We report measurements of the frequency-dependent dielectric constant of UO2 from 4.2 K to above the phase transition at 30 K. The static dielectric constant of 23.6 at 4.2 K is comparable with accepted values at higher temperatures: it is essentially identical in both phases. The effects of undergoing the transition on the dielectric constant are marginal (about 1%) and take place in the temperature range 29 K to 37 K. The displacement of the oxygen sublattice, which occurs at the Ne´el point, should produce only a 0.05% change on the dielectric constant and of the opposite sense to that measured. Hence the structural changes at the transition are not the primary source of the observed small difference between the dielectric constant in the two phases which probably accrues from the influence of the displacements on a defect-related contribution

Hampton, N

Harding, JH

Saunders, GA

Stoneham, AM

English

UCL Discovery

18  Journal  of  iJuclear  Materials  149  (1987)  18-20 North-~oliand.  Amsterdam THE DIELECTRIC CONSTANT  OF U02  BELOW  THE N&EL POINT N.  HAMPTON  and  G.A.  SAUNDERS School  of Physics,  lJniuersity  of  Bath,  Claverton  Down,  Bath.  BAZ  7A Y,  United  Kingdom J.H.  HARDING  and  A.M.  STONEHAM Theoretical  Ph_vsics Diuision,  A ERE  Harwell.  Didcot,  Uxon,  OXI  I  ORA,  kited  Kingdom Received  16  December  1986;  accepted  7  January  1987 We  report  measurements  of  the  frequency-dependent  dielectric  constant  of  UO,  from  4.2  K  to  above  the  phase  transition  at 30  K.  The  static  dielectric  constant  of  23.6  at  4.2  K  is  comparable  with  accepted  values  at  higher  temperatures:  it  is essentially identical  in  both  phases.  The  effects  of  undergoing  the  transition  on  the  dielectric  constant  are  marginal  (about  1 I%) and  take place  in  the  temperature  range  29  K  to  37  K.  The  displacement  of  the  oxygen  sublattice,  which  occurs  at  the  Ntel  point, should  produce  only  a  0.05%  change  on  the  dielectric  constant  and  of  the  opposite  sense  to  that  measured.  Hence  the structural  changes  at  the  transition  are  not  the  primary  source  of  the  observed  small  difference  between  the  dielectric  constant in  the  two  phases  which  probably  accrues  from  the  influence  of  the  displacements  on  a  defect-related  contribution. 1. The  phase transition  in UO, Uranium  dioxide  UO,  undergoes  a  phase  transition at  about  30  K  first  detected  by  a  X-type  feature  in  the specific  heat  [l].  Magnetic  susceptibility  [2-41  and  neu- tron  diffraction  studies  [5] have  indicated  that  the  tran- sition  is  from  a high  temperature  paramagnetic  to  a  low temperature  antiferromagnetic  state.  In  the  para- magnetic  state  the  crystal  structure  is  fee  (fluorite). Below  the  transition  there  is a small  shift  ( -  0.014  A)  of the  oxygen  atoms  from  the  fluorite  structure  positions [6],  the  magnetic  structure  comprising  ferromagnetic (001)  planes  stacked  in  an  alternating  plus-minus  se- quence  (51. The  magnetisation  changes  abruptly  at  the Neel  temperature  [5,7]:  the  transition  is  first  order.  At the  transition  there  is  a  rather  abrupt  change  in  length of  about  20  ppm  and  the  length  continues  to  decrease rapidly  as  the  temperature  is  further  reduced  [8].  The volume  change  at  the  transition  is  consistent  with  its first  order  character.  Little  is  known  about  the  electrical properties  of  the  low  temperature  phase.  The  present objective  has  been  to  measure  the  dielectric  constant  of UO,  (below  77  K)  in  both  phases  to  ascertain  the  effect of  the  phase  transition  on  this  property.  A  theoretical estimate  has  also  been  made  to  establish  whether  the structural  change  could  produce  a  significant  effect  on the  dielectric  constant. 2.  Measurements  of dielectric  constant The  dielectric  constant  has  been  obtained  from  im- pedance  measurements  made  by  an  AC  bridge  tech- nique  on  a  single  crystal  plate  of  UO,  with  evaporated aluminium  electrodes.  Recent  work  [9]  has  identified  a boundary  layer  existing  in  conjunction  with  the  bulk material  for  such  plate  geometry  samples.  The  boundary layer  has  been  found,  using  impedance  plane  tech- niques,  to  dominate  the  dielectric  properties  at  mod- erate  temperatures  (300  K)  but  its  effects  become  in- creasingly  less  important  at  lower  temperatures.  Below 77  K  the  complex  plane  profiles  show  no  further  evi- dence  of  any  influence  due  to  the  boundary  layer.  Thus at  lower  temperatures  the  standard  log  2’  versus  log 2”  profile  is  a  straight  line  with  a  gradient  of  il_,  this  is expected  for  the  equivalent  circuit  of  a  sample  whose dielectric  properties  depend  solely  on  the  bulk  material [lo].  Furthermore  the  sample  impedance  is  independent of  the  applied  test  voltage  over  the  measurement frequency  range  1  kHz  to  5MHz;  the  boundary  layer effects  should  be  voltage  dependent  (111 and  have  been found  to  be  so  in  UO,  at  temperatures  in  excess  of about  150  K  ]9]. Thus  in  the  temperature  range  (below 77  K)  of  this  study,  the  measured  dielectric  properties are  determined  solely  by  the  bulk  crystal  and  the  equiv- alent  circuit  can  be  represented  by  a  parallel  combina- N.  Hampton  et al.  /  Dtelectric  constmt  of  r/O, helm  the  N&l  pornr .  . . .  . .  . .  .  .  . .  . . . 12.01 0  1  2  3  L  5  6 Loglo(f  I Fig.  1. Capacitance  of  the  bulk  material  versus  measurement frequency  at 56 K for test voltage  of 0.5 V. tion  of  a  resistance  and  a  capacitance.  Measurement  of the  capacitance  leads  directly  to  the  dielectric  constants of  the  bulk  material  through  knowledge  of  the  sample dimensions,  only  the  static  constant  E,, being  accessible with  the  frequencies  used  here.  The  capacitance  C  as  a function  of  frequency  f  at  temperatures  below  77  K remains  almost  constant  (dC/dfr  -3  x  lo-l9  F Hz-‘),  a typical  example  of  the  data  (obtained  at  56  K) being  shown  in  fig.  1.  The  gradient  of  the  capacitance versus  frequency  profiles  is  a  slowly  varying  linear function  of  temperature.  The  static  dielectric  constant co  has  been  obtained  by  extrapolation  of  the  capaci- tance  data  towards  zero  frequency  (0.1  Hz).  This  zero frequency  capacitance  can  be  attributed  wholly  to  the bulk  property  of  the  crystal.  This  attribution  has  been validated  in  two  ways:  firstly  the  calculated  characteris- tic  frequency  (7.9  x  10m2  Hz)  that  would  be  expected for  the  boundary  region  is  far  below  the  accessible measurement  frequencies;  secondly  it  has  been  shown experimentally  that  the  capacitance  is  independent  of applied  voltage,  for  voltages  up  to  35  V:  the  boundary contributions  to  the  electrical  properties  of  UO,  depend markedly  upon  the  voltage  [9]. The  dependence  of  c0  upon  temperature  (both  on cooling  and  warming)  is  shown  in  fig.  2.  Here  the  effect of  the  20  ppm  length  change  at  the  phase  transition upon  the  physical  dimensions  has  been  taken  into account  when  calculating  the  dielectric  constant.  The main  source  of  experimental  error  arises  from  the determination  of  the  gradient  of  the  profiles.  The  initial aim  of  the  work  was  to  establish  the  behaviour  of  the 201  I  I 0  10  20  30  LO  50  1 Temperature  (K I 19 0 Fig.  2. Dielectric  constant  of  monocrystalline  UO,  as  a  func- tion  of  temperature.  The  structural  transition  occurs  close  to 30 K. (x)  cooling,  (0) heating. dielectric  constant  co  in  the  vicinity  of  the  phase  transi- tion  and  in  the  low  temperature  phase.  The  effect  on  c,, at  the  transition  is  found  to  be  small  but  identifiable with  the  experimental  methods  used.  The  static  dielec- tric  constant  is  only  about  0.8%  larger  in  the  high temperature  phase  than  in  the  low  temperature  form. The  errors  in  the  absolute  values  of  the  zero  frequency dielectric  constant  are  about  1%.  These  errors  can  be attributed,  almost  wholly,  to  the  extrapolation  proce- dure  because  plots  of  the  capacitance,  at  selected  fre- quencies,  versus  temperature  indicated  a capacitive,  and hence  dielectric  constant,  change  of  approximately  0.8% across  the  transition  region;  the  errors  involved  in  de- termination  of  the  relative  change  in  the  capacitance across  the  transition  is  substantially  less  than  this  (< O.l%),  so  we  are  in  no  doubt  that  the  value  larger  by 0.8%  in  the  high  temperature  phase  shows  a real  effect. The  dielectric  constant  in  the  paramagnetic  phase has  previously  been  measured  by  a  number  of  workers both  at  high  frequencies  [12-161  and  under  static  condi- tions  [9,  16-191.  In  principle  the  results  of  measurement of  the  dielectric  constants  of  UO,  at  microwave  and quasi-DC  frequencies  might  be  expected  to  be  the  same. However,  above  150  K  the  boundary  region  contributes to  the  capacitance  of  plate  geometry  specimens  mea- sured  at  low  frequencies.  A  value  of  co  of  36  measured at  77  K  is  consistent  with  data  previously  reported [9,16];  that  this  value  is  rather  larger  than  that  (c,,  =  24) measured  at  microwave  frequencies  has  been  ascribed 20  N.  Hampton  et al.  /  Dielectrrc  constant  of  110,  helow  the  NGel point to  dipolar  contributions  resulting  from  excess  oxygen beyond  stoichiometry  [9].  The  value  (23.6)  obtained here  at  4.2  K  for  c,,  in  the  antife~omagnetic  phase  is for  most  purposes  identical  with  that  now  accepted  for the  paramagnetic  phase  and  remeasured  here  as  23.8  (at 45  K). 3.  Estimation  of  the change  in dielectric  constant  due  to oxygen  displacements  at the  phase  transition It  is  now  necessary  to  estimate  the  expected  change in  the  dielectric  constant  which  arises  directly  from  the structural  distortion  1201  which  takes  place  at  the  transi- tion.  This  is  not  an  attempt  to  predict  the  lattice  distor- tion  or  its  origin  {see  refs.  [Zl]  and  [22])  but  simply  to ascertain  whether  the  observed  distortion  can  produce  a significant  change  in  dielectric  constant.  The  calcula- tions  are  based  on  a  shell  model  [23]  for  UO,,  and  use the  Harwell  PLUTO  code  1241. The  three  components far,  toy*  co.? of  the  static  dielectric  constant  and  the corresponding  components  e,._,  fmy,  cm=  of  the  optic dielectric  constant  have  been  calculated  as  a  function  of the  distortion.  The  distortion  moves  alternate  (010) layers  of  oxygens  in  the  [loo]  and  [TOO]  directions  and has  the  magnitude  Q  in  units  of  the  anion-anion  dis- tance  12.7341  w  at  298  K).  Since  it  is  anticipated  that the  UO,  sample  will  consist  of  domains  with  different orientations,  the  average  of  the  three  principai  compo- nents  has  been  calculated.  These  averages  are  fitted quite  adequately  by: dr,,‘e,  =  21Q*;  Ar,/r,  =  3&Q*. The  experimental  displacement  at  the  transition  is 0.014 ,k  [20]  which  would  give  a  relative  change  Aea/~a  of 0.05%  which  is  substantially  smaller  than  that  measured experimentally  (0.8%).  It  also  has  the  opposite  sign, predicting  a  smaller  dielectric  constant  in  the  para- magnetic  phase  than  in  the  low  temperature  antiferro- magnetic  phase,  although  the  converse  is  true.  A  natural explanation  of  the  small  difference  between  the  dielec- tric  constant  of  the  two  phases  is  that  the  structural distortion  suppresses  another  contribution  to  the  dielec- tric  constant.  It  is  plausible  that  the  inhibited  contri- bution  is  related  to  that  excess  observed  at  higher temperatures  which  has  been  associated  f9,12]  with  small deviations  from  stoichiometry.  We  have  reported  previ- ously  [19]  dipolar  contributions  to  the  observed  dielec- tric  properties  and  the  suppression  of  a small  fraction  of these  contributions  would  explain  the  observed  change near  the  phase  transition.  Whether  freezing  out  results from  making  previously-equivalent  sites  inequivalent  (so that  reorientation  is  inhibited)  or  from  changes  associ- ated  with  electronic  ordering  is  not  yet  clear. In  conclusion  the  experiments  have  established  that undergoing  the  first  order  magnetic  and  structural  phase transition  has  only  a  small  effect  on  the  dielectric constant  z0  of  UO,,  and  that  this  is  not  related  directly to  the  atomic  displacements  at  the  transition. References [I]  W.M.  Jones,  J.  Gordon  and  E.A. Long,  J.  Chem.  Phys.  20 (1952)  695. [2]  A.  Arrott  and  J.E.  Goldman,  Phys.  Rev.  108  (1957)  948. [3]  W.E.  Henry,  Phys.  Rev.  109  (1958)  1976). [4]  M.J.M.  Leask,  L.E.J.  Roberts,  A.J.  Walter  and  W.P.  Wolf, J.  Chem.  Sot.  (1963)  4788. [5]  B.C.  Frazer,  G.  Shirane,  D.E.  Cox  and  C.E.  Olsen,  Phys. Rev.  140  (1965)  A1448. [6]  J.  Faber  and  G.H.  Lander,  Phys.  Rev.  14  (1976)  1151. [7]  B.T.  Willis  and  R.I.  Taylor,  Phys.  Lett.  17  (1965)  188. [S]  O.G.  Brandt  and  C.T.  Walker,  Phys.  Rev.  Lett.  18  (1967) 191 [lOI [Ill ll21 1131 (141 1151 I161 u71 I181 (191 WI WI WI ~31 1241 11. 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The dielectric constant of UO2 below the Néel point

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