Diﬀuse scattering in α and β Sn Single Crystals
Univ. of Tsukuba Miwako Takahashi
1.Introduction
β-Sn has a body-centered tetragonal structure and is metallic, and transforms to α-Sn at low
temperature which is a semiconductor and has a diamond structure. Detailed mechanism of thetransformation has been still controversial between diﬀusive or martensitic. Diﬀuse scattering in β-Sn
has long been studied since 1943[1]. Its intensity distributions show quite characteristic features ofasymmetrical and anisotropic shapes in reciprocal space. The origin of the characteristic intensity
distributions is regarded to be TDS (Thermal Diﬀuse Scattering) resulting from lattice dynamics
in the β-Sn-structure which belongs to non-symmorphic space group[2]. In our previous neutrondiﬀraction measurements, it was found that intensity maxima appeared at X-points in the diﬀuse
scattering during the β to α transformation. In order to understand the relation between the diﬀuse
maxima and mechanism of the transformation, energy-resolved diﬀuse scattering measurements havebeen performed using a cold-neutron disk chopper spectrometer AMATERAS installed in BL14 atMLF, J-PARC.
2. ExperimentMultiple Ei measurements were performed with Ei =4.688, 7.743, 15.17, and 42.10 meV for β-Sn
single crystals with two diﬀerent crystal orientations: hhl and hk0 reciprocal planes in the equatorial,at 300K and 230K. Data were analyzed with program Utsusemi.
3.Results
Inelastic intensity distributions were compared with diﬀraction patterns observed in the process of
β to α structural transition[3]. Diﬀuse streaks are observed along hhl; l = 2n + 1 with maxima at
X-points hhl; h = (2n + 1)/2 in the inelastic patterns at ∆E > 3meV at 300K (Fig.1). Quite similarintensity distributions have been observed in the diﬀraction patterns during β to α transformation(Fig.2). Considering the fact that the intensities of the diﬀraction patters in Fig.2 include inelasticcomponents around ∆E = 0meV, the X-point-diﬀuse-maxima observed during the phase transformation can be interpreted as a result of softening of the acoustic modes of transverse phonons atX-points. Several dispersion relations at high-symmetrical reciprocal lines are plotted and comparedto the theoretical calculation[2]. The dispersion relations show qualitative agreement between experimental and theoretical results at low energy regions, as shown in Fig.3. Further investigation arenecessary for both experimental and theoretical sides to understand the origin of the X-point diﬀuse
maxima from the view point of the softening of the lattice dynamics.
4. Conclusion
Energy-resolved diﬀuse scattering measurements have been performed for β-Sn single crystals tounderstand the origin of diﬀuse maxima observed in the process of β to α transformation. Inelastic
intensities at ∆E > 3meV show maxima at the same X-points in the diﬀuse scattering. The result
indicates a strong softening of lattice dynamics has taken place at the X-points during the β to αtransformation. Experimental spectra along the high-symmetrical reciprocal lines show qualitative
agreement to the calculated dispersion relations.

(b)

(a)

R.T.

1.0Log0l00

0-2-200l

1.5

100l

β-Sn ∆E= 3meV
(2meV to 4meV)HHL plane, R.T.
Ei = 42meVAMATERAS

2.02T=231K

00.5-1-4-4-6-60.0-2-3-4-2020424062Fig.1 Inelastic intensities of

46hh0hh0hh0Fig.2 Diﬀraction pattern at the (a)initial and (b)middle stages of theβ − α structural transition.

∆E = 3meV.

(a)

(b)
10β-Sn Q-E
H 2 0 line, R.T.
Ei = 7meVAMATERAS/12

Q-E
HH 2 line, R.T.
Ei = 15meVAMATERAS

GX

10G

8/1#

#12

"

2.5

Energy (meV).-&,+*)('&%$!

8662.0441.5#1#
1.02#Γ0/#M!"*#/Γ"

20.5

00-1.5-1.0-0.5

0.0
HH20.51.0

1.5

Fig.3 Observed phonon dispersions along (a)h20 and (b)hh2 reciprocal lines. Black dotted lines represent
results of ab initio calculation[2].

Reference[1] J.J. Arlman and R. Kronig; Investigation of lattice defects by means of X-rays. I. Tin , Physica,10(1943)795.
[2] B.Wehinger, A. Bosak, G. Piccolboni, K. Refson, D. Chernyshov, A. Ivanov, A. Rumiantsev and M.
Krisch; Diﬀuse scattering in metallic tin polymorphs , J. Phys. Condens. Matter. 26(2014)115401.
[3] M. Takahashi, K. Ohshima, and Y. Noda; Measurement of diﬀuse scattering in β-tin single
crystal , Nihon Genshiryoku Kenkyu Kaihatsu Kiko JAEA- Review, 2006.