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44
3. STUDIES ON POTASSIUM LEAD BROMIDE
SINGLE CRYSTALS
3.1 INTRODUCTION
Ternary alkali lead halide single crystals have become important
because of
their potential applications in acousto-optic and
opto-electronic devices .Lead bromide
crystals hold much promise in applications for acouto-optic
devices in signal
processing and optical spectrum analyzing systems. Single
crystals of this material
have favourable acousto-optical properties, the most significant
of which are its a)
spectral transmission range, (b) photo-elastic co-efficient, (c)
acousto-optic figure of
merit, (d)acoustic velocity and (e) acoustic attenuation ,
although its use has been
hampered by difficulties in growing crystals of high optical
quality. Recently, it has
been found that ternary alkali halide single crystals can be
grown by the melt method
and they become important due to their potential applications.
Monoclinic KPb2Br5
(KPB) is among the most promising bromide host materials because
this material
possesses an incorporation of Nd3+, Tb3+, Dy3+ and Er3+ doping
ions and provides
better homogeneity and quality of doped single crystals [57].
The crystal structure of
KPB, (having spacegroup P21/c, lattice parameters a=8.854(2) Å,
b=7.927(2) Å ,
c=12.485(3) Å , β=90.05(3)Å and Z=4), is shown in Figure 3.1
[124]. Complex
polyhedral coordination by bromine atoms was found for both
potassium and lead
atoms. An important step towards practicality was made when the
rare-earth-doped
alkali-lead halide crystals MPb2Hal5 (M = Rb,K and Hal = Cl, Br)
were identified as
promising new low-phonon-energy host materials for mid-IR
applications.
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45
The present investigation deals with the growth of lead bromide
and potassium
bromide mixed crystals by slow evaporation technique. The grown
crystals (expected
to be KPb2Br5, KPbBr3, K2PbBr4 and K3PbBr5) were subjected to
powder X-ray
diffraction (PXRD), single crystal XRD, AAS, EDAS, SEM, TGA/DTA,
UV-Vis-NIR
spectral and electrical (both AC and DC) measurements. The
results of these
experiments are reported and discussed in this chapter.
Figure 3.1: The crystal structure of KPb2Br5 single crystal
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46
3.2 GROWTH OF SINGLE CRYSTALS
Analytical reagent (AR) grade samples of Lead Bromide (PbBr2),
and
Potassium Bromide (KBr) along with double distilled water were
used for the growth
of Potassium Lead Bromide single crystals. Lead Bromide and
Potassium Bromide
were taken in the ratios 1: 0.5, 1:1, 1:2 and 1:3 dissolved in
double distilled water and
maintained at 80o C for about 60 minutes with continous stirring
to ensure
homogenous temperature and concentration over the entire volume
of the solution.
Temperature as low as 80o C was maintained in order to avoid
decomposition of the
salt. The supersaturated solutions were filtered using 4 micro
watman filter paper.
Then the filtered solutions were kept for free evaporation.
Clear tiny needle like
crystals were obtained in about 20 days. A photograph of the
grown crystals is shown
in Figure 3.2.
3.3 CHARACTERIZATION
The powder X- ray diffraction (PXRD) analysis was carried out
using an X-
ray powder diffractometer (PANalytical) with scintillation
counter and
monochromated CuKα (λ = 1.54056 Å) radiation. The samples were
scanned over the
2θ range 10 - 70° at a rate of one degree/minute. The single
crystal XRD data were
collected using an automated 4-circle diffractometer (Enraf
Nonius CAD4). Atomic
absorption spectra were recorded using Perkin Elmer
spectrophotometer. The UV-Vis-
NIR spectrum was recorded in the range of 190 - 900 nm using a
Shimadzu UV-2400
PC spectrometer. SEM and EDAS analysis were carried out to study
the morphology
and elemental compositions .The thermo gravimetric analysis (TG)
of the crystal was
carried out using an Universal V4.1 DTA Instruments, in the
temperature range from
50 to 700o C in nitrogen atmosphere at a scanning rate of 10
K/min.
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47
The AC conductivity, dielectric constant and dielectric loss of
the samples were
determined to an accuracy of ± 2% using an LCR meter (Agilent
4284A) with five
different frequencies (100 Hz, 1 kHz, 10 kHz, 100 kHz and 1 MHz)
at various
temperatures ranging from 40 –150°C. The measurement of DC
electrical conductivity
was done using the conventional two-probe technique using a
million megohm meter
for temperatures ranging from 40 – 150 °C. The crystals grown
are needle shaped ones
with small thickness. So, crystal portion with sufficient size
cannot be out and polished
for the use of electrical measurements. Hence, in order to make
the electrical
measurements, we have made pellets of the grown crystals and
used as the sample for
the AC and DC electrical measurements. The flat surfaces of the
pellet were coated
with graphite to have a good conductive surface layer.
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48
Figure 3.2: Photograph of the sample crystals grown
[From left are: KPb2Br5 K PbBr3, K2PbBr4 and K3PbBr5 ]
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49
3.4 RESULTS OBTAINED
3.4.1 Single Crystal XRD Analysis
It is observed from the single crystal XRD data that all the
crystals crystallize
in the orthorhombic system except KPbBr3. The KPbBr3 crystal
belongs to the
monoclinic system .The single crystal XRD data for the samples
prepared are
presented in Table 3.1.
3.4.2 Powder X-ray Diffraction Analysis
X-ray diffraction data were collected from powder samples using
an automated
X-ray powder diffractometer. The reflections were indexed using
a homely designed
two theta software [125,126]. Figures 3.3-3.6 show the indexed
XRD patterns.
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50
Table 3.1: Single crystal XRD data for potassium lead bromide
crystals grown in
the present study
Crystallographic
data KPb2Br5 KPbBr3 K2PbBr4 K3PbBr5
a (Å)
b (Å)
c (Å)
4.702
8.002
9.469
12.134
4.317
12.357
4.685
7.991
9.450
4.703
8.032
9.493
α(º)
β(º)
γ(º)
90
90
90
90
100.83
90
90
90
90
90
90
90
Volume (Å3) 356.2 636 353.8 358.6
Crystal system orthorhombic monoclinic orthorhombic
orthorhombic
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51
-
52
-
53
-
54
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55
3.4.3 Atomic Absorption Spectra
The AAS measurements were carried out using a Perkin Elmer
spectrophotometer to determine the K and Pb atom contents in the
grown crystals. The
AAS results are given in Table 3.2, which reveal the presence of
K+ and Pb2+ ions in
the crystals.
3.4.4 Energy Dispersive X-ray Absorption Spectra
The EDAS spectra observed are shown in Figures (3.7-3.10).
Results are
summarized in Table 3.3. The dominant peaks correspond quite
well to the energies of
lead and bromine while a small hemp at 3.2 keV corresponds to K
line of potassium
(reported in the EDAS international chart), giving a clue that
lead is dominant over
potassium in the crystals grown.
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56
Table 3.2: Atomic absorption spectral data
Sample
Atomic content (ppm)
Pb K
KPb2Br5 569290 122
KPbBr3 564784 134
K2PbBr4 567966 170
K3PbBr5 561985 199
Table 3.3: Energy dispersive X-ray absorption spectral data for
potassium lead
bromide crystals
Sample
Atomic % of
Pb K Br
KPb2Br5 21.69 0.63 75.68
KPbBr3 35.92 0.47 63.62
K2PbBr4 31.38 0.23 68.39
K3PbBr5 20.63 0.28 79.09
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57
Fig
ure
3.7
: E
DA
S s
pect
rum
fo
r K
Pb
2B
r 5
-
58
Fig
ure
3.8
: E
DA
S s
pect
rum
fo
r K
Pb
Br 3
-
59
Fig
ure
3.9
: E
DA
S s
pec
tru
m f
or
K2P
bB
r 4
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60
Fig
ure
3.1
0:
ED
AS
sp
ectr
um
fo
r K
3P
bB
r5
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61
3.4.5 Scanning electron microscopic pictures
The quality of the grown crystals can be inferred to some extent
by observing
the surface morphology of the cut and polished crystals. The SEM
image of all the 4
crystal samples observed are shown in Figures 3.11-3.14. It is
observed from SEM
photographs that all the crystals are free from cracks and
significant visible inclusions.
They have rod like morphology.
3.4.6 UV- Visible Absorption Spectra
The observed UV- Visible spectra for the four grown potassium
lead bromide
crystals are shown in Figure 3.15. All the four crystals exhibit
absorption edges at
nearly 370 nm and good transmittance in the visible region. The
transmittance (T) in
the order of T for KPb2Br5 > T for K2PbBr4>T for
K3PbBr5>T for KPbBr3.
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62
Figure 3.11: SEM photograph of KPb2Br5 crystals
Figure 3.12: SEM photograph of KPbBr3 crystals
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63
Figure 3.13: SEM photograph of K2PbBr4 crystals
Figure 3.14: SEM photograph of K3PbBr5 crystals
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64
300 350 400 450 500 550 600 650 700 750
0
1
2
3
4
5
ab
so
rption
(arb
.un
it)
Wavelength(nm)
KPb2Br
5
KPbBr3
K2PbBr
4
K3PbBr
5
Figure 3.15: UV-Vis spectra observed for the grown crystals
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65
3.4.7 Thermal Studies
The thermo gravimetric and differential thermal analysis
[127-129] were
carried out for all the four crystals and the patterns observed
are presented in Figures
3.16 to 3.19. The plots are marked with temperature against
weight loss percentage.
The TGA patterns show that all the grown crystals were thermally
stable up to 500oC.
The exothermic peak at 373oC for KPb2Br5 single crystal
corresponds to the phase
transition [130]. For the remaining crystals the phase
transitions occur at 372.6oC,
373oC and 368oC respectively.
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66
Fig
ure
3.1
6:
TG
/ D
TA
pa
tter
n o
f K
Pb
2B
r 5 s
ingle
cry
sta
l
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67
Fig
ure
3.1
7:
TG
/ D
TA
patt
ern
of
KP
bB
r 3 s
ing
le c
ry
sta
l
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68
Fig
ure
3.1
8 :
TG
/ D
TA
patt
ern
of
K2P
bB
r 4 s
ing
le c
ryst
al
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69
Fig
ure
3.1
9:
TG
/ D
TA
pa
tter
n o
f K
3P
bB
r 5 s
ing
le c
ryst
al
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70
3.4.8 Dielectric Parameters
The dielectric parameters, viz. the εr, tanδ and σac values
obtained in the
present study for the pelletised samples are provided in Tables
3.4 – 3.15 and also
shown in Figures 3.20 to 3.31. They are found to increase with
increasing temperature
for all the four crystals considered in the present study. The
εr and tanδ values decrease
while σac value increase with the increase in frequency of the
applied field. This
shows that all the four crystals grown exhibit the normal
dielectric behavior.
3.4.9 The DC conductivities
Table 3.16 provides the σdc values obtained in the present study
for the
pelletized samples. Also σdc values are shown in Figure 3.32.
The DC electrical
conductivity (σdc) increases, in all the four crystals studied,
smoothly with the
temperature increase through the temperature range considered in
the present study. It
should be noted that the σdc values are more than the σac values
at all temperatures for
all the four potassium lead bromide crystals studied in the
present investigation.
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71
Table 3.4: The dielectric constants for KPb2Br5 crystal
Temp
( °C) εr with frequency
100 Hz 1 kHz 10 kHz 100 kHz 1 MHz
40 7.199 5.797 4.744 4.458 4.384 50 8.008 6.126 4.875 4.503
4.413 60 8.518 6.374 5.000 4.537 4.428 70 9.357 6.636 5.208 4.586
4.449 80 10.953 6.927 5.356 4.639 4.471 90 11.587 7.218 5.583 4.709
4.494
100 12.696 7.434 5.753 4.763 4.507 110 14.920 7.768 5.975 4.835
4.524 120 15.403 7.961 6.111 4.883 4.533 130 15.600 8.041 6.234
4.930 4.538
140 16.242 8.192 6.283 4.951 4.539 150 16.771 8.334 6.295 4.972
4.544
Table 3.5: The dielectric constants for KPbBr3 single
crystal
Temp
( °C) εr with frequency
100 Hz 1 kHz 10 kHz 100 kHz 1 MHz
40 17.212 7.499 4.947 4.397 4.266
50 22.300 8.182 5.187 4.437 4.294
60 28.379 8.976 5.443 4.492 4.317
70 36.756 9.892 5.738 4.559 4.363
80 45.017 10.937 6.045 4.632 4.390
90 54.792 12.392 6.372 4.721 4.419
100 64.096 13.874 6.752 4.809 4.444
110 77.670 15.637 7.185 4.926 4.473
120 87.500 16.959 7.471 5.013 4.495
130 93.903 17.983 7.712 5.083 4.517
140 102.807 19.196 8.037 5.190 4.546
150 109.689 21.429 8.936 5.607 4.682
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72
Table 3.6: The dielectric constants for K2PbBr4 crystal
Temp
( °C)
εr with frequency
100 Hz 1 kHz 10 kHz 100 kHz 1 MHz
40 13.411 8.628 6.203 5.173 5.022
50 16.076 8.892 6.442 5.216 5.043
60 20.723 9.453 6.783 5.317 5.082
70 26.768 10.163 7.096 5.432 5.119
80 33.626 11.097 7.382 5.559 5.153
90 40.324 12.259 7.672 5.700 5.188
100 49.240 13.753 8.039 5.886 5.227
110 56.992 15.027 8.289 6.008 5.261
120 61.957 16.385 8.601 6.181 5.287
130 66.788 17.204 8.819 6.306 5.309
140 74.861 17.599 8.937 6.371 5.333
150 79.357 19.423 9.038 6.406 5.343
Table 3.7: The dielectric constants for K3PbBr5 crystal
Temp
( °C) εr with frequency
100 Hz 1 kHz 10 kHz 100 kHz 1 MHz
40 18.692 8.544 6.324 5.232 5.079
50 22.719 9.191 6.589 5.309 5.098
60 27.792 10.048 6.867 5.418 5.125
70 31.979 11.128 7.113 5.529 5.158
80 40.648 12.453 7.374 5.659 5.179
90 48.268 14.290 7.688 5.823 5.213
100 54.120 16.079 7.988 5.958 5.239
110 61.198 18.356 8.411 6.147 5.284
120 66.568 20.161 8.724 6.267 5.314
130 70.970 21.197 8.994 6.378 5.338
140 77.448 22.872 9.351 6.358 5.377
150 85.364 23.862 9.421 6.571 5.394
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73
Table 3.8: The dielectric loss factors for K Pb2Br5 crystal
Temp
( °C) tanδ with frequency
100 Hz 1 kHz 10 kHz 100 kHz 1 MHz
40 0.236 0.169 0.090 0.023 0.005
50 0.308 0.181 0.109 0.031 0.006
60 0.363 0.187 0.125 0.039 0.008
70 0.442 0.206 0.143 0.048 0.01
80 0.526 0.232 0.159 0.059 0.012
90 0.671 0.283 0.173 0.071 0.016
100 0.805 0.311 0.18 0.081 0.019
110 0.815 0.356 0.192 0.095 0.023
120 0.844 0.382 0.196 0.104 0.026
130 0.940 0.403 0.203 0.114 0.029
140 0.952 0.410 0.208 0.116 0.031
150 1.034 0.428 0.218 0.118 0.032
Table 3.9: The dielectric loss factors for KPbBr3 crystal
Temp
( °C) tanδ with frequency
100 Hz 1 kHz 10 kHz 100 kHz 1 MHz
40 1.668 0.686 0.254 0.053 0.008
50 1.762 0.814 0.309 0.070 0.011
60 1.809 0.958 0.360 0.089 0.014
70 1.936 1.115 0.418 0.110 0.018
80 1.993 1.283 0.476 0.134 0.022
90 2.094 1.474 0.549 0.161 0.028
100 2.228 1.646 0.621 0.189 0.034
110 2.467 1.887 0.716 0.225 0.042
120 2.595 2.078 0.783 0.248 0.048
130 2.810 2.239 0.842 0.266 0.053
140 3.141 2.471 0.931 0.298 0.061
150 3.390 2.703 1.273 0.350 0.075
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74
Table 3.10: The dielectric loss factors for K2PbBr4 crystal
Temp
( °C) tanδ with frequency
100 Hz 1 kHz 10 kHz 100 kHz 1 MHz
40 0.705 0.288 0.202 0.061 0.010
50 0.819 0.370 0.226 0.080 0.012
60 0.926 0.469 0.244 0.099 0.016
70 0.942 0.572 0.264 0.118 0.021
80 0.955 0.683 0.321 0.138 0.026
90 0.982 0.773 0.352 0.157 0.031
100 1.042 0.893 0.357 0.182 0.039
110 1.126 0.981 0.395 0.209 0.047
120 1.304 1.077 0.433 0.220 0.055
130 1.398 1.129 0.456 0.230 0.059
140 1.450 1.154 0.459 0.236 0.061
150 1.503 1.203 0.466 0.239 0.066
Table 3.11: The dielectric loss factors for K3PbBr5 crystal
Temp
( °C) tanδ with frequency
100 Hz 1 kHz 10 kHz 100 kHz 1 MHz
40 0.775 0.414 0.209 0.072 0.010
50 0.803 0.506 0.229 0.090 0.013
60 0.876 0.597 0.255 0.111 0.018
70 0.878 0.674 0.282 0.128 0.023
80 0.900 0.754 0.320 0.146 0.028
90 0.908 0.833 0.371 0.166 0.036
100 0.924 0.878 0.418 0.182 0.043
110 1.101 0.954 0.480 0.204 0.052
120 1.125 0.986 0.531 0.217 0.059
130 1.210 1.019 0.556 0.229 0.065
140 1.264 1.065 0.613 0.246 0.073
150 1.366 1.090 0.631 0.250 0.076
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75
Table 3.12: The AC electrical conductivities for K Pb2Br5
crystal
Table 3.13: The AC electrical conductivities for KPbBr3
crystal
Temp
( °C) σac (x 10
-7 mho/m ) with frequency
100 Hz 1 kHz 10 kHz 100 kHz 1 MHz
40 1.597 2.861 6.989 12.961 18.979
50 2.185 3.704 8.913 17.272 26.272
60 2.855 4.782 10.898 22.233 33.610
70 3.958 6.134 13.339 27.893 43.675
80 4.990 7.804 16.003 34.522 53.714
90 6.381 10.159 19.456 42.273 68.813
100 7.942 12.701 23.320 50.554 84.031
110 10.657 16.410 28.611 61.643 104.478
120 12.628 19.599 32.535 69.140 119.996
130 14.675 22.393 36.115 75.193 133.135
140 17.959 26.381 41.612 86.016 154.211
150 20.681 32.214 63.267 109.147 195.304
Temp
( °C) σac (x 10
-7 mho/m ) with frequency
100 Hz 1 kHz 10 kHz 100 kHz 1 MHz
40 0.094 0.545 2.375 5.703 12.191
50 0.137 0.617 2.955 7.764 14.727
60 0.172 0.663 3.476 9.841 19.703
70 0.230 0.760 4.142 12.243 24.743
80 0.320 0.894 4.736 15.222 29.836
90 0.432 1.136 5.372 18.594 39.994
100 0.568 1.286 5.760 21.456 47.628
110 0.676 1.538 6.380 25.546 57.875
120 0.723 1.691 6.662 28.242 65.552
130 0.816 1.802 7.038 31.257 73.188
140 0.860 1.868 7.269 31.942 78.254
150 0.964 1.984 7.632 32.631 80.878
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76
Table 3.14: The AC electrical conductivities for K2PbBr4
crystal
Temp
( °C) σac (x 10
-7 mho/m ) with frequency
100 Hz 1 kHz 10 kHz 100 kHz 1 MHz
40 0.526 1.382 6.969 17.551 27.928
50 0.732 1.830 8.097 23.208 33.659
60 1.067 2.466 9.204 29.276 45.219
70 1.402 3.233 10.418 35.650 59.785
80 1.786 4.215 13.178 42.669 74.518
90 2.202 5.270 15.019 49.770 89.451
100 2.854 6.830 15.961 59.574 113.367
110 3.569 8.199 18.210 69.839 137.522
120 4.493 9.814 20.712 75.629 161.729
130 5.193 10.802 22.365 80.658 174.220
140 6.037 11.295 22.815 83.623 180.917
150 6.633 12.995 23.425 85.144 196.134
Table 3.15: The AC electrical conductivities for K3PbBr5
crystal
Temp
( °C) σac (x 10
-7 mho/m ) with frequency
100 Hz 1 kHz 10 kHz 100 kHz 1 MHz
40 0.806 1.967 7.351 20.949 28.250
50 1.015 2.587 8.392 26.576 36.857
60 1.354 3.336 9.738 33.449 51.305
70 1.562 4.171 11.155 39.359 65.976
80 2.035 5.222 13.124 45.954 80.656
90 2.438 6.620 15.864 53.762 104.368
100 2.781 7.851 18.571 60.311 125.287
110 3.747 9.739 22.452 69.738 152.827
120 4.165 11.056 25.765 75.630 174.366
130 4.776 12.013 27.811 81.227 192.962
140 5.443 13.547 31.878 86.984 218.312
150 6.485 14.465 33.060 91.356 227.988
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77
40 60 80 100 120 140 160
4
6
8
10
12
14
16
18 100 Hz 1kHz 10kHz 100kHz 1MHz
εε εε r
Temperature(oC)
Figure 3.20: Temperature dependence of dielectric constant
for KPb2Br5 crystal for various frequencies
40 60 80 100 120 140 160
0
20
40
60
80
100
100 Hz 1kHz 10kHz 100kHz 1MHz
εε εε r
Temperature(oC)
Figure 3.21: Temperature dependence of dielectric constant
for KPbBr3 crystal for various frequencies
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78
40 60 80 100 120 140 160
0
10
20
30
40
50
60
70
80
100 Hz
1kHz
10kHz
100kHz
1MHz
εε εε r
Temperature(oC)
Figure 3.22: Temperature dependence of dielectric constant
for K2PbBr4 crystal for various frequencies
40 60 80 100 120 140 160
10
20
30
40
50
60
70
80
90 100 Hz
1kHz
10kHz
100kHz
1MHz
εε εε r
Temperature (oC)
Figure 3.23: Temperature dependence of dielectric constant
for K3PbBr5 crystal for various frequencies
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79
40 60 80 100 120 140 160
0.0
0.2
0.4
0.6
0.8
1.0
tanδδδδ
Temperature(oC)
100 Hz 1kHz 10kHz 100kHz 1MHz
Figure 3.24: Temperature dependence of dielectric loss
factor
for KPb2Br5 crystal for various frequencies
40 60 80 100 120 140 160
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
Temperature(o C)
B B B B B
tan
δδ δδ
Temperature(o C)
Figure 3.25: Temperature dependence of dielectric loss
factor
for KPbBr3 crystal for various frequencies
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80
40 60 80 100 120 140 160
0.0
0.4
0.8
1.2
1.6 100 Hz
1kHz
10kHz
100kHz
1MHz
tan δδδδ
Temperature(o C)
Figure 3.26: Temperature dependence of dielectric loss
factor
for K2PbBr4 crystal for various frequencies
40 60 80 100 120 140 160
0.0
0.3
0.6
0.9
1.2
1.5 100 Hz
1kHz
10kHz
100kHz
1MHz
tan δδ δδ
Temperature(oC)
Fig 3.27: Temperature dependence of dielectric loss factor
for K3PbBr5 crystal for various frequencies
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81
40 60 80 100 120 140 160
0
10
20
30
40
50
60
70
80
90
σσ σσac
Temperature(oC)
100 Hz
1kHz
10kHz
100kHz
1MHz
Figure 3.28: The AC electrical conductivities (x10-7
mho/m)
for K Pb2Br5 crystal for various frequencies
40 60 80 100 120 140 160
0
30
60
90
120
150
180
210 100 Hz 1kHz 10kHz 100kHz 1MHz
σσ σσac
Temperature(oC)
Fig 3.29: The AC electrical conductivities (x10-7
mho/m)
for KPbBr3 crystal for various frequencies
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82
40 60 80 100 120 140 160
0
30
60
90
120
150
180
210
Temperature(oC)
100 Hz
1kHz
10kHz
100kHz
1MHz
σσ σσac
Fig 3.30: The AC electrical conductivities (x10-7
mho/m)
for K2PbBr4 crystal for various frequencies
40 60 80 100 120 140 160
0
50
100
150
200
250
Temperature(oC)
σσ σσac
Fig 3.31:The AC electrical conductivities (x10-7
mho/m)
for K3PbBr5 crystal for various frequencies
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83
Table 3.16: The DC electrical conductivities for potassium lead
bromide crystals
Temperature
(o C)
σσσσdc ( x 10-5
mho / m ) for
K Pb2Br5 KPbBr3 K2PbBr4 K3PbBr5
40 4.990 7.885 7.769 7.764 50 5.106 7.900 7.809 7.814
60 5.166 7.935 7.950 8.156
70 5.196 7.955 7.965 8.191
80 5.271 7.975 7.990 8.226
90 5.402 7.990 8.035 8.246
100 5.533 8.005 8.819 8.256
110 5.668 8.015 9.317 8.538
120 5.759 8.020 9.382 8.749
130 6.975 8.030 9.533 8.809
140 7.417 8.040 9.568 8.920
150 7.548 8.091 9.875 9.312
40 60 80 100 120 140 160
5
6
7
8
9
10
σσ σσdc
Temperature(oC)
KPb2Br
5
KPbBr3
K2PbBr
4
K3PbBr
5
Figure 3.32: The DC electrical conductivities (x10-5
mho/m)
for potassium lead bromide crystals
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84
3.5 DISCUSSION
All the four single crystals (KPb2Br5, KPbBr3, K2PbBr4 and
K3PbBr5 as per the
initial composition considered for crystallization) grown are of
needle shape. The
grown crystals show considerable transparency and mechanical and
thermal stabilities.
Growth of high quality crystals with uniform composition is of
great
importance for high performance devices manufacturing. Among the
requirements to
crystal properties, well-defined composition, macro- and micro-
uniformity should be
mentioned in the first instance. For example, in electronic and
optoelectronic
applications the quality of the active epilayers often depends
directly on the chemical
homogeneity of the substrate. In case of quasibinary solid
solutions (A1-xBx)1-sX1+s,
the composition is characterized by the mole fraction x (which
defines the energy band
gap) and the deviation from stoichiometry δ (which influences
the carrier
concentration) [133]. It should be noted that in the case of
lead chalcogenides, the
deviation from stoichiometry can be effectively controlled by a
post -growth annealing
under Pb or chalcogen vapour, whereas the x value should be
fixed during the growth
process. Axial or radial segregation, both at the macroscopic
and the microscopic
scale, is one of the major factors limiting the yield of bulk
crystals grown from the
melt or from the vapour. Besides, it should be mentioned that
essential axial and radial
segregation causes noticeable increase of the dislocation
density in the grown crystals.
The crystals of alloys are frequently subjected to serious
distillation-like (i.e.,
thermodynamically imposed) segregation [134] leading to
essential variation in
composition between the initially and finally grown fragments of
the crystals, which
restricts the applicability of the obtained materials for the
device manufacturing.
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85
Shtanov and Yashine [133] have illustrated using
(Pb1-xSnx)1-δSe1+δ solid solutions as
an example the application of T-x-y phase diagram for the
control of the crystal
composition of alloy crystals during Bridgman growth.
The alloying of two or more metals has always been
systematically used in
order to modify and improve the properties of the metallurgical
materials. The mixing
of ionic solids has been equally investigated in the purpose of
obtaining new materials
with specific properties. A very important situation that is
special to ionic crystals
arises when these crystals are doped (or added) with impurities.
The behavior depends
on the valence state of impurity ions. When an ion like Ca2+
replaces a Na+ ion in
NaCl crystal it results in the creation of a positive ion
vacancy or a negative ion
interstitial. Anion impurities also produce corresponding charge
compensating point
defects. Whether an impurity ion goes to substitutional position
or interstitial position,
is determined by the ionic radius of the doped (or added) ion
and also on the electronic
configuration of the ion. If the impurity ion behaves in the
same way as the lattice ion,
a wide range of solubility may be possible. To describe this,
the term ‘mixed crystal’ is
used. It should be realized, however, that the impurity ions are
all distributed at
random throughout the lattice so that the term ‘solid solution’
is more appropriate.
Two compounds or elements are said to form a continuous solid
solution if a
single lattice parameter as measured by X-ray powder diffraction
patterns, can be
assigned to the solid solution at all compositions. In the
continuous solid solutions of
alkali halides, Retger’s law (additivity of molar volumes) [135]
and Vegard’s law
(linear variation of lattice parameter with composition) [136]
are closely followed as
indicated by X-ray diffraction studies.
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86
Potassium and lead halides are soluble in water. It is possible
to grow, in
certain cases, mixed crystals by evaporation of aqueous
solution. However, the melt
technique is the commonly employed technique to grow mixed
crystals.
Tobolsky [137] showed that for ionic crystals like alkali
halides, complete
miscibility is possible only above a particular temperature
given by T=4.5δ2, where δ
being the percentage deviation in the lattice parameter. As per
this, alkali halide
solutions have got only limited miscibility at room
temperature.
Vertical Bridgman technique (melt technique) is mostly used for
growing
single crystals of alkali lead halides and alkali halides. At
temperatures nearer to the
freezing point, the crystals are observed to be fairly
transparent. When the crystals are
cooled from high temperature to the room temperature in a
relatively short time the
transparency of the crystals is found to be reduced and becoming
white. This is partly
due to the introduction of thermal defects since the rate of
cooling is high.
Transparency can be improved by reducing the rate of cooling and
consequently
reducing the introduction of thermal defects. In this situation,
growth of crystals by
the solution methods at near ambient temperatures can be
considered to be useful.
A3MX5.2H2O (where A is a univalent cation, M is a divalent metal
and X is a
halogen) crystals exhibit unusual physical properties. They have
attracted a great deal
of attention owing to the occurrence of varying stoichiometries
in these compounds
[138]. A3MX5.2H2O crystals are closely related to A2MX4 and both
represent the
largest known group of insulating crystals with structurally
incommensurate phases
[139]. Byrappa et al [140] have mentioned that no detailed X-ray
crystal structure
(refinement) is available for A3MX5.2H2O type crystals. However,
Krishna kumar et al
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[141], without giving any experimental details, have described
in brief the crystal
structure of Na3BaCl5. 2H2O crystals. The structure described by
them is as shown in
Figure 3.33. The Na3BaCl5. 2H2O crystals consist of metal ions
such as Na and Ba,
Cl- ions and two H2O molecules. The chlorine atoms lie at the
vertices of trigonal
bipyramidal geometery. Three Cl- ions form electrovalent bonds
between the adjacent
Na+ and central Ba2+ ions. This bond is naturally the attractive
electrostatic force
existing between positive and negative ions when they are
brought into a closer
distance. The two H2O molecules are stacked diagonally up and
down, which may
have a linkage with the adjacent Na+ ions.
Figure 3.33: Crystal structure of Na3BaCl5.2H2O
Manonmani et al [142,143,113] have attempted to grow from
aqueons
solutions by the slow (free) evaporation of solution method
single crystals of
(composition considered in the solution) K3BaCl5.2H2O,
K3CaCl5.2H2O, and
Na3CaCl5.2H2O and characterize them. They have confirmed by
experimental means
(XRD, TGA, AAS and FTIR and Raman spectroscopic measurements)
that non
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88
stoichiometry is present in all these crystals grown. These
compositions were
estimated as K3.088 Ba0.912Cl4.832.1.369H2O for
K3BaCl5.2H2O,
K3.611Ca0.389Cl4.389.1.177H2O for K3CaCl5.2H2O and Na3.665
Ca0.335 Cl4.335.0.153H2O
for Na3CaCl5.2H2O. The variation of DC electrical conductivity
with temperature
observed by them indicates that KCl-BaCl2 is a dielectric
material while the others
(KCl-CaCl2 and NaCl-CaCl2) are ionic conductors. Less non
stoichiometry retains the
dielectric nature (usual for ionic substances) and higher non
stoichiometry leads to
ionic conductors.
Keller [144] has reported that orthorhombic symmetry is shown by
single
crystals of K2PbBr4.H2O: a=8.537 Å, b=13.083Å,c=4.594Å. Z=2,
space group
222 11P . He has demonstrated the analogy between the crystal
structure of
K2PbBr4.H2O and KPb2Br5 by group – subgroup relations of space
groups.
Iwadate et al [145] investigated the complex formation and ionic
aggregation in
PbBr2-NaBr and PbBr2-KBr melts by Raman spectroscopy with
supplementary use of
molecular orbital calculations (MO). Their results suggest that
there existed PbBr42-
complex ions in the mixture melts, which might not form further
clustering or
network.
Kusumoto et al [146] have mentioned that as PbBr2 hardly
dissolves in water
(0.97g/100g water), it is not suitable for aqueous solution
growth. So, they have grown
PbBr2 single crystals in silica gel and obtained the following
results: i) Transparent
PbBr2 single crystals were obtained in a high-acidic gel, ii)
sizable single crystals of
PbBr2 were also grown in the liquid placed over a gel because
the gel barrier had the
task of slowing down the diffusion rate of reacting ions. Also,
they have mentioned
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89
that it was difficult for them to grow a PbBr2 crystal of
optical high quality from the
melt even though they used a 99.999% purity material.
Rademaker et al [72] observed that the KPb2Br5 (KPB) crystal
grown by the
Bridgman (melt) method is biaxial and has a monoclinic crystal
structure with a space
group symmetry cP /21 . From an X-ray single–crystal diffraction
study of KPB, they
determined the lattice parameters to be a=9.256 (2) Å, b=8.365
(2) Å, c=13.025 (3) Å
and β=90.00 (3) , Z=4. These values were obtained for crystals
evidencing substantial
micro twinning. For crystals with no twinning structures, the
given lattice parameters
will change, but further research is needed to clarify this
situation. Determined from
lattice constants, the density was found to be 5.62g/cm3 which
matched with that
available in other literature, 5.60g/cm3 [91]. Rademaker et al
[72] also have observed
a phase transition in KPB at a temperature of 249°C which
matched with that of 242°C
reported in other literature [89,91].
Hommerich et al [147] have investigated KPb2Br5 (KPB) as a
potential new
solid state laser host material. The fundamental absorption edge
of KPB is located at
~400nm. At longer wavelength the transmission ranged between
~75-77% without
any significant absorption features.
According to Beck et al [90] KPb2Br5 (KPB) is monoclinic (space
group
cP /21 ) with an angle β very close to 90°. The unit cell
parameters are a=9.264,
b=8.380, c=13.063 Å and β=90.06°; Z=4. Pb2+ ions occupy two
non-equivalent lattice
sites of low symmetry, one site is a distorted octahedron and
the second site is a
distorted trigonal prism.
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90
Lead bromide belongs to the orthorhombic symmetry class D2h and
mmm
space group [148]. The lattice parameters are: a=8.0620(1)Å,
b=9.53930(13) Å and
c=4.73480(6)Å. V=364.134Å3, Z=4, ρ=6.695gcm-1. PbBr2 exhibits
extraordinary
properties, including a very large optical transparency range,
an anomalously slow
longitudinal wave velocity in the [010] direction, a large
birefringence and a high
figure of merit (M2-550, about twelve times higher than that of
PbMoO4). Therefore
this material has good application potential, especially for
infrared devices where large
diffraction efficiencies are needed. Crystals were grown by the
vertical Bridgman
method.
Singh et al [49] observed that lead bromide crystals severely
cracked during the
cool down period after the growth, due to destructive phase
transformation. The
energy of phase transformation was suppressed by silver doping
and large crystals
were grown from the melt. The acoustic attenuation constant, an
important parameter
for the devices, was almost identical for doped (below 3000 ppm)
and undoped
crystals.
In the present study, the results obtained through X-ray
diffraction, AAS and
EDAS measurements indicate the absence of proper mixing of KBr
and PbBr2 in all
the four potassium lead bromide crystals grown. The grown
crystals may be
considered as K+ doped PbBr2 single crystals. However, the
thermal stability and the
temperature at which the phase transition occurs in all the four
crystals studied are
similar. The phase transition occurs at ~370°C (see section
3.4.7) which is largely
deviated from that observed for KPb2Br5 crystals grown by the
melt method (~245°C)
[16-18]. Singh et al [49] have presented a solid/solid phase
transformation observed
by DTA in PbBr2 at 365°C. So, the results obtained in the
present study through
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91
thermal analysis also evidence the formation of KBr added PbBr2
crystals and not the
proposed mixed crystals. So, the chemical formulae used to
represent the grown
potassium lead bromide crystals are not correct. However, we use
here as the sample
representation. Since the initial composition used for the
growth of crystal is the same.
The lattice parameters obtained in the present study for
KPb2Br5, K2PbBr4 and
K3PbBr5 are nearly same with the orthorhombic crystal system.
However, the lattice
parameters obtained for KPbBr3 are highly deviated and also with
a different crystal
system (monoclinic). This may be due to lattice distortion which
is evident from the
considerably lower Br- and higher Pb2+ contents when compared to
the other three
crystals considered (see table 3.3).
The optical absorption edges observed for all the four potassium
lead bromide
crystals grown in the present study are nearly 370 nm which is
significantly less than
that observed for the melt grown KPb2Br5 (~400 nm) [147]. Like
PbBr2 crystal, the
four crystals considered in the present study exhibit a large
optical transparency.
Moreover, the transmittance observed is significantly more than
that observed for
PbBr2 [148]. Even though they are not properly mixed potassium
lead bromide
crystals, all the four single crystals grown in the present
study exhibit superior optical
characteristics required for acousto-optical (AO) devices. The
large optical
transparency range of these crystals is very useful for wide
band or multiple band AO
tuneable filters (AOTF) applications.
The intrinsic point defects in lead bromide are supposed to be
either of the
Schottky or of the Frenkel type. Tubandt et al [149] concluded
from transport
measurements that the electric current in lead bromide is
carried exclusively by the
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92
bromine ions. Therefore it is not necessary to consider the
lattice defects in the lead
ion sub-lattice as charge carriers. The crystal structure of
lead bromide was
determined by Brackken and Harang [150] and by Nieuwenkamp [151]
and shown a
coordination structure formed by a disturbed hexagonal packing
of bromine ions
between which the lead ions are placed. These lead ions are
surrounded by 9 bromine
ions at different distances (3.0 to 4.1 Å). In lead bromide the
ions at interstitial sites
might occur only in the mirror planes (100)0 and *
21)100( , while in the neighbourhood
of the gliding mirror planes at (001)1/4 and *
43)001( bromine ions at 4.1 Å have left
enough space for ions with a radius of at most 0.94 Å.
The Pauling radii of bromine and lead ions are 1.95 and 1.21Å,
respectively, so
we may disregard the occurrence of interstitial bromine and lead
ions and so we
consider anion and cation vacancies to be the only intrinsic
point defects in lead
bromide. According to a Schottky mechanism their thermal
generation is given by
−+ +⇔BrPb
VVO 22 ,
where VPb2+, VBr
- denote a missing lead ion at a lead ion site and a missing
bromine
ion at bromine ion site, respectively, and O denotes the perfect
lattice.
We assume that the foreign ions keep their normal valency
states. The electro-
neutrality condition upon doping with monovalent cations Me+,
divalent ions A2-, or
trivalent cations Me3+, according to the Koch and Wagner system
is then given by
][][][2][][ 223 −+
++
−++=+ AMeVMeV
PbBr
,
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93
where square brackets denote concentrations. Upon doping with
monovalent
cations in concentrations well above those of the intrinsic
lattice defects this relation
becomes
][][ +−
= MeVBr
All foreign ions have radii greater than 0.94Å, so in all cases
the bromine ion
vacancies are to be considered to carry the electrical current
in lead bromide [152]. In
the case of potassium doped PbBr2 crystals the K+ ions may not
occur at interstitial
sites since the Pauling radius of the monovalent potassium ion
is 1.51Å.