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Temperature-electrical domains in metals at low temperatures
Physica 108B ( 1981 } 887-888 North-Holland Publishing Company
N F 16
TEbIPERATUP~E-ELECTRICAL
DO~AINS
A.M.Kadi~robov
IN METALS
AT LOW TEMPERATURES
and A.A.Slutskin
>~ysico-Technical Institute of Low T~mperatures, Academy of Sciences, ~larkov, USSR
UkrSSR
The formation kinetics and the structur~ of moving temperature-electric domains spontaneously arisinF dud to the Joule beatin~ in a metallic rin~ upon t]}e ~xcitation of the el~ctric current in it by the w~ak oscillatin~ marn~t~c fiold ~ave been studied. Th~ influence of various dpfects disturbing the, sample uniformity (such as the nonuniform heat re:~oval) on the kinetics has been investigated. At quit( small uniformity disturbance any initial temperature distribution is s~'own to dev~lop into t~e "cyclic" t~mp~rature-~]ectric domain wbic ~, mov~s at a constant velocity. As the nonuniformity increases the system asymptotically goes into th~ static domain state (the domain "sits down" on th~ defect). Rr-cently it ~as be:~: shown by t'ne aut~ors (I) that in metals the Joul~ heatin~ of the sample st low temperatures may lead to the formation of the N shaped current-voltaFe characteristic and, as 8 result of it, to th~ instability of the uniform el~ctric field distribution and to the spontaneous arising of moving temperature-electric domains. For the situation to srise it is n~c~ssary that the Joul~ heatinff should raise th ,~ sample temperatur~ up to values st which tbp temperature d~pendence of th~ metal conductivity becomes essential. The temperature-electrical instability whicb develops in a thin metallic rin~ located in sn oscillstin~ magnetic field is studied in this work. The structure of "cyclic" temperature-electric domains arising in t~is case for different types of temperature dependence of conductivity is st~,]J~ ]. The spe=d of t!~ moving cyclic domains is shown to be proportional to tbe thermoelectric coefficient. Farameters determining the shape af domains are expressed in terms of conductivity, the beat conduction coefficient and heat removal characteristics. The influenco of various defects, disturbing the sample uniformity(such as the heat removal nonuniformity), on the kinetics of moving temperature-electric domain formation is considered. The investigation is carried out for the case of not so large deviations of temperature distributions and that of the electric field from the uniform one. It seems possible to essentially reduce the description, i.e. to go from the set of nonlinear equations in partial derivatives 03784363/81/0000-0000/$02.50
© North-HollandPublishingCompany
into the sot of two first order conventional differential equations. At quite small disturbances of the sample uniformity any initial temperatur~ distribution (as well as the electric field distribution) is shown to inevitably develop into the "cyclic" temperatureeloctric domain moving at a constant velocity. As th~ nonuniformity increases (the forco of defects) the bifiJrcation occurs: the phase spac~ of initial conditions divides into two regions. From one region of initial conditions the system asymptotically ~oes into the state of s static domain (the domain "connects" with the defect) while from the other one it ~oes into the moving cyclic domain. It is interesting to note that at high enough amplitude of the initial temperature field space c h a n ~ tbe system develops inevitably into the movin~ domain state. The described picture of the temperatur~-electric instability development agrees with the exporimental data. REFERENCES [I] Sluts~in, A.A. and Kadigrobov,A.~., Pis'ma Zh.Eksp.Teor.Fiz, 32 (I978)
363.
887
N F 16
TEbIPERATUP~E-ELECTRICAL
DO~AINS
A.M.Kadi~robov
IN METALS
AT LOW TEMPERATURES
and A.A.Slutskin
>~ysico-Technical Institute of Low T~mperatures, Academy of Sciences, ~larkov, USSR
UkrSSR
The formation kinetics and the structur~ of moving temperature-electric domains spontaneously arisinF dud to the Joule beatin~ in a metallic rin~ upon t]}e ~xcitation of the el~ctric current in it by the w~ak oscillatin~ marn~t~c fiold ~ave been studied. Th~ influence of various dpfects disturbing the, sample uniformity (such as the nonuniform heat re:~oval) on the kinetics has been investigated. At quit( small uniformity disturbance any initial temperature distribution is s~'own to dev~lop into t~e "cyclic" t~mp~rature-~]ectric domain wbic ~, mov~s at a constant velocity. As the nonuniformity increases the system asymptotically goes into th~ static domain state (the domain "sits down" on th~ defect). Rr-cently it ~as be:~: shown by t'ne aut~ors (I) that in metals the Joul~ heatin~ of the sample st low temperatures may lead to the formation of the N shaped current-voltaFe characteristic and, as 8 result of it, to th~ instability of the uniform el~ctric field distribution and to the spontaneous arising of moving temperature-electric domains. For the situation to srise it is n~c~ssary that the Joul~ heatinff should raise th ,~ sample temperatur~ up to values st which tbp temperature d~pendence of th~ metal conductivity becomes essential. The temperature-electrical instability whicb develops in a thin metallic rin~ located in sn oscillstin~ magnetic field is studied in this work. The structure of "cyclic" temperature-electric domains arising in t~is case for different types of temperature dependence of conductivity is st~,]J~ ]. The spe=d of t!~ moving cyclic domains is shown to be proportional to tbe thermoelectric coefficient. Farameters determining the shape af domains are expressed in terms of conductivity, the beat conduction coefficient and heat removal characteristics. The influenco of various defects, disturbing the sample uniformity(such as the heat removal nonuniformity), on the kinetics of moving temperature-electric domain formation is considered. The investigation is carried out for the case of not so large deviations of temperature distributions and that of the electric field from the uniform one. It seems possible to essentially reduce the description, i.e. to go from the set of nonlinear equations in partial derivatives 03784363/81/0000-0000/$02.50
© North-HollandPublishingCompany
into the sot of two first order conventional differential equations. At quite small disturbances of the sample uniformity any initial temperatur~ distribution (as well as the electric field distribution) is shown to inevitably develop into the "cyclic" temperatureeloctric domain moving at a constant velocity. As th~ nonuniformity increases (the forco of defects) the bifiJrcation occurs: the phase spac~ of initial conditions divides into two regions. From one region of initial conditions the system asymptotically ~oes into the state of s static domain (the domain "connects" with the defect) while from the other one it ~oes into the moving cyclic domain. It is interesting to note that at high enough amplitude of the initial temperature field space c h a n ~ tbe system develops inevitably into the movin~ domain state. The described picture of the temperatur~-electric instability development agrees with the exporimental data. REFERENCES [I] Sluts~in, A.A. and Kadigrobov,A.~., Pis'ma Zh.Eksp.Teor.Fiz, 32 (I978)
363.
887