Phonon density of states for GaN

D(ω) [10¹⁵ s/rad m^-3]
	ω [10¹² rad/s]

The density of GaN is 6.15 g/cm³. The mass of an gallium atom plus a nitrogen atom is 83.7297×1.66054×10^-27 kg. The density of GaN pairs is 4.423×10²⁸ 1/m³. Each atom has three degrees of freedom so the integral over all frequencies is 6×4.423×10²⁸ m^-3 = 2.654×10²⁹.

ω [rad/s] D(ω) [s rad^-1m^-3]
1.3977e+11 2.2019e+13 2.7955e+11 1.9711e+13 4.1932e+11 1.7414e+13 5.5910e+11 1.5278e+13 6.9887e+11 1.3455e+13 8.3865e+11 1.2094e+13 9.7842e+11 1.1347e+13 1.1182e+12 1.1363e+13 1.2580e+12 1.2293e+13 1.3977e+12 1.4287e+13 1.5375e+12 1.7497e+13 1.6773e+12 2.2057e+13 1.8171e+12 2.7628e+13 1.9568e+12 3.3317e+13 2.0966e+12 3.8199e+13 2.2364e+12 4.1395e+13 2.3762e+12 4.2781e+13 2.5159e+12 4.2832e+13 2.6557e+12 4.2041e+13 2.7955e+12 4.0899e+13 2.9353e+12 3.9898e+13 3.0750e+12 3.9460e+13 3.2148e+12 3.9499e+13 3.3546e+12 3.9706e+13 3.4944e+12 3.9768e+13 3.6341e+12 3.9482e+13 3.7739e+12 3.9127e+13 3.9137e+12 3.9122e+13 4.0535e+12 3.9885e+13 4.1932e+12 4.1702e+13 4.3330e+12 4.4459e+13 4.4728e+12 4.7967e+13 4.6126e+12 5.2042e+13 4.7523e+12 5.6495e+13 4.8921e+12 6.1142e+13 5.0319e+12 6.5918e+13 5.1717e+12 7.0955e+13 5.3114e+12 7.6402e+13 5.4512e+12 8.2391e+13 5.5910e+12 8.8599e+13 5.7308e+12 9.4206e+13 5.8705e+12 9.8366e+13 6.0103e+12 1.0031e+14 6.1501e+12 1.0036e+14 6.2899e+12 9.9644e+13 6.4296e+12 9.9304e+13 6.5694e+12 1.0037e+14 6.7092e+12 1.0291e+14 6.8490e+12 1.0650e+14 6.9887e+12 1.1070e+14 7.1285e+12 1.1508e+14 7.2683e+12 1.1921e+14 7.4081e+12 1.2278e+14 7.5478e+12 1.2594e+14 7.6876e+12 1.2897e+14 7.8274e+12 1.3216e+14 7.9671e+12 1.3578e+14 8.1069e+12 1.4011e+14 8.2467e+12 1.4521e+14 8.3865e+12 1.5065e+14 8.5262e+12 1.5593e+14 8.6660e+12 1.6055e+14 8.8058e+12 1.6434e+14 8.9456e+12 1.6758e+14 9.0853e+12 1.7059e+14 9.2251e+12 1.7369e+14 9.3649e+12 1.7720e+14 9.5047e+12 1.8143e+14 9.6444e+12 1.8636e+14 9.7842e+12 1.9172e+14 9.9240e+12 1.9724e+14 1.0064e+13 2.0266e+14 1.0204e+13 2.0790e+14 1.0343e+13 2.1302e+14 1.0483e+13 2.1807e+14 1.0623e+13 2.2311e+14 1.0763e+13 2.2818e+14 1.0902e+13 2.3333e+14 1.1042e+13 2.3861e+14 1.1182e+13 2.4404e+14 1.1322e+13 2.4941e+14 1.1462e+13 2.5452e+14 1.1601e+13 2.5912e+14 1.1741e+13 2.6310e+14 1.1881e+13 2.6661e+14 1.2021e+13 2.6983e+14 1.2160e+13 2.7296e+14 1.2300e+13 2.7619e+14 1.2440e+13 2.7969e+14 1.2580e+13 2.8350e+14 1.2719e+13 2.8740e+14 1.2859e+13 2.9115e+14 1.2999e+13 2.9453e+14 1.3139e+13 2.9731e+14 1.3279e+13 2.9934e+14 1.3418e+13 3.0164e+14 1.3558e+13 3.0617e+14 1.3698e+13 3.1490e+14 1.3838e+13 3.2940e+14 1.3977e+13 3.4740e+14 1.4117e+13 3.6465e+14 1.4257e+13 3.7687e+14 1.4397e+13 3.8079e+14 1.4537e+13 3.7883e+14 1.4676e+13 3.7540e+14 1.4816e+13 3.7490e+14 1.4956e+13 3.8173e+14 1.5096e+13 4.0031e+14 1.5235e+13 4.3099e+14 1.5375e+13 4.6239e+14 1.5515e+13 4.8520e+14 1.5655e+13 4.9995e+14 1.5795e+13 5.0863e+14 1.5934e+13 5.1320e+14 1.6074e+13 5.1565e+14 1.6214e+13 5.1792e+14 1.6354e+13 5.2130e+14 1.6493e+13 5.2621e+14 1.6633e+13 5.3300e+14 1.6773e+13 5.4199e+14 1.6913e+13 5.5264e+14 1.7052e+13 5.6368e+14 1.7192e+13 5.7383e+14 1.7332e+13 5.8223e+14 1.7472e+13 5.9290e+14 1.7612e+13 6.1146e+14 1.7751e+13 6.3312e+14 1.7891e+13 6.4922e+14 1.8031e+13 6.5957e+14 1.8171e+13 6.6738e+14 1.8310e+13 6.7584e+14 1.8450e+13 6.8678e+14 1.8590e+13 6.9628e+14 1.8730e+13 7.0085e+14 1.8870e+13 7.0333e+14 1.9009e+13 7.0788e+14 1.9149e+13 7.1868e+14 1.9289e+13 7.3783e+14 1.9429e+13 7.6297e+14 1.9568e+13 7.9109e+14 1.9708e+13 8.1901e+14 1.9848e+13 8.4357e+14 1.9988e+13 8.6165e+14 2.0128e+13 8.7208e+14 2.0267e+13 8.7611e+14 2.0407e+13 8.7692e+14 2.0547e+13 8.7948e+14 2.0687e+13 8.8882e+14 2.0826e+13 9.0939e+14 2.0966e+13 9.3841e+14 2.1106e+13 9.6820e+14 2.1246e+13 9.9095e+14 2.1386e+13 1.0013e+15 2.1525e+13 1.0115e+15 2.1665e+13 1.0380e+15 2.1805e+13 1.0717e+15 2.1945e+13 1.0974e+15 2.2084e+13 1.1135e+15 2.2224e+13 1.1266e+15 2.2364e+13 1.1571e+15 2.2504e+13 1.2134e+15 2.2643e+13 1.2567e+15 2.2783e+13 1.2645e+15 2.2923e+13 1.2790e+15 2.3063e+13 1.3228e+15 2.3203e+13 1.3606e+15 2.3342e+13 1.3778e+15 2.3482e+13 1.4054e+15 2.3622e+13 1.4505e+15 2.3762e+13 1.4820e+15 2.3901e+13 1.4903e+15 2.4041e+13 1.4931e+15 2.4181e+13 1.5126e+15 2.4321e+13 1.5717e+15 2.4461e+13 1.6496e+15 2.4600e+13 1.6963e+15 2.4740e+13 1.7088e+15 2.4880e+13 1.7128e+15 2.5020e+13 1.7220e+15 2.5159e+13 1.7432e+15 2.5299e+13 1.7836e+15 2.5439e+13 1.8457e+15 2.5579e+13 1.9070e+15 2.5719e+13 1.9443e+15 2.5858e+13 1.9693e+15 2.5998e+13 2.0047e+15 2.6138e+13 2.0790e+15 2.6278e+13 2.1985e+15 2.6417e+13 2.3009e+15 2.6557e+13 2.3418e+15 2.6697e+13 2.3452e+15 2.6837e+13 2.3522e+15 2.6976e+13 2.4166e+15 2.7116e+13 2.5389e+15 2.7256e+13 2.6356e+15 2.7396e+13 2.6740e+15 2.7536e+13 2.6941e+15 2.7675e+13 2.7328e+15 2.7815e+13 2.8154e+15 2.7955e+13 2.9152e+15 2.8095e+13 2.9671e+15 2.8234e+13 2.9894e+15 2.8374e+13 3.0558e+15 2.8514e+13 3.1845e+15 2.8654e+13 3.3577e+15 2.8794e+13 3.5321e+15 2.8933e+13 3.6525e+15 2.9073e+13 3.6636e+15 2.9213e+13 3.5565e+15 2.9353e+13 3.5579e+15 2.9492e+13 3.8518e+15 2.9632e+13 4.1469e+15 2.9772e+13 4.1645e+15 2.9912e+13 4.0635e+15 3.0052e+13 4.0563e+15 3.0191e+13 4.2613e+15 3.0331e+13 4.6305e+15 3.0471e+13 4.7964e+15 3.0611e+13 4.6589e+15 3.0750e+13 4.6535e+15 3.0890e+13 4.9384e+15 3.1030e+13 5.2010e+15 3.1170e+13 5.3033e+15 3.1309e+13 5.3550e+15 3.1449e+13 5.4178e+15 3.1589e+13 5.4908e+15 3.1729e+13 5.5641e+15 3.1869e+13 5.6212e+15 3.2008e+13 5.6348e+15 3.2148e+13 5.5772e+15 3.2288e+13 5.4840e+15 3.2428e+13 5.4169e+15 3.2567e+13 5.3734e+15 3.2707e+13 5.3257e+15 3.2847e+13 5.2695e+15 3.2987e+13 5.2089e+15 3.3127e+13 5.1480e+15 3.3266e+13 5.0916e+15 3.3406e+13 5.0462e+15 3.3546e+13 5.0144e+15 3.3686e+13 4.9848e+15 3.3825e+13 4.9485e+15 3.3965e+13 4.9091e+15 3.4105e+13 4.8722e+15 3.4245e+13 4.8430e+15 3.4385e+13 4.8225e+15 3.4524e+13 4.8038e+15 3.4664e+13 4.7832e+15 3.4804e+13 4.7614e+15 3.4944e+13 4.7405e+15 3.5083e+13 4.7235e+15 3.5223e+13 4.7133e+15 3.5363e+13 4.7118e+15 3.5503e+13 4.7019e+15 3.5643e+13 4.6564e+15 3.5782e+13 4.5885e+15 3.5922e+13 4.5330e+15 3.6062e+13 4.4977e+15 3.6202e+13 4.4756e+15 3.6341e+13 4.4557e+15 3.6481e+13 4.4277e+15 3.6621e+13 4.3946e+15 3.6761e+13 4.3630e+15 3.6900e+13 4.3327e+15 3.7040e+13 4.3026e+15 3.7180e+13 4.2742e+15 3.7320e+13 4.2499e+15 3.7460e+13 4.2318e+15 3.7599e+13 4.2204e+15 3.7739e+13 4.2131e+15 3.7879e+13 4.2066e+15 3.8019e+13 4.1984e+15 3.8158e+13 4.1857e+15 3.8298e+13 4.1660e+15 3.8438e+13 4.1437e+15 3.8578e+13 4.1307e+15 3.8718e+13 4.1228e+15 3.8857e+13 4.0998e+15 3.8997e+13 4.0659e+15 3.9137e+13 4.0448e+15 3.9277e+13 4.0376e+15 3.9416e+13 4.0299e+15 3.9556e+13 4.0186e+15 3.9696e+13 4.0071e+15 3.9836e+13 3.9973e+15 3.9976e+13 3.9904e+15 4.0115e+13 3.9854e+15 4.0255e+13 3.9812e+15 4.0395e+13 3.9763e+15 4.0535e+13 3.9698e+15 4.0674e+13 3.9632e+15 4.0814e+13 3.9581e+15 4.0954e+13 3.9564e+15 4.1094e+13 3.9576e+15 4.1233e+13 3.9552e+15 4.1373e+13 3.9455e+15 4.1513e+13 3.9326e+15 4.1653e+13 3.9153e+15 4.1793e+13 3.8820e+15 4.1932e+13 3.8370e+15 4.2072e+13 3.8073e+15 4.2212e+13 3.7753e+15 4.2352e+13 3.6748e+15 4.2491e+13 3.5553e+15 4.2631e+13 3.5685e+15 4.2771e+13 3.6644e+15 4.2911e+13 3.6454e+15 4.3051e+13 3.5030e+15 4.3190e+13 3.3470e+15 4.3330e+13 3.2164e+15 4.3470e+13 3.1110e+15 4.3610e+13 3.0300e+15 4.3749e+13 2.9713e+15 4.3889e+13 2.9246e+15 4.4029e+13 2.8800e+15 4.4169e+13 2.8421e+15 4.4309e+13 2.8173e+15 4.4448e+13 2.8020e+15 4.4588e+13 2.7913e+15 4.4728e+13 2.7817e+15 4.4868e+13 2.7717e+15 4.5007e+13 2.7638e+15 4.5147e+13 2.7610e+15 4.5287e+13 2.7661e+15 4.5427e+13 2.7750e+15 4.5566e+13 2.7715e+15 4.5706e+13 2.7389e+15 4.5846e+13 2.6616e+15 4.5986e+13 2.5614e+15 4.6126e+13 2.4981e+15 4.6265e+13 2.4743e+15 4.6405e+13 2.4427e+15 4.6545e+13 2.3869e+15 4.6685e+13 2.3166e+15 4.6824e+13 2.2560e+15 4.6964e+13 2.2338e+15 4.7104e+13 2.2436e+15 4.7244e+13 2.2636e+15 4.7384e+13 2.2875e+15 4.7523e+13 2.3149e+15 4.7663e+13 2.3454e+15 4.7803e+13 2.3779e+15 4.7943e+13 2.4070e+15 4.8082e+13 2.4272e+15 4.8222e+13 2.4347e+15 4.8362e+13 2.4261e+15 4.8502e+13 2.3984e+15 4.8642e+13 2.3650e+15 4.8781e+13 2.3763e+15 4.8921e+13 2.4378e+15 4.9061e+13 2.4658e+15 4.9201e+13 2.4167e+15 4.9340e+13 2.3206e+15 4.9480e+13 2.2137e+15 4.9620e+13 2.1312e+15 4.9760e+13 2.0850e+15 4.9900e+13 2.0629e+15 5.0039e+13 2.0517e+15 5.0179e+13 2.0389e+15 5.0319e+13 2.0219e+15 5.0459e+13 2.0043e+15 5.0598e+13 1.9903e+15 5.0738e+13 1.9823e+15 5.0878e+13 1.9723e+15 5.1018e+13 1.9471e+15 5.1157e+13 1.8935e+15 5.1297e+13 1.8076e+15 5.1437e+13 1.7292e+15 5.1577e+13 1.6937e+15 5.1717e+13 1.6669e+15 5.1856e+13 1.6157e+15 5.1996e+13 1.5639e+15 5.2136e+13 1.5361e+15 5.2276e+13 1.5293e+15 5.2415e+13 1.5366e+15 5.2555e+13 1.5508e+15 5.2695e+13 1.5650e+15 5.2835e+13 1.5721e+15 5.2975e+13 1.5715e+15 5.3114e+13 1.5707e+15 5.3254e+13 1.5715e+15 5.3394e+13 1.5683e+15 5.3534e+13 1.5669e+15 5.3673e+13 1.5829e+15 5.3813e+13 1.6169e+15 5.3953e+13 1.6581e+15 5.4093e+13 1.6995e+15 5.4233e+13 1.7382e+15 5.4372e+13 1.7803e+15 5.4512e+13 1.8338e+15 5.4652e+13 1.8843e+15 5.4792e+13 1.9122e+15 5.4931e+13 1.9229e+15 5.5071e+13 1.9306e+15 5.5211e+13 1.9494e+15 5.5351e+13 1.9876e+15 5.5490e+13 2.0326e+15 5.5630e+13 2.0712e+15 5.5770e+13 2.1030e+15 5.5910e+13 2.1296e+15 5.6050e+13 2.1531e+15 5.6189e+13 2.1959e+15 5.6329e+13 2.3193e+15 5.6469e+13 2.5177e+15 5.6609e+13 2.6764e+15 5.6748e+13 2.7612e+15 5.6888e+13 2.8525e+15 5.7028e+13 2.9975e+15 5.7168e+13 3.1995e+15 5.7308e+13 3.4524e+15 5.7447e+13 3.7400e+15 5.7587e+13 3.9980e+15 5.7727e+13 4.1373e+15 5.7867e+13 4.1732e+15 5.8006e+13 4.1782e+15 5.8146e+13 4.1762e+15 5.8286e+13 4.1673e+15 5.8426e+13 4.1511e+15 5.8566e+13 4.1274e+15 5.8705e+13 4.0960e+15 5.8845e+13 4.0571e+15 5.8985e+13 4.0132e+15 5.9125e+13 3.9687e+15 5.9264e+13 3.9324e+15 5.9404e+13 3.9056e+15 5.9544e+13 3.8665e+15 5.9684e+13 3.8093e+15 5.9823e+13 3.7701e+15 5.9963e+13 3.6993e+15 6.0103e+13 3.3891e+15 6.0243e+13 2.8403e+15 6.0383e+13 2.3767e+15 6.0522e+13 2.1376e+15 6.0662e+13 2.0107e+15 6.0802e+13 1.9211e+15 6.0942e+13 1.8468e+15 6.1081e+13 1.7720e+15 6.1221e+13 1.6837e+15 6.1361e+13 1.5691e+15 6.1501e+13 1.4203e+15 6.1641e+13 1.2757e+15 6.1780e+13 1.1915e+15 6.1920e+13 1.1622e+15 6.2060e+13 1.1546e+15 6.2200e+13 1.1354e+15 6.2339e+13 1.0807e+15 6.2479e+13 1.0130e+15 6.2619e+13 9.6076e+14 6.2759e+13 9.2368e+14 6.2899e+13 8.9451e+14 6.3038e+13 8.6602e+14 6.3178e+13 8.3099e+14 6.3318e+13 7.8222e+14 6.3458e+13 7.1971e+14 6.3597e+13 6.5787e+14 6.3737e+13 6.0655e+14 6.3877e+13 5.6513e+14 6.4017e+13 5.3202e+14 6.4157e+13 5.0561e+14 6.4296e+13 4.8379e+14 6.4436e+13 4.6393e+14 6.4576e+13 4.4333e+14 6.4716e+13 4.1934e+14 6.4855e+13 3.8927e+14 6.4995e+13 3.5088e+14 6.5135e+13 3.0680e+14 6.5275e+13 2.6274e+14 6.5414e+13 2.2447e+14 6.5554e+13 1.9545e+14 6.5694e+13 1.6335e+14 6.5834e+13 1.1415e+14 6.5974e+13 6.1128e+13 6.6113e+13 2.2742e+13 6.6253e+13 0.0000 6.6393e+13 0.0000 6.6533e+13 0.0000 6.6672e+13 0.0000 6.6812e+13 0.0000 6.6952e+13 0.0000 6.7092e+13 1.5723e+12 6.7232e+13 6.4294e+12 6.7371e+13 9.6369e+12 6.7511e+13 1.1414e+13 6.7651e+13 1.1979e+13 6.7791e+13 1.1553e+13 6.7930e+13 1.0353e+13 6.8070e+13 8.6000e+12 6.8210e+13 6.5122e+12 6.8350e+13 4.3091e+12 6.8490e+13 2.2101e+12 6.8629e+13 4.3397e+11 6.8769e+13 0.0000 6.8909e+13 0.0000 6.9049e+13 0.0000 6.9188e+13 0.0000 6.9328e+13 0.0000 6.9468e+13 0.0000 6.9608e+13 0.0000 6.9747e+13 0.0000 6.9887e+13 3.2700e+11 7.0027e+13 5.2759e+11 7.0167e+13 6.2054e+11 7.0307e+13 6.2628e+11 7.0446e+13 5.6511e+11 7.0586e+13 4.5763e+11 7.0726e+13 3.2429e+11 7.0866e+13 1.8555e+11 7.1005e+13 6.1682e+10 7.1145e+13 0.0000 7.1285e+13 0.0000 7.1425e+13 0.0000 7.1565e+13 0.0000 7.1704e+13 0.0000 7.1844e+13 0.0000 7.1984e+13 1.2843e+10 7.2124e+13 2.7208e+10 7.2263e+13 3.3122e+10 7.2403e+13 3.2615e+10 7.2543e+13 2.7377e+10 7.2683e+13 1.9096e+10 7.2823e+13 9.8015e+9 7.2962e+13 1.0139e+9 7.3102e+13 0.0000 7.3242e+13 0.0000 7.3382e+13 0.0000 7.3521e+13 0.0000 7.3661e+13 0.0000 7.3801e+13 0.0000 7.3941e+13 0.0000 7.4081e+13 0.0000 7.4220e+13 0.0000 7.4360e+13 6.7596e+8 7.4500e+13 2.7039e+9 7.4640e+13 4.3938e+9 7.4779e+13 5.5767e+9 7.4919e+13 6.0837e+9 7.5059e+13 6.0837e+9 7.5199e+13 5.7457e+9 7.5338e+13 4.5628e+9 7.5478e+13 3.0418e+9 7.5618e+13 1.0139e+9 7.5758e+13 0.0000 7.5898e+13 0.0000 7.6037e+13 0.0000 7.6177e+13 0.0000 7.6317e+13 0.0000 7.6457e+13 0.0000 7.6596e+13 0.0000 7.6736e+13 0.0000 7.6876e+13 7.4356e+9 7.7016e+13 1.6223e+10 7.7156e+13 2.2476e+10 7.7295e+13 2.3321e+10 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