X-ray diffraction measurements of the c-axis Debye-Waller factors of YBa2Cu3O7 and HgBa2CaCu2O6

5 Pages·0.16 MB·English

by  C. Kim

X-ray diffraction measurements of the c-axis Debye-Waller factors of YBa Cu O and
2 3 7
HgBa CaCu O
2 2 6
C. Kim1,2, A. Mehta1, D.L. Feng3,4, K.M. Shen3, N.P. Armitage3, K. Char5, S.H. Moon6, Y.Y. Xie7, and J. Wu7
1Stanford Synchrotron Radiation Laboratory, Stanford, California 94309
2Institute of Physics and Applied Physics, Yonsei University, Seoul, Korea
3 3Department of Physics and Applied Physics, Stanford University, California 94305
0 4Department of Physics, Fudan University, Shanghai 200433, People’s Republic of China
0 5School of Physics and Center for Strongly Correlated Materials Research,
2 Seoul National University, Seoul 151-742, Korea
6LG Electronics Institute of Technology, Seoul 137-724, Korea and
n
a 7Department of Physics and Astronomy, University of Kansas, Lawrence, Kansas 66045
J (Dated: February 2, 2008)

7
Wereportthefirstapplicationofx-raystothemeasurementofthetemperaturedependentBragg

peak intensities to obtain Debye-Waller factors on high-temperature superconductors. Intensities
]
n of (0,0,l) peaks of YBa2Cu3O7 and HgBa2CaCu2O6 thin films are measured to obtain the c-axis
o Debye-Wallerfactors. While lattice constant and some Debye-Waller factor measurements on high
c Tc superconductors show anomalies at the transition temperature, our measurements by x-ray
- diffraction show a smooth transition of the c-axis Debye-Waller factors through Tc. This suggests
r
p thatthedynamicdisplacementsoftheheavyelementsalongthec-axisdirectioninthesecompounds
u donot haveanomalies at Tc. This method in combination with measurements by othertechniques
s will give more details concerning dynamicsof thelattice.
.
t
a PACSnumbers: PACSnumbers: 74.25.-q,61.10.Eq,74.25.Kc
m
-
d The majority of efforts to understand the mechanism latedtothedynamicpropertiesofphonons. Itwillthere-
n of the high T superconductivity (HTSC) have been in fore be interesting to measure the Debye-Waller factors
c
o terms of pure electronic effects, primarily because of the (DWF) of HTSC materials.
c
conjecture that electron-phonon coupling alone cannot
[
givesuchahighTc. However,therehavebeenpersistent Incomplexmaterials,the DWFs areusuallymeasured
1 effortstostudythe roleofthelatticeinHTSC1,2,3,4,5,6,7. by extended x-ray absorption fine structure (EXAFS).
v In addition to the fact that the structural information In the HTSCs there have been efforts to measure the
7 provides important information about the materials,the temperaturedependentmean-squaredisplacementσ2(T)
5 lattice can still play an important role as it affects both (whichisinverselyrelatedtotheDWF)byEXAFS8,9,10,
0
the hopping (t) and magnetic exchange (J) energies of with essentially only Hg based samples showing anoma-
1
0 these materials, the two most important parameters in lies at Tc10. EXAFS measures local coordinates at a
3 the physics of these correlated systems. Indeed, there certain atom and therefore has an important advantage
0 have been theoretical efforts to study the role of lattice of being element specific. It, however, measures only
/ vibration in the cuprates1,2. Therefore, experimental in- relative atomic motions (for example, O relative to Cu
t
a vestigation of the temperature dependent lattice vibra- or optical phonons in the Cu-O plane) and is insensi-
m
tion in these materials, especially the critical behavior tive to collective motions of the atoms, for instance, the
- aroundT ,is essentialandcanprovidevitalinformation low frequency acoustic phonons. To see the effect in the
d c
concerning the low energy degrees of freedom. phonon population, the necessary condition is to have
n
amplephononsinthefirstplace. Thismaybedifficultfor
o
c Experimentalevidencethatshowsclearcorrelationbe- opticalphononsastheirenergyscaleisusuallyveryhigh
: tween the critical behaviors in the electronic and crys- comparedtotheexperimentaltemperaturescales(which
v
tal structures are anomalies in lattice constants at T . are set by T ). This may be related to the fact that
i c c
X These have been observedin variousHTSC materials by EXAFS results largely show no anomalies. In contrast,
r x-ray3,4 andmore accuratelyby capacitancedilatometry even though they have their own disadvantages which
a methods5,6,7. They have shown that the lattice constant willbe discussedlater,diffractiontechniques inprinciple
generally decreases at a much faster rate at T than at measure the integratedphononeffects11. Here we report
c
other temperatures as the temperature decreases. Sub- novelapplicationofx-raydiffractionthatcaninprinciple
sequently, the thermal expansion coefficient α shows an measure DWFs. This is to our knowledge the first ap-
anomaly that is of similar shape to the heat capacity plication of this method by x-rays to complex materials
anomaliesobservedatT . Thisenhanceddecreaseinthe like HTSCs. We have measured the temperature depen-
c
lattice constant has been related to the specific heat ca- dence of the Bragg peak intensities, a quantity that can
pacity through the thermodynamic Ehrenfest relations7. berelatedtothedynamiclatticemotion. Theresultsare
Yetthemicroscopicreasonbehindsuchalatticeanomaly discussed along with various aspects of x-ray diffraction
isnotwellunderstood. Onenaturalquestionisifitisre- and possible future experiments.
2
The experiments were performed at beamline 2-1 of (a)
the Stanford Synchrotron Radiation Laboratory (SSRL) X-ray
which is equipped with a 2-axis Huber diffractometer.
The diffractometer has an open cycle He cryostat. hν = Sample
8.8 keV x-rays, just below the Cu K edge, were used to
reducethebackgroundfromthefluorescentlight. Forthe Cryostat
reasons explained below, intensities of the (0,0,l) peaks (at 10 K)
Sample
of YBa Cu O (YBCO) and HgBa CaCu O (Hg1212)
2 3 7 2 2 6
holder
thinfilmsamplesgrownonSrTiO3substratesweretaken. Glass
These materials were grownaccording to the procedures
described elsewhere12,13. The YBCO film has Tc of (b)
90.5K with the ∆T less than 1K. The Hg1212 sample
c
has the ∆T less than 1K locally but shows distribution PMT
c
of T ’s from 123K at the center to 118K at the edge. Detector
c
In order to obtain highly reliable intensities, it is es-
sentialtoreducetheerrorsfromthebeamandsamplein-
stabilities and detector non-uniformity. The beam drifts
weremonitoredinthe I sectionandcorrectedforbefore X-ray 2q
0
eachmeasurement. Thebiggesteffectcamefromthemo-
Sample
tion of the cryo-head during the temperature cycle. To
reduce such effects, a special manipulator has been de-
signedasshowninFigure1. Thesampleholderisinweak FIG.1: (a)Theschematicofthecryostatdesignedfortheex-
thermalcontactwiththecryo-headandhasitsowntem- periments. Thesampleholderisinweakthermalcontactwith
peraturesensorandheater. Thethermalcontactisweak the cryo-head with its own temperature sensor and heater.
enoughsothatthetemperatureofthesampleholdercan Duetotheweakthermalcontact,thetemperatureofthesam-
be variedbetween10K and200K withthe temperature ple holder can be varied between 10 K and 200 K while the
temperature of the cryo-head fixed at 10 K. (b) Illustration
ofthe cryo-headmaintainedat10K.This removedmost
of the experimental configuration. The detector is fixed at
of the sample motion and greatly improved the repro-
the 2θ position while θ is scanned. The detector slit is wide
ducibility of the data.
enough to accept the whole Bragg peak as illustrated unlike
Thespecialmanipulatordidnotcompletelyremovethe the conventional setup. The 2θ position is adjusted at each
samplemotionwithrespecttothebeamduringtempera- temperature so that thesame part of thedetector is used.
ture cycling. If the sample was completely homogeneous
then the relative motion of the sample will have no ef-
fect on the measurement. In our experience, the only theaccuracy/reproducibilityofthemeasurementshadto
high Tc samples which are homogeneous to a highly col- be better than 0.5%. Therefore, care had to be taken
limated and monochromatic synchrotron beam are fine to remove any factor that affects the data quality. The
grain powders. However, in a powder sample the high following somewhat unconventional procedure was per-
index peaks, the peaks more sensitive to the DWF (as formed to obtain reliable data. First, the detector slit
DWF ∼ l2), were too weak to measure with sufficient was set wide enough (∆2θ ∼ 4 degrees) to accept all the
statisticalaccuracyinareasonableamountoftime. Even diffracted x-ray within a certain Bragg peak (Fig. 1).
thoughtheintensitiesofthehighindexBraggpeakswere This is to minimize the detector non-uniformity effect as
acceptableinasinglecrystalwediscovered,afterlooking use of angle limiting devices such as Soller slits resulted
at high Tc single crystals from several different sources, in very unreliable data. However, some degree of non-
thatthesesampleswerereallyabundleofseverallowan- uniformity still existed and it was necessary to make it
gle grain boundary crystallites. Even a small motion of sure that the same part of the detector is used for each
suchasamplewithrespecttotheincidentbeamchanged scan. To ensurethis, wescanned2θ ateachtemperature
thefractionofthediffractingdomaininthebeam,which to locate the detector so that the centroid of the diffrac-
resultedinasignificantchangeinthediffractedbeamin- tion peak is at the center of the detector. In this way,
tensity. Thinfilmsofsufficientlyhighqualityandlateral the detector is essentially tracking the temperature de-
homogeneity for synchrotron measurements were avail- pendent motion (in 2θ) of the diffraction peak. As the
able but they were all (0,0,l) orientation14. Hence, as laststep,theθscans(rockingcurves)weretakentomea-
acompromisebetweenhighintensityandsufficiently ho- sure the diffraction peak intensity. The above procedure
mogeneous samples, we performed our measurements on produced the most reliable data.
the (0,0,l) peaks of thin film samples. Fig. 2 shows θ scans as well as temperature depen-
In addition to the motion of the cryostat upon the dent intensity plots measured as described above. Panel
temperature change, other factors such as detector non- (a) shows normalized θ scans of the (0,0,13) peak from
uniformity contributed to the irreproducibility of the YBCO.The peak position in θ decreasesas temperature
data. Sincetheeffectwewerelookingforwasverysmall, increases,implying the increase of the c-axis lattice con-
3
constant. Therefore, one would expect linear tempera-
0.6 1.0 ture dependence of the DWFs for T≪ 1/λl2. The in-
YBCO 15 K YBCO
0.5 6900 KK tensities in the figure show linear temperature depen-
120 K
180 K dence and no anomaly is found within the experimen-
0.4
tal error16. Also shown in the panel is the temperature
0.3 0.9 dependent intensity of the (0,0,11) peak from YBCO.
N
o TheratiooftheDWFsofthe(0,0,13)and(0,0,11)peaks
0.2 rm
Intensity (arb. uinit)00..051 aH)g511.251252.0 52.5 51583800. 0KKK 53.5 0b) (((0005,,,0000,,,111331))) idinnecc1crrr0eee0aaasssiiinnnggg TTTH15g0121220001..80alized integrated inte vtpDdishaaeWelnt1urad.Fme2ef8onrawoftl±mi1pitn03hht.H2oo0e/unng51to1s1win22ta1ihne=e2isyffcshe1saacu.4mtnigssogfp.omselorseTatsmmhl.nyeeo.oOwnrmthmaPheataaeaotrnlsmcuebtlilrheocsehasdse(anycvtst)tietoohmearemtnpohldseaferrwta(gehditxeetu)rphrceres-pcohautdcxoerkewides--
0.4 111148000 KKK nsity iYnBgCwOidtcha,set,hsehbowehinagvionroissigmnoroef aonrolmesaslythaetsTamc ewiwthitinh
0.3 the experimental error. The deviation of (0,0,10) data
0.9
from the linear behavior is related to the fact that, un-
0.2
like other peaks, it was measured along with substrate
0.1 (0,0,10) increasing T peakshence producing largerexperimentalerrors,andis
c) d) (0,0,14) increasing T assumed to be extrinsic effect.
(0,0,14) decreasing T
0 0.8
49 50 θ51 52 53 54 0 50 100 150 200 Interpretation of the above results, however, is not as
(degree) Temperature (K) easy as the case for monatomic systems such as Si. The
expression of a Bragg peak intensity contains in general
FIG. 2: (a)Series of θ scans of (0,0,13) peak from YBCO at
exponential functions of the displacement parameters of
differenttemperatures. Thechangesintotalintensityaswell
the atoms in the unit cell. For a monatomic case, it
asthepeakposition areseen. (b)Temperaturevs. integrated
could be reduced to a single exponential function of the
intensity plot of the data. The data were taken with the
temperature cycled and normalized at T=0. Also shown is displacement parameter (assuming the displacement pa-
the data for (0,0,11) peak. (c)Scans of (0,0,14) from Hg1212 rameters for the atoms in the unit cell are the same)
samples. (d)Temperature vs. intensity plot for (0,0,14) and and the DWF can be interpreted with a relative ease.
(0,0,10) peaks. The form factorsfor polyatomic compounds howeverare
different and the Bragg peak intensity is expressed by a
combinationofexponentialfunctions. Itisthereforevery
stant as expected. In addition to the decrease in the θ hardtoextracttheinformationonthedynamicdisplace-
position,wenotethattheBraggpeakintensitydecreases mentsfromDWFs. Theotheraspectisthattheobserved
as the temperature increases (increased constant back- temperature dependence does not solely come from the
ground due to incoherent scattering was also observed dynamic displacements. Not only the phonons but also
but subtractedin the plot and analysis). No appreciable thechangesinthestaticatomicpositionswithintheunit
change in the diffraction line shape, that is, no q depen- cell affect the intensities.
dence is observed and thus the role of thermal diffuse Inspiteofthedifficulties,wecanstillextractusefulin-
scattering is not considered in the following discussions. formationfromthe results. Eventhoughthe Braggpeak
Since the detector slit was wide open (in 2θ) to accept intensityexpressioncontainsmultipleexponentialterms,
allthex-raysofthepeak,eachpointontheθ scanrepre- it shows linear temperature dependence if the displace-
sentsBraggpeakintensityi.e.,integrationofa2θscanat ments are purely due to thermal vibrations. Therefore,
the given θ value. Therefore, the integration of the area the fact that experimental data show linear temperature
represents the sum of the intensities from all the grains dependence strongly suggests that the major contribu-
of the sample. It is apparent from the figures that the tor to the DWF is the dynamic displacements as there
peak intensity decreases as the temperature increases. is no intrinsic reason for such temperature dependence
To quantify the temperature dependent peak inten- from the static displacements. Indeed, detailed neutron
sities, the peaks shown in Fig. 2a are integrated over diffraction experiments on YBCO show that the mean
the whole angular range. The results are normalized square displacements are mostly dynamic19. We also
to a common linear extrapolated T=0 value and plot- note that heavy elements contribute more to the diffrac-
tedagainstthetemperatureinpanel(b). Formonatomic tion intensities in our x-ray measurements due to their
systems,theintensityofa(0,0,l)Braggpeakisexpressed greater high Z sensitivity. To see the different contribu-
as I =I0exp(−21hz2il2) where the exponent is the DWF tions, we list in Table 1 calculated fractions of the pla-
and hz2i is the thermally averaged mean square mo- nar oxygen and Cu-O planar contributions to the total
tion of the atoms in z direction15. For a classical Har- diffraction peak intensities of YBCO and Hg1212 using
monic oscillator, hz2i ∝ T and the intensity thus be- the published structural information17,18. Note that the
comes I = I exp(−λl2T) ∝ I (1−λl2T) where λ is a fractions do not add up to make the total due to the in-
0 0
4
Sample Fc2(total) Fc2(Cu-O plane) Fc2(planar O) ature change are insignificant compared to the neutron
beamsize. This will allow us to investigate a- and b-axis
YBCO 50.0 2.58 1.00
DWFs by a diffraction technique. In addition, its sensi-
Hg1212 1386 1.90 1.00 tivitytolowZatomswillallowmoreaccurateestimation
oftheoxygencontributiontotheDWFs. Thereindeedis
TABLE I: Calculated Fc2’s for YBCO (0,0,13)and Hg1212 a strong indication that temperature dependent (1,2,12)
(0,0,14)normalizedtoplaneOvalues. Cu-Oplaneandplanar
neutron Bragg peak intensities of YBCO crystals have
oxygencontributionshavebeencalculated withtheoccupan-
anomalies at the T 19.
cies of theother atoms set to zero. c
In conclusion, temperature dependent c-axis DWFs of
YBCO and Hg1212 thin films are obtained by measur-
terferencebutroughlyshowtheinsignificantCu-Oplane ing the temperature dependent(0,0,l)x-rayBraggpeak
contribution to the total intensity. It is thus conceivable intensities. The measured DWFs show linear tempera-
that the phonon anomalies in the Cu-O plane measured ture dependence within the experimental errors, show-
byEXAFS10 maybeburiedunderthecontributionsfrom ing no anomalous effects near T . Considering the fact
c
the heavy elements. Based on these, it is reasonable to thatthex-raydiffractionintensityismuchmoresensitive
conclude that at least the heavy elements do not show to the heavy elements, the results suggest that there is
anomaly at Tc in their c-axis dynamic properties. no anomalous lattice dynamics of heavy elements along
Onthe morefundamentalside,the anomaliesinthe c- the c-axis. Further studies of a- and b-axis temperature
axis lattice constants are generally relatively small com- dependent DWFs by neutron diffraction in combination
pared to those along a- or b-axes4,6,7. Therefore, it is with temperature dependent structural studies by EX-
possiblethatthec-axisphononpopulationanomalymay AFSmayshedmorelightonthe temperature dependent
wellbeverysmallandundetectable. Lookingata-andb- lattice dynamics, i.e., role of the phonons in HTSCs.
axisDebye-Wallerfactorsisthereforeessential. Thismay
explain the absence of the anomaly in the Hg1212 data We would like to thank F. Bridges and J. Arthur for
whilemeasurementbyEXAFSonpowdersamplesofsim- helpful discussions, and H. Shin for statistical analy-
ilar compound HgBa CuO shows anomaly in the mean sis. SSRL is operated by the DOE office of Basic En-
2 4
square dispacements10. Use of Rietveld refinement with ergy Research, Division of Chemical Sciences. The of-
powder diffraction at a brighter x-ray source could give fice’s division of Material Science provided support for
an answer to this. Better yet, considering all the factors this research. This work is supported (in part) by the
discussed above, similar experiments by neutron diffrac- Korean Science and Engineering Foundation (KOSEF)
tion may resolve most of the problems; the typical grain through Center for Strongly Correlated Materials Re-
sizes of HTSC crystalsand sample motionupon temper- search (CSCMR) at Seoul National University.
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153-155, 1028 (1988). making those film sample useless for our experiments.
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& Sons, Inc.,New York,1986. which is isostructural with Hg1212 were used. For
5
TlBa2CaCu2O7 structure,seeB.Morosin,D.S.Ginley,P. 19 P.Schweiss,W.Reichardt,M.Braden,G.Collin,G.Heger,
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