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Submitted on 1 Jan 1972
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INCOHERENT NEUTRON SCATTERING FROM HYDROGEN BOND IN KDP AND ADP
M. Antonini, I. Sosnowska, M. Vadacchino
To cite this version:
M. Antonini, I. Sosnowska, M. Vadacchino. INCOHERENT NEUTRON SCATTERING FROM HY- DROGEN BOND IN KDP AND ADP. Journal de Physique Colloques, 1972, 33 (C2), pp.C2-83-C2-84.
�10.1051/jphyscol:1972224�. �jpa-00214960�
JOURNAL DE PHYSIQUE Colloque C2, supplkment au no 4, Tome 33, Avril 1972, page C2-83
INCOHERENT NEUTRON SCATTERING FROM HYDROGEN BOND IN KDP AND ADP
M. ANTONINI, I. SOSNOWSKA (*) and M. VADACCHINO (**) Comitato Nazionale per 1'Energia Nucleare, Ispra (Varese), Italy
Abstract. - Neutron interference effects, already observed by Stiller and Grimm et al., are further examined in KH2P04 (KDP) and NH4HzP04 (ADP) in the paraelectric phase. The measurements are performed with a triple axis spectrometer at a neutron energy of 84 meV. A maximum value of 12 A-I is achieved for the scattering vector k. For KDP, in the adopted geometry, k rotates in the plane defined by the vectors b + a and c of the single crystal. A preliminary experi- mental evidence for a similar interference effect observed also in the ADP crystal, is reported.
It has been shown by calculations and experiments performed by Stiller [l] and Grimm et al. [2] that the neutron elastic incoherent scattering cross section of paraelectric KH,P04 (KDP) has a typical behavior which depends on the orientation of the scattering vector with respect to the hydrogen bonds (see Fig. 1).
J X
FIG. 1. - Relative orientation of the scattering vector k with
respects to the hydrogen bonds in the KDP and ADP cell.
This behavior is attributed to the density distribution of the proton clouds, which has been found in KDP to be highly anisotropic 131 and extended along the lines connecting different PO4 groups. This distribution can be explained both in terms of a single anisotropic model potential and in terms of a double well model potential. For a harmonic, anisotropic single oscillator, the elastic incoherent cross section is proportional to [4] :
C ~ P f i c l h a r m . = 4 ~ x P [ - 2(b, 1 k: + b.22 ki + b33 k:)] + + 4 exp[- 2(b,, kg + b,, k,2 + b33 k,2)], (1) where k,, k,, k, are the components of the scattering vector k along the edges of the KDP cell, b,, is the
(*) Permanent address : Institute of Experimental Physics, University of Warsaw, Warsaw, Poland.
(**) Permanent address : Istituto di Fisica Sperimentale del
Politecnico di Torino, Torino, Italy.
mean square displacement of the proton along the hydrogen bond, and b,,, b3, are the mean square displacements of the proton perpendicular to the hydrogen bond.
Assuming a double well potential, the cross section has the form [2] :
where b is the mean square displacement of the proton from either one of the two equilibrium positions and R is the vector distance between the two minima. The parameters ci derive from the expansion of the proton ground states in the double well potential.
In the previous experiment [ 2 ] , the corrected experi- mental data have been fitted withexpressions (1) and (2).
Only at large values of k, however, the difference between the behavior of the two cross sections would be more appreciable. Unfortunately, the data are less accurate in that region and can be fitted by a rather large range of values of the various parameters.
An alternative way to distinguish between the two models, at large momentum transfer, has been sug- gested by Schenk and Weckermann [ 5 ] , in terms of the ratio between the maximum and the minimum of the cross sections. In figure 2a, this ratio is plotted for the two models and a geometry of scattering specified by cp = 0 in figure 1. The analogous quantity is repre- sented also in figure 2b for the geometry specified by 9 = 450 in figure 1. This geometry was adopted in our experiments since it provides, at large k, a bigger difference between the two models.
The measurements were performed by means of a triple axis spectrometer installed at the 5 MW Ispra-1 reactor. Neutrons with energy of 84 meV were used.
In our experimental conditions, this energy allows to achieve a maximum value of 11.7 A-1 for the scattering vector. The correspondent energy resolution was measured to be about 9 meV. The single crystal of KDP was cut as a slab of 50 x 50 x 3 mm3, the Iong dimensions being parallel to c and (a + b) axis. The
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1972224
C2-84 M. ANTONINI, J. SOSNOWSKA AND M. VADACCHINO
"+ I
0.8 1
= O 0 k y
--&==/ 'd. 'harm. w.
OL
FIG. 2. - Calculated ratios between the maximum and the minimum intensities for the harmonic and the double well model potentials. The values of the quantities bii (eq. (1) in the text) are obtained from reference (4). The values of the quantities b, R and s (eq. (2) in the text) are obtained from reference (2).
preliminary data, subtracted from background, are reported in figure 3. The background was measured by shielding the neutron beam scattered directly by the sample.
Beside the value k = 11.7 A-l, the intensities were also recorded for k = 3.7 A-1 and k = 8 Ad'. A further correction for multiple scattering and inelastic
- V) 1 -
C z
3 > LOO - n 3
k -
m n a - 200 -
>
A K=11.68 i'' K D P
W K = 8 i-' & ~ O C U ~
FIG. 3. - Intensity of elastically scattered neutrons in KDP as a function of the orientation 6 and y, = 450 as defined in figure 1.
contributions is presently under progress. It can be noticed that the obtained results indicate the perma- nence of a modulated cross section when k = 11.7 A- l.
At this value of the scattering vector, it would be expected that the exponential factor exp(- bk2), appearing in eq. (2) and independent from the orienta- tion of k, may strongly depress the intensity of the scattered neutrons.
Measurements have been performed also in the paraelectric NH,H,PO, (ADP). This system is antiferroelectric in the ordered phase and his lattice is isomorphous to that of KDP. The adopted scattering geometry is specified by q = 00 in figure 1. The obtained results, subtracted for background similarly to the KDP data, are reported in figure 4. Some analogy with the modulated behavior of the scattered intensities for KDP can be noticed for k
-
3.7and 8 A-l.
o I d
O0 SO0 lSO" 270' 360q
e
FIG. 4. - Intensity of elastically scattered neutrons in ADP as a function of the orientation 0 and y, = O0 defined in figure 1.
The analysis of the data for ADP is complicated by the relatively large contribution to the total scattered intensity, originated by incoherent scattering from protons in the NH, groups. Some features of our results, which appear to be more specific of the ADP sample are now under investigation.
We wish to thank. Prof. G. Caglioti who suggested the present experiment and promoted many stimulating discussions. Mr. G. Contadini, Mr. G. De Giorgi and Mr. E. Ferrari gave a valuable contribution to solve many technical problems arising in the course of the experiment. Two of us (I. S. and M. V.) are grateful to the Comitato Nazionale per 1'Energia Nucleare for having made this collaboration possible.
References
[I] STILLER (H.), Ber. Bunsenges. Phys. Chem., 1968,72,94. [4] FELCHER (G.) and PELAH (I.), J. Chem. Phys., 1970,52, [21 GRIMM (H.), STILLER (H.) and PLESSER (Th.), Phys. 905.
Stat. Sol., 1970, 42, 207. [5] SCHENK (C.) and WECKERMANN (B.), Phys. Letters [3] BACON (G.) and PEASE (R.), Proc. Roy. Soc. (London), (Netherlands), 1968,27, 582.
1953, A 220,397 and 1955, A 230,359.
