[Pw_forum] question about the negative frequency of phonon
Shaorui Sun
sunsr at ihep.ac.cn
Fri Jan 7 08:07:18 CET 2005
Dear all:
I have calculated the phonon at Gamma point of ZnO with hexgonal structure under ambient condition.I find some modes with negative frequency as follows:
**************************************************************************
omega( 1) = -6.023360 [THz] = -200.919008 [cm-1]
( -0.000260 0.000000 -0.000147 0.000000 0.330600 0.000000 )
( 0.000256 0.000000 0.000145 0.000000 0.330106 0.000000 )
( 0.000292 0.000000 0.000182 0.000000 0.627531 0.000000 )
( -0.000289 0.000000 -0.000180 0.000000 0.622846 0.000000 )
omega( 2) = -0.299189 [THz] = -9.979948 [cm-1]
( -0.417072 0.000000 -0.241569 0.000000 -0.000508 0.000000 )
( 0.469981 0.000000 0.271913 0.000000 -0.000476 0.000000 )
( 0.450138 0.000000 0.260507 0.000000 -0.000209 0.000000 )
( -0.389246 0.000000 -0.225555 0.000000 -0.000180 0.000000 )
omega( 3) = 0.275355 [THz] = 9.184911 [cm-1]
( 0.237017 0.000000 -0.409752 0.000000 0.000011 0.000000 )
( -0.276542 0.000000 0.477420 0.000000 -0.000009 0.000000 )
( -0.264391 0.000000 0.456506 0.000000 -0.000002 0.000000 )
( 0.220039 0.000000 -0.380530 0.000000 0.000001 0.000000 )
omega( 4) = 1.100562 [THz] = 36.711029 [cm-1]
( 0.279712 0.000000 -0.456681 0.000000 -0.000118 0.000000 )
( 0.237728 0.000000 -0.387807 0.000000 0.000120 0.000000 )
( 0.244071 0.000000 -0.398114 0.000000 0.000013 0.000000 )
( 0.280438 0.000000 -0.457804 0.000000 -0.000013 0.000000 )
omega( 5) = 1.170953 [THz] = 39.059037 [cm-1]
( -0.450273 0.000000 -0.275967 0.000000 0.000207 0.000000 )
( -0.396246 0.000000 -0.242718 0.000000 -0.000272 0.000000 )
( -0.405025 0.000000 -0.248069 0.000000 0.000257 0.000000 )
( -0.450841 0.000000 -0.276283 0.000000 -0.000281 0.000000 )
omega( 6) = 6.662384 [THz] = 222.234680 [cm-1]
( -0.000176 0.000000 0.000057 0.000000 -0.602850 0.000000 )
( -0.000171 0.000000 0.000061 0.000000 0.606833 0.000000 )
( -0.000777 0.000000 -0.000465 0.000000 -0.368226 0.000000 )
( -0.000772 0.000000 -0.000464 0.000000 0.364325 0.000000 )
omega( 7) = 10.028040 [THz] = 334.501631 [cm-1]
( -0.000227 0.000000 -0.000147 0.000000 0.299125 0.000000 )
( 0.000239 0.000000 0.000152 0.000000 0.295094 0.000000 )
( -0.000184 0.000000 -0.000172 0.000000 -0.645232 0.000000 )
( 0.000136 0.000000 0.000148 0.000000 -0.638059 0.000000 )
omega( 8) = 11.000946 [THz] = 366.954510 [cm-1]
( -0.117921 0.000000 0.118231 0.000000 -0.000089 0.000000 )
( -0.122596 0.000000 0.122893 0.000000 0.000096 0.000000 )
( 0.490765 0.000000 -0.491427 0.000000 0.000517 0.000000 )
( 0.479041 0.000000 -0.479741 0.000000 -0.000537 0.000000 )
omega( 9) = 11.004772 [THz] = 367.082115 [cm-1]
( -0.117814 0.000000 -0.117740 0.000000 -0.000393 0.000000 )
( -0.122545 0.000000 -0.122442 0.000000 0.000417 0.000000 )
( 0.491707 0.000000 0.490773 0.000000 0.001216 0.000000 )
( 0.479808 0.000000 0.478952 0.000000 -0.001280 0.000000 )
omega(10) = 13.060803 [THz] = 435.664405 [cm-1]
( 0.130505 0.000000 0.094044 0.000000 0.000121 0.000000 )
( -0.128151 0.000000 -0.092347 0.000000 0.000102 0.000000 )
( 0.550546 0.000000 0.396919 0.000000 -0.000356 0.000000 )
( -0.566967 0.000000 -0.408750 0.000000 -0.000262 0.000000 )
omega(11) = 13.078335 [THz] = 436.249187 [cm-1]
( 0.093791 0.000000 -0.130068 0.000000 -0.000002 0.000000 )
( -0.092121 0.000000 0.127752 0.000000 -0.000005 0.000000 )
( 0.397022 0.000000 -0.550781 0.000000 0.000006 0.000000 )
( -0.408702 0.000000 0.566970 0.000000 0.000028 0.000000 )
omega(12) = 14.976799 [THz] = 499.575570 [cm-1]
( -0.000317 0.000000 -0.000169 0.000000 0.102943 0.000000 )
( -0.000309 0.000000 -0.000166 0.000000 -0.104318 0.000000 )
( 0.001156 0.000000 0.000475 0.000000 -0.695521 0.000000 )
( 0.001206 0.000000 0.000497 0.000000 0.703397 0.000000 )
**************************************************************************
Who could tell what is the meaning of the negative frequency of the first two modes for the system with stable state?
Best Regards!
S. R. Sun
---------------------------------------------
Beijing Synchrotron Radiation Facility
Institute of High Energy Physics
Chinese Academy of Sciences
P. O. Box 918, 100049 Beijing
P. R. China
Tel: 0086+10 88236710
email:sunsr at ihep.ac.cn
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