374e+25 2.4228e-17 3.6786e+07 4 12 = 2^2 * 3 [mixed_ 26 Fe 55.8450 BCC 2.8665 8 1.2578e+25 2.3834e-17 1.2027e+07 4 8 = 2^3 [pure_2] 27 Co 58.9330 HCP 2.5071 12 1.3274e+25 2.2585e-17 1.1101e+07 3 12 = 2^2 * 3 [mixed_ 28 Ni 58.6930 FCC 3.5240 12 1.3220e+25 2.2678e-17 1.5539e+07 3 12 = 2^2 * 3 [mixed_ 29 Cu 63.5460 FCC 3.6149 12 1.4313e+25 2.0946e-17 1.7258e+07 3 12 = 2^2 * 3 [mixed_ 30 Zn 65.3800 HCP 2.6650 12 1.4726e+25 2.0358e-17 1.3090e+07 3 12 = 2^2 * 3 [mixed_ 31 Ga 69.7230 ortho 4.5186 7 1.5704e+25 1.9090e-17 2.3670e+07 None 7 = 7 [prime] 32 Ge 72.6300 diamond 5.6575 4 1.6359e+25 1.8326e-17 3.0871e+07 3 4 = 2^2 [pure_2] 33 As 74.9220 rhombo 3.7598 3 1.6875e+25 1.7765e-17 2.1164e+07 3 3 = 3 [pure_3] 34 Se 78.9710 hex 4.3662 2 1.7787e+25 1.6855e-17 2.5905e+07 3 2 = 2 [pure_2] 35 Br 79.9040 ortho 6.6700 2 1.7997e+25 1.6658e-17 4.0041e+07 None 2 = 2 [pure_2] 36 Kr 83.7980 FCC 5.7210 12 1.8874e+25 1.5884e-17 3.6018e+07 3 12 = 2^2 * 3 [mixed_ 37 Rb 85.4680 BCC 5.5850 8 1.9250e+25 1.5573e-17 3.5862e+07 4 8 = 2^3 [pure_2] 38 Sr 87.6200 FCC 6.0849 12 1.9735e+25 1.5191e-17 4.0056e+07 3 12 = 2^2 * 3 [mixed_ 39 Y 88.9060 HCP 3.6482 12 2.0025e+25 1.4971e-17 2.4368e+07 3 12 = 2^2 * 3 [mixed_ 40 Zr 91.2240 HCP 3.2316 12 2.0547e+25 1.4591e-17 2.2148e+07 3 12 = 2^2 * 3 [mixed_ 41 Nb 92.9060 BCC 3.3004 8 2.0926e+25 1.4327e-17 2.3037e+07 4 8 = 2^3 [pure_2] 42 Mo 95.9500 BCC 3.1470 8 2.1611e+25 1.3872e-17 2.2686e+07 4 8 = 2^3 [pure_2] 43 Tc 97.0000 HCP 2.7350 12 2.1848e+25 1.3722e-17 1.9932e+07 3 12 = 2^2 * 3 [mixed_ 44 Ru 101.0700 HCP 2.7059 12 2.2764e+25 1.3169e-17 2.0547e+07 3 12 = 2^2 * 3 [mixed_ 45 Rh 102.9100 FCC 3.8034 12 2.3179e+25 1.2934e-17 2.9407e+07 3 12 = 2^2 * 3 [mixed_ 46 Pd 106.4200 FCC 3.8907 12 2.3969e+25 1.2507e-17 3.1107e+07 3 12 = 2^2 * 3 [mixed_ 47 Ag 107.8700 FCC 4.0862 12 2.4296e+25 1.2339e-17 3.3116e+07 3 12 = 2^2 * 3 [mixed_ 48 Cd 112.4100 HCP 2.9793 12 2.5319e+25 1.1841e-17 2.5161e+07 3 12 = 2^2 * 3 [mixed_ 49 In 114.8200 BCT 3.2523 12 2.5861e+25 1.1592e-17 2.8056e+07 4 12 = 2^2 * 3 [mixed_ 50 Sn 118.7100 BCT 5.8318 6 2.6738e+25 1.1212e-17 5.2012e+07 4 6 = 2 * 3 [mixed_23] 51 Sb 121.7600 rhombo 4.3084 3 2.7425e+25 1.0932e-17 3.9413e+07 3 3 = 3 [pure_3] 52 Te 127.6000 hex 4.4572 2 2.8740e+25 1.0431e-17 4.2729e+07 3 2 = 2 [pure_2] 53 I 126.9000 ortho 7.2700 2 2.8582e+25 1.0489e-17 6.9312e+07 None 2 = 2 [pure_2] 54 Xe 131.2900 FCC 6.1970 12 2.9571e+25 1.0138e-17 6.1126e+07 3 12 = 2^2 * 3 [mixed_ 55 Cs 132.9100 BCC 6.1410 8 2.9936e+25 1.0014e-17 6.1321e+07 4 8 = 2^3 [pure_2] 56 Ba 137.3300 BCC 5.0280 8 3.0931e+25 9.6922e-18 5.1877e+07 4 8 = 2^3 [pure_2] 57 La 138.9100 HCP 3.7740 12 3.1287e+25 9.5819e-18 3.9387e+07 3 12 = 2^2 * 3 [mixed_ 58 Ce 140.1200 FCC 5.1610 12 3.1560e+25 9.4992e-18 5.4331e+07 3 12 = 2^2 * 3 [mixed_ 59 Pr 140.9100 HCP 3.6721 12 3.1738e+25 9.4459e-18 3.8875e+07 3 12 = 2^2 * 3 [mixed_ 60 Nd 144.2400 HCP 3.6582 12 3.2488e+25 9.2278e-18 3.9643e+07 3 12 = 2^2 * 3 [mixed_ 61 Pm 145.0000 HCP 3.6500 12 3.2659e+25 9.1795e-18 3.9763e+07 3 12 = 2^2 * 3 [mixed_ 62 Sm 150.3600 rhombo 3.6290 12 3.3866e+25 8.8523e-18 4.0995e+07 3 12 = 2^2 * 3 [mixed_ 63 Eu 151.9600 BCC 4.5827 8 3.4227e+25 8.7590e-18 5.2320e+07 4 8 = 2^3 [pure_2] 64 Gd 157.2500 HCP 3.6336 12 3.5418e+25 8.4644e-18 4.2928e+07 3 12 = 2^2 * 3 [mixed_ 65 Tb 158.9300 HCP 3.6055 12 3.5796e+25 8.3749e-18 4.3051e+07 3 12 = 2^2 * 3 [mixed_ 66 Dy 162.5000 HCP 3.5915 12 3.6601e+25 8.1909e-18 4.3847e+07 3 12 = 2^2 * 3 [mixed_ 67 Ho 164.9300 HCP 3.5778 12 3.7148e+25 8.0702e-18 4.4333e+07 3 12 = 2^2 * 3 [mixed_ 68 Er 167.2600 HCP 3.5592 12 3.7673e+25 7.9578e-18 4.4726e+07 3 12 = 2^2 * 3 [mixed_ 69 Tm 168.9300 HCP 3.5375 12 3.8049e+25 7.8792e-18 4.4897e+07 3 12 = 2^2 * 3 [mixed_ 70 Yb 173.0500 FCC 5.4848 12 3.8977e+25 7.6916e-18 7.1309e+07 3 12 = 2^2 * 3 [mixed_ 71 Lu 174.9700 HCP 3.5031 12 3.9409e+25 7.6072e-18 4.6050e+07 3 12 = 2^2 * 3 [mixed_ 72 Hf 178.4900 HCP 3.1946 12 4.0202e+25 7.4571e-18 4.2839e+07 3 12 = 2^2 * 3 [mixed_ 73 Ta 180.9500 BCC 3.3013 8 4.0756e+25 7.3558e-18 4.4880e+07 4 8 = 2^3 [pure_2] 74 W 183.8400 BCC 3.1652 8 4.1407e+25 7.2401e-18 4.3717e+07 4 8 = 2^3 [pure_2] 75 Re 186.2100 HCP 2.7609 12 4.1941e+25 7.1480e-18 3.8625e+07 3 12 = 2^2 * 3 [mixed_ 76 Os 190.2300 HCP 2.7344 12 4.2846e+25 6.9969e-18 3.9080e+07 3 12 = 2^2 * 3 [mixed_ 77 Ir 192.2200 FCC 3.8394 12 4.3295e+25 6.9245e-18 5.5447e+07 3 12 = 2^2 * 3 [mixed_ 78 Pt 195.0800 FCC 3.9242 12 4.3939e+25 6.8230e-18 5.7515e+07 3 12 = 2^2 * 3 [mixed_ 79 Au 196.9700 FCC 4.0782 12 4.4364e+25 6.7575e-18 6.0351e+07 3 12 = 2^2 * 3 [mixed_ 80 Hg 200.5900 rhombo 3.0050 6 4.5180e+25 6.6356e-18 4.5286e+07 3 6 = 2 * 3 [mixed_23] 81 Tl 204.3800 HCP 3.4566 12 4.6033e+25 6.5125e-18 5.3076e+07 3 12 = 2^2 * 3 [mixed_ 82 Pb 207.2000 FCC 4.9502 12 4.6669e+25 6.4239e-18 7.7060e+07 3 12 = 2^2 * 3 [mixed_ 83 Bi 208.9800 rhombo 4.5461 3 4.7069e+25 6.3692e-18 7.1377e+07 3 3 = 3 [pure_3] 84 Po 209.0000 SC 3.3590 6 4.7074e+25 6.3685e-18 5.2744e+07 4 6 = 2 * 3 [mixed_23] 85 At 210.0000 unknown N/A N/A 4.7299e+25 6.3382e-18 N/A None N/A 86 Rn 222.0000 FCC 6.1970 12 5.0002e+25 5.9956e-18 1.0336e+08 3 12 = 2^2 * 3 [mixed_ 87 Fr 223.0000 BCC 5.7000 8 5.0227e+25 5.9687e-18 9.5498e+07 4 8 = 2^3 [pure_2] 88 Ra 226.0000 BCC 5.1480 8 5.0903e+25 5.8895e-18 8.7410e+07 4 8 = 2^3 [pure_2] 89 Ac 227.0000 FCC 5.3110 12 5.1128e+25 5.8635e-18 9.0577e+07 3 12 = 2^2 * 3 [mixed_ 90 Th 232.0400 FCC 5.0842 12 5.2263e+25 5.7362e-18 8.8634e+07 3 12 = 2^2 * 3 [mixed_ 91 Pa 231.0400 BCT 3.9250 10 5.2038e+25 5.7610e-18 6.8130e+07 4 10 = 2 * 5 [has_othe 92 U 238.0300 ortho 2.8537 12 5.3613e+25 5.5918e-18 5.1033e+07 None 12 = 2^2 * 3 [mixed_ 93 Np 237.0000 ortho 6.6630 8 5.3381e+25 5.6161e-18 1.1864e+08 None 8 = 2^3 [pure_2] 94 Pu 244.0000 mono 6.1830 16 5.4957e+25 5.4550e-18 1.1335e+08 None 16 = 2^4 [pure_2] 95 Am 243.0000 HCP 3.4681 12 5.4732e+25 5.4775e-18 6.3316e+07 3 12 = 2^2 * 3 [mixed_ 96 Cm 247.0000 HCP 3.4960 12 5.5633e+25 5.3888e-18 6.4876e+07 3 12 = 2^2 * 3 [mixed_ 97 Bk 247.0000 HCP 3.4160 12 5.5633e+25 5.3888e-18 6.3391e+07 3 12 = 2^2 * 3 [mixed_ 98 Cf 251.0000 HCP 3.3800 12 5.6534e+25 5.3029e-18 6.3739e+07 3 12 = 2^2 * 3 [mixed_ 99 Es 252.0000 FCC 5.7500 12 5.6759e+25 5.2818e-18 1.0886e+08 3 12 = 2^2 * 3 [mixed_ 100 Fm 257.0000 unknown N/A N/A 5.7885e+25 5.1791e-18 N/A None N/A 101 Md 258.0000 unknown N/A N/A 5.8110e+25 5.1590e-18 N/A None N/A 102 No 259.0000 unknown N/A N/A 5.8336e+25 5.1391e-18 N/A None N/A 103 Lr 266.0000 unknown N/A N/A 5.9912e+25 5.0039e-18 N/A None N/A 104 Rf 267.0000 unknown N/A N/A 6.0138e+25 4.9851e-18 N/A None N/A 105 Db 268.0000 unknown N/A N/A 6.0363e+25 4.9665e-18 N/A None N/A 106 Sg 269.0000 unknown N/A N/A 6.0588e+25 4.9480e-18 N/A None N/A 107 Bh 270.0000 unknown N/A N/A 6.0813e+25 4.9297e-18 N/A None N/A 108 Hs 277.0000 unknown N/A N/A 6.2390e+25 4.8051e-18 N/A None N/A 109 Mt 278.0000 unknown N/A N/A 6.2615e+25 4.7879e-18 N/A None N/A 110 Ds 281.0000 unknown N/A N/A 6.3291e+25 4.7367e-18 N/A None N/A 111 Rg 282.0000 unknown N/A N/A 6.3516e+25 4.7199e-18 N/A None N/A 112 Cn 285.0000 unknown N/A N/A 6.4192e+25 4.6703e-18 N/A None N/A 113 Nh 286.0000 unknown N/A N/A 6.4417e+25 4.6539e-18 N/A None N/A 114 Fl 289.0000 unknown N/A N/A 6.5093e+25 4.6056e-18 N/A None N/A 115 Mc 290.0000 unknown N/A N/A 6.5318e+25 4.5897e-18 N/A None N/A 116 Lv 293.0000 unknown N/A N/A 6.5994e+25 4.5427e-18 N/A None N/A 117 Ts 294.0000 unknown N/A N/A 6.6219e+25 4.5273e-18 N/A None N/A 118 Og 294.0000 unknown N/A N/A 6.6219e+25 4.5273e-18 N/A None N/A ========================================================================================== SECTION B: SUMMARY STATISTICS ========================================================================================== Crystal structure distribution: HCP: 32 elements FCC: 22 elements unknown: 20 elements BCC: 17 elements ortho: 8 elements rhombo: 6 elements diamond: 3 elements mono: 3 elements BCT: 3 elements SC: 2 elements hex: 2 elements Expected N-match distribution: N= 3: 65 elements N= 4: 22 elements N=None: 31 elements {2,3} cipher classification: mixed_23: 63 elements pure_2: 29 elements unknown: 20 elements pure_3: 4 elements prime: 1 elements has_other: 1 elements Coordination number distribution: CN= 12: 59 elements CN=None: 20 elements CN= 8: 17 elements CN= 2: 8 elements CN= 6: 4 elements CN= 3: 4 elements CN= 4: 3 elements CN= 7: 1 elements CN= 10: 1 elements CN= 16: 1 elements {2,3} factorizability summary: Factorizable (2^a * 3^b): 96 elements Non-factorizable: 2 elements Unknown/trivial (CN=None/0/1): 20 elements TOTAL: 118 elements ========================================================================================== SECTION C: ANOMALIES ========================================================================================== Elements with non-{2,3} coordination numbers: ------------------------------------------------------------ Z= 31 Ga (Gallium ): CN=7, crystal=ortho, 7 = 7 [prime] Z= 91 Pa (Protactinium ): CN=10, crystal=BCT, 10 = 2 * 5 [has_other] Elements with no clear N match (anisotropic structures): ------------------------------------------------------------ Z= 8 O (Oxygen ): crystal=mono, CN=2 Z= 9 F (Fluorine ): crystal=mono, CN=2 Z= 15 P (Phosphorus ): crystal=ortho, CN=3 Z= 16 S (Sulfur ): crystal=ortho, CN=2 Z= 17 Cl (Chlorine ): crystal=ortho, CN=2 Z= 31 Ga (Gallium ): crystal=ortho, CN=7 Z= 35 Br (Bromine ): crystal=ortho, CN=2 Z= 53 I (Iodine ): crystal=ortho, CN=2 Z= 92 U (Uranium ): crystal=ortho, CN=12 Z= 93 Np (Neptunium ): crystal=ortho, CN=8 Z= 94 Pu (Plutonium ): crystal=mono, CN=16 Elements with unknown crystal structure (synthetic/radioactive): ------------------------------------------------------------ Z= 85 At (Astatine ): mass=210.0 amu. Radioactive, extremely short-lived. No crystal structure measured. Predicted FCC Z=100 Fm (Fermium ): mass=257.0 amu. Radioactive, no bulk crystal structure measured. Predicted FCC Z=101 Md (Mendelevium ): mass=258.0 amu. Radioactive, no crystal structure measured Z=102 No (Nobelium ): mass=259.0 amu. Radioactive, no crystal structure measured. Predicted FCC Z=103 Lr (Lawrencium ): mass=266.0 amu. Radioactive, no crystal structure measured. Predicted HCP Z=104 Rf (Rutherfordium ): mass=267.0 amu. Synthetic, t_1/2 ~1.3 h. Predicted HCP (analog Hf) Z=105 Db (Dubnium ): mass=268.0 amu. Synthetic, t_1/2 ~28 h. Predicted BCC (analog Ta) Z=106 Sg (Seaborgium ): mass=269.0 amu. Synthetic, t_1/2 ~14 min. Predicted BCC (analog W) Z=107 Bh (Bohrium ): mass=270.0 amu. Synthetic, t_1/2 ~61 s. Predicted HCP (analog Re) Z=108 Hs (Hassium ): mass=277.0 amu. Synthetic, t_1/2 ~16 s. Predicted HCP (analog Os) Z=109 Mt (Meitnerium ): mass=278.0 amu. Synthetic, t_1/2 ~4.5 s. Predicted FCC (analog Ir) Z=110 Ds (Darmstadtium ): mass=281.0 amu. Synthetic, t_1/2 ~12.7 s. Predicted BCC Z=111 Rg (Roentgenium ): mass=282.0 amu. Synthetic, t_1/2 ~100 s. Predicted FCC (analog Au) Z=112 Cn (Copernicium ): mass=285.0 amu. Synthetic, t_1/2 ~29 s. Predicted to be liquid/gas at STP (relativistic effects) Z=113 Nh (Nihonium ): mass=286.0 amu. Synthetic, t_1/2 ~9.5 s. Predicted HCP (analog Tl) Z=114 Fl (Flerovium ): mass=289.0 amu. Synthetic, t_1/2 ~1.9 s. Predicted FCC or possibly noble-gas-like Z=115 Mc (Moscovium ): mass=290.0 amu. Synthetic, t_1/2 ~0.65 s. Predicted BCC (analog Bi) Z=116 Lv (Livermorium ): mass=293.0 amu. Synthetic, t_1/2 ~60 ms. Predicted SC (analog Po) Z=117 Ts (Tennessine ): mass=294.0 amu. Synthetic, t_1/2 ~78 ms Z=118 Og (Oganesson ): mass=294.0 amu. Synthetic, t_1/2 ~0.7 ms. Predicted solid at STP (relativistic effects). Possibly FCC Elements with unusual coordination: ------------------------------------------------------------ Z= 31 Ga (Gallium ): CN=7, crystal=ortho. Gallium-I, orthorhombic. b=7.6570, c=4.5258. Unique structure Z= 91 Pa (Protactinium ): CN=10, crystal=BCT. Body-centered tetragonal. Radioactive Z= 94 Pu (Plutonium ): CN=16, crystal=mono. alpha-Pu monoclinic (most complex elemental structure, 16 atoms/cell). b=4.822, c=10.963, beta=101.79 ========================================================================================== SECTION D: CROSS-ELEMENT ANALYSIS ========================================================================================== Scale ratios (a/lambda_C) grouped by crystal structure: ---------------------------------------------------------------------- FCC (22 elements): Range: [6.7149e+06, 1.0886e+08] Mean: 4.9035e+07 StdDev: 3.0491e+07 Z= 10 Ne: a=4.4290 A, a/lambda_C = 6.714916e+06 Z= 13 Al: a=4.0495 A, a/lambda_C = 8.208982e+06 Z= 18 Ar: a=5.3111 A, a/lambda_C = 1.594018e+07 Z= 20 Ca: a=5.5884 A, a/lambda_C = 1.682702e+07 Z= 28 Ni: a=3.5240 A, a/lambda_C = 1.553946e+07 Z= 29 Cu: a=3.6149 A, a/lambda_C = 1.725831e+07 Z= 36 Kr: a=5.7210 A, a/lambda_C = 3.601798e+07 Z= 38 Sr: a=6.0849 A, a/lambda_C = 4.005627e+07 Z= 45 Rh: a=3.8034 A, a/lambda_C = 2.940650e+07 Z= 46 Pd: a=3.8907 A, a/lambda_C = 3.110748e+07 Z= 47 Ag: a=4.0862 A, a/lambda_C = 3.311571e+07 Z= 54 Xe: a=6.1970 A, a/lambda_C = 6.112613e+07 Z= 58 Ce: a=5.1610 A, a/lambda_C = 5.433101e+07 Z= 70 Yb: a=5.4848 A, a/lambda_C = 7.130930e+07 Z= 77 Ir: a=3.8394 A, a/lambda_C = 5.544670e+07 Z= 78 Pt: a=3.9242 A, a/lambda_C = 5.751454e+07 Z= 79 Au: a=4.0782 A, a/lambda_C = 6.035071e+07 Z= 82 Pb: a=4.9502 A, a/lambda_C = 7.705951e+07 Z= 86 Rn: a=6.1970 A, a/lambda_C = 1.033590e+08 Z= 89 Ac: a=5.3110 A, a/lambda_C = 9.057658e+07 Z= 90 Th: a=5.0842 A, a/lambda_C = 8.863378e+07 Z= 99 Es: a=5.7500 A, a/lambda_C = 1.088635e+08 BCC (17 elements): Range: [1.8301e+06, 9.5498e+07] Mean: 3.6185e+07 StdDev: 2.6578e+07 Z= 3 Li: a=3.5100 A, a/lambda_C = 1.830123e+06 Z= 11 Na: a=4.2906 A, a/lambda_C = 7.410897e+06 Z= 19 K : a=5.3280 A, a/lambda_C = 1.565066e+07 Z= 23 V : a=3.0240 A, a/lambda_C = 1.157368e+07 Z= 24 Cr: a=2.8839 A, a/lambda_C = 1.126585e+07 Z= 25 Mn: a=8.9125 A, a/lambda_C = 3.678630e+07 Z= 26 Fe: a=2.8665 A, a/lambda_C = 1.202680e+07 Z= 37 Rb: a=5.5850 A, a/lambda_C = 3.586249e+07 Z= 41 Nb: a=3.3004 A, a/lambda_C = 2.303690e+07 Z= 42 Mo: a=3.1470 A, a/lambda_C = 2.268587e+07 Z= 55 Cs: a=6.1410 A, a/lambda_C = 6.132118e+07 Z= 56 Ba: a=5.0280 A, a/lambda_C = 5.187695e+07 Z= 63 Eu: a=4.5827 A, a/lambda_C = 5.231961e+07 Z= 73 Ta: a=3.3013 A, a/lambda_C = 4.488047e+07 Z= 74 W : a=3.1652 A, a/lambda_C = 4.371746e+07 Z= 87 Fr: a=5.7000 A, a/lambda_C = 9.549783e+07 Z= 88 Ra: a=5.1480 A, a/lambda_C = 8.740993e+07 HCP (32 elements): Range: [2.8551e+05, 6.4876e+07] Mean: 3.3230e+07 StdDev: 1.9104e+07 Z= 1 H : a=3.7700 A, a/lambda_C = 2.855063e+05 Z= 2 He: a=3.5700 A, a/lambda_C = 1.073555e+06 Z= 4 Be: a=2.2866 A, a/lambda_C = 1.548228e+06 Z= 12 Mg: a=3.2094 A, a/lambda_C = 5.860481e+06 Z= 21 Sc: a=3.3090 A, a/lambda_C = 1.117630e+07 Z= 22 Ti: a=2.9508 A, a/lambda_C = 1.061182e+07 Z= 27 Co: a=2.5071 A, a/lambda_C = 1.110054e+07 Z= 30 Zn: a=2.6650 A, a/lambda_C = 1.309049e+07 Z= 39 Y : a=3.6482 A, a/lambda_C = 2.436820e+07 Z= 40 Zr: a=3.2316 A, a/lambda_C = 2.214830e+07 Z= 43 Tc: a=2.7350 A, a/lambda_C = 1.993163e+07 Z= 44 Ru: a=2.7059 A, a/lambda_C = 2.054697e+07 Z= 48 Cd: a=2.9793 A, a/lambda_C = 2.516129e+07 Z= 57 La: a=3.7740 A, a/lambda_C = 3.938666e+07 Z= 59 Pr: a=3.6721 A, a/lambda_C = 3.887497e+07 Z= 60 Nd: a=3.6582 A, a/lambda_C = 3.964304e+07 Z= 61 Pm: a=3.6500 A, a/lambda_C = 3.976259e+07 Z= 64 Gd: a=3.6336 A, a/lambda_C = 4.292809e+07 Z= 65 Tb: a=3.6055 A, a/lambda_C = 4.305119e+07 Z= 66 Dy: a=3.5915 A, a/lambda_C = 4.384732e+07 Z= 67 Ho: a=3.5778 A, a/lambda_C = 4.433324e+07 Z= 68 Er: a=3.5592 A, a/lambda_C = 4.472581e+07 Z= 69 Tm: a=3.5375 A, a/lambda_C = 4.489697e+07 Z= 71 Lu: a=3.5031 A, a/lambda_C = 4.605003e+07 Z= 72 Hf: a=3.1946 A, a/lambda_C = 4.283948e+07 Z= 75 Re: a=2.7609 A, a/lambda_C = 3.862491e+07 Z= 76 Os: a=2.7344 A, a/lambda_C = 3.908002e+07 Z= 81 Tl: a=3.4566 A, a/lambda_C = 5.307638e+07 Z= 95 Am: a=3.4681 A, a/lambda_C = 6.331574e+07 Z= 96 Cm: a=3.4960 A, a/lambda_C = 6.487571e+07 Z= 97 Bk: a=3.4160 A, a/lambda_C = 6.339114e+07 Z= 98 Cf: a=3.3800 A, a/lambda_C = 6.373885e+07 diamond (3 elements): Range: [3.2186e+06, 3.0871e+07] Mean: 1.5183e+07 StdDev: 1.1592e+07 Z= 6 C : a=3.5668 A, a/lambda_C = 3.218635e+06 Z= 14 Si: a=5.4310 A, a/lambda_C = 1.145956e+07 Z= 32 Ge: a=5.6575 A, a/lambda_C = 3.087126e+07 SC (2 elements): Range: [5.9573e+06, 5.2744e+07] Mean: 2.9350e+07 StdDev: 2.3393e+07 Z= 7 N : a=5.6610 A, a/lambda_C = 5.957335e+06 Z= 84 Po: a=3.3590 A, a/lambda_C = 5.274364e+07 BCT (3 elements): Range: [2.8056e+07, 6.8130e+07] Mean: 4.9399e+07 StdDev: 1.6464e+07 Z= 49 In: a=3.2523 A, a/lambda_C = 2.805575e+07 Z= 50 Sn: a=5.8318 A, a/lambda_C = 5.201202e+07 Z= 91 Pa: a=3.9250 A, a/lambda_C = 6.813035e+07 rhombo (6 elements): Range: [4.1095e+06, 7.1377e+07] Mean: 3.7057e+07 StdDev: 2.0836e+07 Z= 5 B : a=5.0600 A, a/lambda_C = 4.109509e+06 Z= 33 As: a=3.7598 A, a/lambda_C = 2.116352e+07 Z= 51 Sb: a=4.3084 A, a/lambda_C = 3.941254e+07 Z= 62 Sm: a=3.6290 A, a/lambda_C = 4.099520e+07 Z= 80 Hg: a=3.0050 A, a/lambda_C = 4.528637e+07 Z= 83 Bi: a=4.5461 A, a/lambda_C = 7.137687e+07 hex (2 elements): Range: [2.5905e+07, 4.2729e+07] Mean: 3.4317e+07 StdDev: 8.4121e+06 Z= 34 Se: a=4.3662 A, a/lambda_C = 2.590509e+07 Z= 52 Te: a=4.4572 A, a/lambda_C = 4.272938e+07 ortho (8 elements): Range: [7.7110e+06, 1.1864e+08] Mean: 4.4029e+07 StdDev: 3.3746e+07 Z= 15 P : a=3.3136 A, a/lambda_C = 7.711008e+06 Z= 16 S : a=10.4650 A, a/lambda_C = 2.520673e+07 Z= 17 Cl: a=6.2400 A, a/lambda_C = 1.661937e+07 Z= 31 Ga: a=4.5186 A, a/lambda_C = 2.366975e+07 Z= 35 Br: a=6.6700 A, a/lambda_C = 4.004130e+07 Z= 53 I : a=7.2700 A, a/lambda_C = 6.931222e+07 Z= 92 U : a=2.8537 A, a/lambda_C = 5.103332e+07 Z= 93 Np: a=6.6630 A, a/lambda_C = 1.186402e+08 mono (3 elements): Range: [6.4944e+06, 1.1335e+08] Mean: 4.2563e+07 StdDev: 5.0053e+07 Z= 8 O : a=5.4030 A, a/lambda_C = 6.494438e+06 Z= 9 F : a=5.5000 A, a/lambda_C = 7.850265e+06 Z= 94 Pu: a=6.1830 A, a/lambda_C = 1.133451e+08 Scale ratio trend with Z: ---------------------------------------------------------------------- Elements with known a: 98 Global ratio range: [2.8551e+05, 1.1864e+08] Ratio at Z=1 (H): 2.8551e+05 Ratio at Z=6 (C): 3.2186e+06 Ratio at Z=26 (Fe): 1.2027e+07 Ratio at Z=79 (Au): 6.0351e+07 Mass * lattice_constant product (a * m in A*amu): ---------------------------------------------------------------------- (If decoherence is universal, a*m should be proportional for same crystal type) FCC: Z= 10 Ne: a*m = 4.4290 * 20.180 = 89.38 Z= 13 Al: a*m = 4.0495 * 26.982 = 109.26 Z= 18 Ar: a*m = 5.3111 * 39.948 = 212.17 Z= 20 Ca: a*m = 5.5884 * 40.078 = 223.97 Z= 28 Ni: a*m = 3.5240 * 58.693 = 206.83 Z= 29 Cu: a*m = 3.6149 * 63.546 = 229.71 Z= 36 Kr: a*m = 5.7210 * 83.798 = 479.41 Z= 38 Sr: a*m = 6.0849 * 87.620 = 533.16 Z= 45 Rh: a*m = 3.8034 * 102.910 = 391.41 Z= 46 Pd: a*m = 3.8907 * 106.420 = 414.05 Z= 47 Ag: a*m = 4.0862 * 107.870 = 440.78 Z= 54 Xe: a*m = 6.1970 * 131.290 = 813.60 Z= 58 Ce: a*m = 5.1610 * 140.120 = 723.16 Z= 70 Yb: a*m = 5.4848 * 173.050 = 949.14 Z= 77 Ir: a*m = 3.8394 * 192.220 = 738.01 Z= 78 Pt: a*m = 3.9242 * 195.080 = 765.53 Z= 79 Au: a*m = 4.0782 * 196.970 = 803.28 Z= 82 Pb: a*m = 4.9502 * 207.200 = 1025.68 Z= 86 Rn: a*m = 6.1970 * 222.000 = 1375.73 Z= 89 Ac: a*m = 5.3110 * 227.000 = 1205.60 Z= 90 Th: a*m = 5.0842 * 232.040 = 1179.74 Z= 99 Es: a*m = 5.7500 * 252.000 = 1449.00 Range: [89.38, 1449.00], spread factor: 16.21x BCC: Z= 3 Li: a*m = 3.5100 * 6.940 = 24.36 Z= 11 Na: a*m = 4.2906 * 22.990 = 98.64 Z= 19 K : a*m = 5.3280 * 39.098 = 208.31 Z= 23 V : a*m = 3.0240 * 50.942 = 154.05 Z= 24 Cr: a*m = 2.8839 * 51.996 = 149.95 Z= 25 Mn: a*m = 8.9125 * 54.938 = 489.63 Z= 26 Fe: a*m = 2.8665 * 55.845 = 160.08 Z= 37 Rb: a*m = 5.5850 * 85.468 = 477.34 Z= 41 Nb: a*m = 3.3004 * 92.906 = 306.63 Z= 42 Mo: a*m = 3.1470 * 95.950 = 301.95 Z= 55 Cs: a*m = 6.1410 * 132.910 = 816.20 Z= 56 Ba: a*m = 5.0280 * 137.330 = 690.50 Z= 63 Eu: a*m = 4.5827 * 151.960 = 696.39 Z= 73 Ta: a*m = 3.3013 * 180.950 = 597.37 Z= 74 W : a*m = 3.1652 * 183.840 = 581.89 Z= 87 Fr: a*m = 5.7000 * 223.000 = 1271.10 Z= 88 Ra: a*m = 5.1480 * 226.000 = 1163.45 Range: [24.36, 1271.10], spread factor: 52.18x HCP: Z= 1 H : a*m = 3.7700 * 1.008 = 3.80 Z= 2 He: a*m = 3.5700 * 4.003 = 14.29 Z= 4 Be: a*m = 2.2866 * 9.012 = 20.61 Z= 12 Mg: a*m = 3.2094 * 24.305 = 78.00 Z= 21 Sc: a*m = 3.3090 * 44.956 = 148.76 Z= 22 Ti: a*m = 2.9508 * 47.867 = 141.25 Z= 27 Co: a*m = 2.5071 * 58.933 = 147.75 Z= 30 Zn: a*m = 2.6650 * 65.380 = 174.24 Z= 39 Y : a*m = 3.6482 * 88.906 = 324.35 Z= 40 Zr: a*m = 3.2316 * 91.224 = 294.80 Z= 43 Tc: a*m = 2.7350 * 97.000 = 265.30 Z= 44 Ru: a*m = 2.7059 * 101.070 = 273.49 Z= 48 Cd: a*m = 2.9793 * 112.410 = 334.90 Z= 57 La: a*m = 3.7740 * 138.910 = 524.25 Z= 59 Pr: a*m = 3.6721 * 140.910 = 517.44 Z= 60 Nd: a*m = 3.6582 * 144.240 = 527.66 Z= 61 Pm: a*m = 3.6500 * 145.000 = 529.25 Z= 64 Gd: a*m = 3.6336 * 157.250 = 571.38 Z= 65 Tb: a*m = 3.6055 * 158.930 = 573.02 Z= 66 Dy: a*m = 3.5915 * 162.500 = 583.62 Z= 67 Ho: a*m = 3.5778 * 164.930 = 590.09 Z= 68 Er: a*m = 3.5592 * 167.260 = 595.31 Z= 69 Tm: a*m = 3.5375 * 168.930 = 597.59 Z= 71 Lu: a*m = 3.5031 * 174.970 = 612.94 Z= 72 Hf: a*m = 3.1946 * 178.490 = 570.20 Z= 75 Re: a*m = 2.7609 * 186.210 = 514.11 Z= 76 Os: a*m = 2.7344 * 190.230 = 520.16 Z= 81 Tl: a*m = 3.4566 * 204.380 = 706.46 Z= 95 Am: a*m = 3.4681 * 243.000 = 842.75 Z= 96 Cm: a*m = 3.4960 * 247.000 = 863.51 Z= 97 Bk: a*m = 3.4160 * 247.000 = 843.75 Z= 98 Cf: a*m = 3.3800 * 251.000 = 848.38 Range: [3.80, 863.51], spread factor: 227.23x diamond: Z= 6 C : a*m = 3.5668 * 12.011 = 42.84 Z= 14 Si: a*m = 5.4310 * 28.085 = 152.53 Z= 32 Ge: a*m = 5.6575 * 72.630 = 410.90 Range: [42.84, 410.90], spread factor: 9.59x