Phonon density of states of a fcc crystal

Student Project by Christian Neubauer and Gernot Kraberger (2010)

The form below generates a table of where the first column is the angular frequency ω in rad/s and the second column is the density of states D(ω) in units of s/(rad m³).

D(ω) [10¹⁵ s/(rad m³)]
	ω [10¹² rad/s]

Mass: m =	[10^-24 kg]
Spring constant: C =	[N/m]
Lattice constant: a =	[Ångström]

1.2552409e-002	9.0571710e-001
2.5890500e-002	3.3209627e+000
3.9228591e-002	7.6684048e+000
5.2566682e-002	1.2015847e+001
6.5904772e-002	1.8838916e+001
7.9242863e-002	2.6929988e+001
9.2580954e-002	3.6772114e+001
1.0591904e-001	4.6674621e+001
1.1925714e-001	5.9173517e+001
1.3259523e-001	7.2457368e+001
1.4593332e-001	8.5016645e+001
1.5927141e-001	1.0107803e+002
1.7260950e-001	1.1786399e+002
1.8594759e-001	1.3754824e+002
1.9928568e-001	1.5753439e+002
2.1262377e-001	1.8283409e+002
2.2596186e-001	2.0571854e+002
2.3929995e-001	2.3144091e+002
2.5263804e-001	2.5764632e+002
2.6597613e-001	2.8844071e+002
2.7931422e-001	3.1615565e+002
2.9265232e-001	3.4839918e+002
3.0599041e-001	3.8414481e+002
3.1932850e-001	4.1983007e+002
3.3266659e-001	4.5442846e+002
3.4600468e-001	4.9482344e+002
3.5934277e-001	5.3624491e+002
3.7268086e-001	5.8430829e+002
3.8601895e-001	6.2977529e+002
3.9935704e-001	6.7548381e+002
4.1269513e-001	7.2910227e+002
4.2603322e-001	7.8628321e+002
4.3937131e-001	8.3380316e+002
4.5270940e-001	8.9080296e+002
4.6604750e-001	9.5921479e+002
4.7938559e-001	1.0171203e+003
4.9272368e-001	1.0800978e+003
5.0606177e-001	1.1481474e+003
5.1939986e-001	1.2084681e+003
5.3273795e-001	1.2778461e+003
5.4607604e-001	1.3521149e+003
5.5941413e-001	1.4263233e+003
5.7275222e-001	1.5051207e+003
5.8609031e-001	1.5997379e+003
5.9942840e-001	1.6871698e+003
6.1276649e-001	1.7797341e+003
6.2610458e-001	1.8770081e+003
6.3944268e-001	1.9811656e+003
6.5278077e-001	2.0862288e+003
6.6611886e-001	2.1964244e+003
6.7945695e-001	2.3160998e+003
6.9279504e-001	2.4369828e+003
7.0613313e-001	2.5665607e+003
7.1947122e-001	2.6952330e+003
7.3280931e-001	2.8309698e+003
7.4614740e-001	2.9719597e+003
7.5948549e-001	3.1319697e+003
7.7282358e-001	3.2969914e+003
7.8616167e-001	3.4776518e+003
7.9949976e-001	3.6561988e+003
8.1283786e-001	3.8530413e+003
8.2617595e-001	4.0464421e+003
8.3951404e-001	4.2603725e+003
8.5285213e-001	4.4855338e+003
8.6619022e-001	4.7329153e+003
8.7952831e-001	5.0013095e+003
8.9286640e-001	5.2983243e+003
9.0620449e-001	5.6059662e+003
9.1954258e-001	5.9387870e+003
9.3288067e-001	6.3232338e+003
9.4621876e-001	6.7412524e+003
9.5955685e-001	7.2148821e+003
9.7289494e-001	7.9228509e+003
9.8623304e-001	8.6755018e+003
9.9957113e-001	9.3313014e+003
1.0129092e+000	9.9325768e+003
1.0262473e+000	1.0416592e+004
1.0395854e+000	1.0616212e+004
1.0529235e+000	1.0712641e+004
1.0662616e+000	1.0838898e+004
1.0795997e+000	1.0929590e+004
1.0929378e+000	1.1029521e+004
1.1062759e+000	1.1153182e+004
1.1196139e+000	1.1293266e+004
1.1329520e+000	1.1391204e+004
1.1462901e+000	1.1519272e+004
1.1596282e+000	1.1627234e+004
1.1729663e+000	1.1731935e+004
1.1863044e+000	1.1822929e+004
1.1996425e+000	1.1923584e+004
1.2129806e+000	1.2030399e+004
1.2263187e+000	1.2153455e+004
1.2396568e+000	1.2237506e+004
1.2529949e+000	1.2352291e+004
1.2663329e+000	1.2465686e+004
1.2796710e+000	1.2546778e+004
1.2930091e+000	1.2621168e+004
1.3063472e+000	1.2733054e+004
1.3196853e+000	1.2852971e+004
1.3330234e+000	1.2957612e+004
1.3463615e+000	1.3086404e+004
1.3596996e+000	1.3220209e+004
1.3730377e+000	1.3331733e+004
1.3863758e+000	1.2936599e+004
1.3997138e+000	1.1871536e+004
1.4130519e+000	1.0772901e+004
1.4263900e+000	9.6454041e+003
1.4397281e+000	8.5061327e+003
1.4530662e+000	7.8124138e+003
1.4664043e+000	7.7811364e+003
1.4797424e+000	7.7503420e+003
1.4930805e+000	7.7246196e+003
1.5064186e+000	7.7177362e+003
1.5197567e+000	7.6964216e+003
1.5330948e+000	7.6812660e+003
1.5464328e+000	7.6342894e+003
1.5597709e+000	7.5990872e+003
1.5731090e+000	7.5323057e+003
1.5864471e+000	7.4499458e+003
1.5997852e+000	7.3569589e+003
1.6131233e+000	7.2649380e+003
1.6264614e+000	7.1418813e+003
1.6397995e+000	6.9885132e+003
1.6531376e+000	6.8027204e+003
1.6664757e+000	6.5884277e+003
1.6798138e+000	6.3283662e+003
1.6931518e+000	5.9750761e+003
1.7064899e+000	5.6249259e+003
1.7198280e+000	5.6507086e+003
1.7331661e+000	6.1446867e+003
1.7465042e+000	7.3063595e+003
1.7598423e+000	8.8251867e+003
1.7731804e+000	1.0567243e+004
1.7865185e+000	1.2194937e+004
1.7998566e+000	1.3586541e+004
1.8131947e+000	1.4608372e+004
1.8265328e+000	1.5543192e+004
1.8398708e+000	1.6504762e+004
1.8532089e+000	1.6655836e+004
1.8665470e+000	1.6036385e+004
1.8798851e+000	1.4851587e+004
1.8932232e+000	1.3235969e+004
1.9065613e+000	1.1158133e+004
1.9198994e+000	9.4704195e+003
1.9332375e+000	8.1529031e+003
1.9465756e+000	6.9346532e+003
1.9599137e+000	5.7047497e+003
1.9732518e+000	4.2469679e+003
1.9865898e+000	2.8392218e+003
1.9999279e+000	7.4661280e+002
1.9999279e+000	0
2.1	0

The Matlab files used to calculate the data are base.m, kvals.m, disp_solver.m and analy.m.

The density of states can be used to calculate the temperature dependence of thermodynamic quantities.