Output File

LANL RPRcode Ver. 6.0
Sample Isotropic
free moduli are c11, c44
using 12 order polynomials mass= 1.3396 gm rho=15.467 gm/cc

n fex fr %err wt k i df/d(moduli)
1 0.089937 0.089652 -0.32 1.00 4 1 0.00 1.00
2 0.122485 0.122452 -0.03 0.00 4 2 0.00 1.00
3 0.123037 0.122865 -0.14 1.00 7 2 0.06 0.94
4 0.133300 0.133424 0.09 1.00 2 2 0.02 0.98
5 0.136562 0.136834 0.20 1.00 1 2 0.14 0.86
6 0.140502 0.140666 0.12 1.00 6 2 0.13 0.87
7 0.144324 0.144503 0.12 1.00 7 3 0.41 0.59
8 0.000000 0.149675 0.00 0.00 8 2 0.01 0.99
9 0.150841 0.150817 -0.02 1.00 3 2 0.01 0.99
10 0.150964 0.151325 0.24 1.00 5 1 0.00 1.00
11 0.162553 0.162600 0.03 1.00 5 2 0.07 0.93
12 0.163018 0.163070 0.03 1.00 3 3 0.17 0.83
13 0.164211 0.164305 0.06 1.00 8 3 0.17 0.83
14 0.171321 0.171782 0.27 1.00 5 3 0.09 0.91
15 0.190858 0.190920 0.03 1.00 1 3 0.26 0.74
16 0.191871 0.191886 0.01 1.00 6 3 0.26 0.74
17 0.194339 0.194121 -0.11 1.00 3 4 0.03 0.97
18 0.197951 0.197765 -0.09 1.00 8 4 0.03 0.97
19 0.198913 0.198762 -0.08 1.00 2 3 0.18 0.82
20 0.200511 0.200241 -0.13 1.00 5 4 0.38 0.62
21 0.203233 0.203585 0.17 1.00 4 3 0.07 0.93
22 0.207026 0.206429 -0.29 1.00 7 4 0.13 0.87
23 0.207831 0.207623 -0.10 1.00 5 5 0.39 0.61
24 0.209198 0.209190 0.00 1.00 6 4 0.05 0.95
25 0.209741 0.209538 -0.10 1.00 1 4 0.05 0.95

For a useful fit, the following must be true:

1. The fit must be predictive – if a mode is missing, and the code predicts it is there, one may be able to find it by re-measuring, or remounting the sample.
2. The RMS error should be below 0.8%, often below 0.2% – sometimes as low as 0.03%.
3. "chisquare increased 2% by the..." must be small – the largest number in the first column below "chisquare..." is computed from the effective curvature of the minimum in elastic-modulus space for c11, the next column for the next free modulus (in this case c44) etc. The largest number in each column represents a real-world measure of the accuracy of the measurement tested by much experience – the accuracy is very definitely not the rms error.
4. There must be many modes that are not pure shear. Note that the first mode is pure shear (df/dmoduli is 0. for c11 and 1.00 for c44 – again, these derivatives are in order of the free moduli, just as are the chisquare columns). But the 7th mode is 41% c11, so it provides a strong constraint for c11. Typically, one must use 40 modes for orthorhombic symmetry, but maybe only 15 for isotropic.
5. The Q of the modes must be high-of order a few hundred and up – we have observed a Q of 1.5x106 for diamond.

For more information, contact Albert Migliori at Los Alamos National Laboratory.