Elastic study of Potassium Sulphamate crystal using ultrasonic Pulse Echo Overlap technique

Article abstract of DOI:10.1016/j.ssc.2009.01.018

Elastic properties of Potassium Sulphamate single crystal with chemical formula, KNH₂SO₃ are studied by ultrasonic Pulse Echo Overlap (PEO) technique. It crystallizes in the orthorhombic symmetry with space group Pbcm The study invol

Full text of DOI:10.1016/j.ssc.2009.01.018

Solid State Communications 149 (2009) 645–647
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Solid State Communications
journal homepage: www.elsevier.com/locate/ssc
Elastic study of Potassium Sulphamate crystal using ultrasonic Pulse Echo
Overlap technique
George Varughesea,∗, A. Santhosh Kumarb, J. Philipc, Godfrey Louisd
a Department of Physics, Catholicate College, Pathanamthitta, Kerala-689 645, India
b SPAP, Mahatma Gandhi University, Kottayam–686 560, India
c STIC, Cochin University of Science & Technology, Cochin-22, India
d Department of Physics, Cochin University of Science & Technology, Cochin-22, India
a r t i c l e i n f o
a b s t r a c t
Article history:
Elastic properties of Potassium Sulphamate single crystal with chemical formula, KNH2SO3 are studied
by ultrasonic Pulse Echo Overlap (PEO) technique. It crystallizes in the orthorhombic symmetry with
space group Pbcm The study involves measuring ultrasonic velocity in the crystal in certain specified
crystallographic directions; all the nine elastic stiffness constants, compliance constants and Poisson’s
ratios are evaluated. The polar plots in a–b, a–c and b–c planes of Phase velocity, Slowness, Young’s
modulus and Linear compressibility reveal the anisotropy in elastic properties.
Received 23 October 2008
Received in revised form
7 January 2009
Accepted 10 January 2009 by P. Chaddah
Available online 18 January 2009
© 2009 Elsevier Ltd. All rights reserved.
PACS:
81.10Dn
62.20Dc
43.35+d
Keywords:
B. Crystal growth
D. Elasticity
E. Ultrasonics
1. Introduction
2. Experimental procedure
Large single crystals of size (50 × 35 × 12) mm3 have been
grown from supersaturated aqueous solution of the salt by slow
evaporation technique over a period of 60–65 days. The solution
has been prepared by dissolving equimolar fraction of K2CO3 and
sulfamic acid in double distilled water. The temperature of the
bath is maintained constant at 305 K and controlled to an accuracy
of ±0.1 K. The photograph and morphology of the grown crystal
is shown in Figs. 1 and 2. The interfacial angles of the grown
crystal are measured using an accurate contact goniometer. The
natural faces of the sample have been identified by comparing the
measured interfacial angle with that of the computed values from
the reported lattice parameters [6]. Bulk samples have been cut
using a slow speed diamond wheel saw. The samples are polished
carefully using cerium oxide powder to optical reflection level.
Potassium Sulphamate crystal with chemical formula, KNH2SO3,
is a ferroelectric and piezoelectric crystal [1]. The structure of the
crystal has been studied using x-ray diffraction technique. It crys-
11
tallizes in the orthorhombic symmetry with space group Pbcm[D ]
2h
and lattice parameters a = 5.907 Å, b = 8.333 Å and c =
8.302 Å, Z = 4 molecules/unit cell, Density = 2.2078 g/cm3,
−30
MV = 102.16 × 10
m3 [1]. Cox et al. [2] carried out neutron
diffraction study on the crystal structure of Potassium Sulphamate.
The elastic constants are tensors, which measure the crystal elas-
tic property. The information on elastic constants is of fundamental
importance in describing how the energy density of a solid changes
with respect to various volume and shear deformations; they are
useful in determining the nature of binding forces and interatomic
potentials [3]. We have thus studied the elastic properties of these
samples using ultrasonic Pulse Echo Overlap (PEO) technique. The
elastic constants, thermo elastic constant Tij, thermal expansion αij
and Gruneisen tensor G were studied using Resonant Ultrasound
Technique (RUT) by Haussuhl et al. [4,5].
3. Results and discussions
3.1. Velocity measurements
∗
X-cut and Y-cut quartz transducers of fundamental frequency
10 MHz and diameter 6 mm are mounted on the sample using
Corresponding author. Tel.: +91 944 7248 977.
E-mail address: gvushakoppara@yahoo.co.in (G. Varughese).
0038-1098/$ – see front matter © 2009 Elsevier Ltd. All rights reserved.
doi:10.1016/j.ssc.2009.01.018

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G. Varughese et al. / Solid State Communications 149 (2009) 645–647
Table 1
Measured ultrasonic velocity and elastic stiffness constants at 300 K. L, T, QL represent longitudinal, transverse and quasi longitudinal modes respectively.
Sl. no
Mode
Direction of propagation
Direction of polarization
Velocity measured (m/s)
Elastic constant (GPa)
V–Cij relation
1
2
3
4
5
6
7
8
9
L
L
L
T
T
T
QL
QL
QL
[100]
[010]
[001]
[010]
[001]
[100]
[110]
[011]
[101]
[100]
[010]
[001]
[001]
[100]
[010]
⊥c
V1 = 4168 ± 4
V2 = 4444 ± 4
V3 = 4479 ± 4
V4 = 2178 ± 2
V5 = 2403 ± 2
V6 = 2415 ± 2
V7 = 4302 ± 4
V8 = 4113 ± 4
V9 = 4269 ± 4
38.34 ± 0.07
43.58 ± 0.08
44.28 ± 0.08
10.41 ± 0.02
7.96 ± 0.016
12.87 ± 0.024
12.70 ± 0.024
9.93 ± 0.02
C11 = ρv12
C22 = ρv22
C33 = ρv32
C44 = ρv42
C55 = ρv52
C66 = ρv62
C12 = fab
⊥a
C23 = fbc
⊥b
14.44 ± 0.28
C13 = fac
1
1
2
2
2
2
2
fab = {1/C2S2[(C2C11 + s2C66 − ρv72)(C2C66
+
S C22 − ρv7 )]} − C66; C23
=
fbc = {1/(C2S2)[(C2C22 + s2C44 − ρv82)(C2C44
+
S C33 − ρv8 )]} − C44
;
2
C12
=
1
C13 = fac = {1/(C2S2)[(s2C11 + C2C55 − ρv92)(S2C55 + C2C33 − ρv9 )]} − C55; where s = Sinθ c = Cosθ where v is the velocity of propagation of respective modes.
2
2
3
◦
◦
◦
The angle θ = 35.13 for a–b plane, θ = 45 for b–c plane and θ = 35 for a–c plane. Density ρ = 2.207 g/cm .
Table 2
Elastic stiffness constants, elastic compliance constants and Poisson’s ratios of
Potassium sulphamate crystal at 300 K.
Elastic stiffness
constant (GPa)
Elastic compliance constant
Poisson’s ratio
−10
−1
)
(10
m2
N
C11 = 38.34 ± 0.07
C22 = 43.58 ± 0.08
C33 = 44.28 ± 0.08
C44 = 10.41 ± 0.02
C55 = 7.96 ± 0.016
C66 = 12.87 ± 0.024
C12 = 12.70 ± 0.024
C23 = 9.93 ± 0.02
C13 = 14.44 ± 0.28
S11 = 0.318
S22 = 0.258
S33 = 0.262
S44 = 0.96
S55 = 1.256
S66 = 0.777
ν12 = 0.283
ν21 = 0.23
ν23 = 0.13
ν32 = 0.132
ν13 = 0.332
ν31 = 0.274
S12 = −0.073
S23 = −0.034
S13 = −0.087
Fig. 1. Photograph of the grown crystal.
Fig. 2. Morphology of the crystal.
suitable material like silicon grease. Absolute velocities at room
temperature (303 K) have been measured for the selected direction
and modes. Details of measurement of the elastic constants of
orthorhombic crystals are reported in the literature [6]. The
ultrasonic velocities are measured by the Pulse Echo Overlap(PEO)
technique [7,8] using MATEC model 7700 pulse modulator and
receiving system. KNH2SO3, being an orthorhombic crystal, has
Fig. 3. Polar plot of phase velocity.
0.2% for diagonal elastic constants and 1% for off diagonal elastic
constants.
Velocity of propagation of various ultrasonic modes measured
along selected directions in the crystal is listed in Table 1. By
measuring ultrasonic velocity in the Potassium Sulphamate crystal
in certain specified crystallographic directions; the anisotropy in
the elastic properties of the crystal is studied. The second order
elastic stiffness constants, compliance constants and Poisson’s
ratios [11,12] are evaluated and tabulated in Table 2.
The elastic constants of the crystal measured by this study
(PEO method) show appreciable deviation from those measured
using Resonant Ultrasound Technique (RUT). Out of the diagonal
constants the constants C11(0.91%), C33(4.8%) and C44(1.9%) show
appreciable deviation below 5%, whereas constants C22(7.7%),
the following nine second-order elastic stiffness constants C11
,
C
C
22, C33, C44,
C55, C66,C16, C13and C23. The diagonal elastic constants
11, C22, C33, C44,C55 and C66 have direct relationship with suitable
ultrasonic mode velocity, given by Cij = ρV2. The relationship
between elastic constants with relevant ultrasonic wave velocity
for the orthorhombic system are reported in literature [6,9].
The McSkimin ∆t criterion [10] for bond correction has been
applied to correct for the phase lag introduced by the bonding
medium on the RF echoes. This technique enables one to measure
the ultrasonic transit time in the sample to an accuracy of a few
parts per million. Considering all experimental uncertainties the
absolute accuracy of elastic value is estimated to be better than

G. Varughese et al. / Solid State Communications 149 (2009) 645–647
647
Fig. 4. Polar plot of slowness.
Fig. 6. Polar plot of linear compressibility.
linear compressibility surfaces of KNH2SO3 have been plotted in
the a–b, b–c and a–c planes and are shown in Figs. 5 and 6.
The volume compressibility [12], Siikk, of this crystal = 0.45 ×
−10 −1
10
N
m2. Bulk modulus of this crystal = 22.22 GPa.
4. Conclusions
A detailed study on elastic properties are carried out, using
ultrasonic PEO technique, for evaluating all the nine elastic
constants, compliance constants, Poisson’s ratios, bulk modulus
and volume compressibility of Potassium Sulphamate crystal.
The anisotropy in elastic properties is well demonstrated by the
surface plots of phase velocity, slowness, linear compressibility
and Young’s moduli.
Acknowledgement
One of the authors [GV] thanks UGC for a Teacher Fellowship.
Fig. 5. Polar plot of Young’s modulus.
References
[1] C.J. Brown, E.G. Cox, J. Chem. Soc. 1 (1940) 10.
C
55(41.6%) and C66(60.7%) exhibit deviation above 5%. While
[2] G.W. Cox, T.M. Sabine, Acta Crystallogr. 23 (1967) 578.
[3] J. Holder, A.V. Granato, in: W.P. Mason, R.N. Thurston (Eds.), Physical Acoustics,
vol. VIII, Academic Press, New York, 1971, p. 237.
off diagonal constants C12(21.5%), C13(375%) and C23(268%) have
exhibited large deviation from the RUT [4, 5] values.
[4] E. Haussühl, S. Haussühl, Z. Kristallogr. 210 (1995) 269.
[5] A. Meinhart, E. Haussuhl, L. Bohaty, E. Tillmanns, Z. Kristallogr. 216 (2001) 513.
[6] L. Godfrey, J. Philip, J. Appl. Phys. 75 (5) (1994) 2393.
3.2. Polar plots of phase velocity, slowness, Young’s moduli and linear
compressibility
[7] J.E. May Jr., IRE. Natl. Conv. Rec. 6 (part 2) (1958) 134.
[8] E.P. Papadakis, in: W.P. Mason, R.N. Thurston (Eds.), Physical Acoustics, vol. XII,
Academic Press, New York, 1976, p. 227.
The anisotropy of elastic wave propagation in KNH2SO3 single
crystal can be made clear by drawing the phase velocity and
slowness polar plots, Figs. 3 and 4, in the a–b, b–c and a–c planes
following a well known procedure [12,13]. The velocity polar plots
alone cannot completely describe the anisotropy of the elastic
properties of a crystal. The cross sections of Young’s moduli and
[9] H.J. McSkimin, in: W.P. Mason (Ed.), Physical Acoustics, Volume I, Part A,
Academic Press, New York, 1964, p. 271.
[10] H.J. McSkimin, P. Andreatch, Acou. Soc. Am. 34 (1962) 609.
[11] N.F. Nye, Physical Properties of Crystals, Oxford U.P, London, 1957, p. 143.
[12] A.V. Alex, J. Philip, Mater. Sci. Eng. B 90 (2000) 241.
[13] M.J.P. Musgrave, Crystal Acoustics, Introduction to Study of Elastic Waves and
Vibration in Crystals, Holden-Day, SanFrancisco, 1970, p. 61.