Advances in Materials Physics and Chemistry, 2011, 1, 31-38
doi:10.4236/ampc.2011.12006 Published Online September 2011 (http://www.SciRP.org/journal/ampc)
Temperatur e and Orientation Dependence of
Ultrasonic Parameters in Americium Monopnictides
Devraj Singh1*, Raj Kumar2, Dharmendra Kumar Pandey3
1Department of Appli e d Sci en ces , Amity School of Engineering and Technology, New Delhi, India
2Department of Physics, NIMS University, Jaipur, Indi a
3Department of Physics, P.P.N. P.G. College, Kanpur, India
*
Received June 28, 2011; revised July 30, 2011; accepted August 10, 2011
Abstract
The temperature dependence of the ultrasonic parameters like ultrasonic velocities and Grüneisen parameters
in americium monopnictides AmY (Y: N, P, As, Sb and Bi) have been studied for longitudinal and shear
waves along <100>, <110> and <111> crystallographic directions in the temperature range 100 K - 500 K.
The second- and third- order elastic constants have also been evaluated for these monopnictides using Cou-
lomb and Born-Mayer potential. The values of elastic constants are the highest for AmN. Hence the me-
chanical properties of AmN are better than other monopnictides AmP, AmAs, AmSb and AmBi. Ultrasonic
velocity is found large for AmP. So the ultrasonic wave propagation will be much better than others in AmP.
Obtained results are compared with available results of same type of materials.
Keywords: Americium Monopnictides, Coulomb and Born-Mayer Potential, Elastic Constants, Ultrasonic
Velocity, Grüneisen Parameters
1. Introduction
Generally, a crystalline material has anisotropic proper-
ties. Properties such as thermal expansion and conduc-
tion, temperature dependence specific heat, temperature
and pressure variation of elastic constants, damping of
high frequency acoustic waves and damping of moving
dislocations by phonon viscosity are determined by the
intrinsic nonlinearity of solids. This emphasizes the im-
portance of non-linear characteristics of solids. Recent
developments in the experimental capabilities and theo-
retical understanding have provided further impetus to
the study of the non-linearity in solids [1].
Wave velocity is a key parameter in u ltrasonic charac-
terization and can provide information about crystallo-
graphic texture. The ultrasonic velocity (V) is related to
the elastic constant by the relatio n

The Grüneisen parameter is of considerable impor-
tance to Earth’s scientists, because it sets limitations on
the thermoelastic properties of lower mantle [3]. The
study of Grüneisen parameters for a solid enable us to
describe and discuss various physical properties of a
system such as high temperature specific heats of lattice,
thermal expansion, thermal conductivity and temperatur e
variation of the elastic constants. The Grüneisen para-
meters play a significant role in study of thermoelastic
properties. It has fundamental importance to the equation
of state and related to thermodynamic properties of the
solids [4]. The calculation of anharmonic effects in solids
such as thermal expansion or the interaction of acoustic
and thermal phonons involves Grüneisen parameters,
which describe the volume and strain dependence of the
lattice vibrational frequencies. In the Debye model, these
vibrations are replaced by standing wave modes of a
dispersionless elastic continuum. The Grüneisen pa-
rameters are then no longer frequency dependent an d can
be expressed in terms of second- and third- order elastic
constants [5].

V= C

, where C
is the relevant elastic constant and  is the density of that
particular material. Particularly, the elastic constant pro-
vides valuable information on stability and stiffness of
the materials. The elastic constant of solids also prov ides
a link between the mechanical and dynamical behaviours
of crystals and gives important information concerning
the nature of forces operating in solids [2].
Yet, the americium monopnictides have not been in-
vestigated in detail, but few studies are found elsewhere
[6-10]. The ground state and optical properties of ameri-

D. SINGH ET AL.
32
cium monopnictides were investigated theoretically by
Ghosh et al. [6]. The crystal structure of AmAs, AmSb
and AmBi were determined by Roddy [7]. The 237Np
emission spectra in 241Am: AmO2, AmAs and AmBi
sources have been reported by Friedt et al. [8]. The
preparation and XRD of AmBi have been made by Gib-
son and Haire [9]. Petit et al. calculated the electronic
structure of Am monopnictides with the help of ab-initio
self-interaction-correlated local spin density approxima-
tion [10] .
Ultrasonic study is non-destructive in nature and is
helpful for the determination of inherent properties of
materials. The elastic constants of materials are directly
related to their microstructure and are used to obtain the
Debye average velocity, Grüneisen parameter (GP) and
other physical properties; and therefore, these are of
great interest in applications where the mechanical
strength and durability are important. To the best of our
knowledge, no experimental or theoretical reports on
ultrasonic velocity and Grüneisen parameters on these
materials have been seen in the literature. The grounds
mentioned abov e motivate us to choose th ese compou nds
for characterization through ultrasonic non-destructive
evaluation technique. For which, we performed theoreti-
cal investigation of elastic constants, ultrasonic velocities
and Grüneisen parameters in Am monopnictides along
<100>, <110> and <111> direction s at temperatu re r ange
100 K - 500 K. The results provide reference data for
experimentali st s an d op en a new basi s for further study.
2. Theory
The theory is categorized into three phases. In the first
phase, temperature dependence of second- and third-
order elastic constants (SOEC and TOEC) has been dis-
cussed while temperature dependence ultrasonic velocity
along different directions has been described in second
phase. Temperature dependent Grüneisen parameters
along <100>, <110> and <111> orientations have been
clarified in the final phase.
2.1. Temperature Dependence of Higher Order
Elastic Constants
Elastic properties of a solid are important because they
relate to various fundamental solid-state properties such
as interatomic potentials, equation of state and phonon
spectra. Elastic properties are also linked thermody-
namically to the specific heat, thermal expansion, Debye
temperature, melting po int and Grüneisen parameter. So,
it is important to calculate elastic constants of solids.
From the calculated elastic constants one can derive the
anisotropy in the elastic properties.
The elastic energy density (U) is function of th e strain
components.




xxyy zzyz zxxy12 3 4 5 6
UFe,e,e,e ,e,eFe,e,e,e,e,e
(1)
where eij (i or j = x, y, z) is component of strain tensor.
The second (CIJ) and third (CIJK) order elastic constants
of material are defined by following expressions:
2
IJ IJ
U
C; I or J1,
ee


 ,6 (2)
3
IJK IJK
U
C; I or J or K1,,6
eee


  (3)
The elastic energy density is well related to interaction
potential


r  between atoms. The potential used for
evaluation of SOEC and TOEC is taken as sum of Cou-
lomb and Born-Mayer potentials.






rC   B (4)
where


C  is electrostatic/Coulomb potential and


B 
is the repulsive/Born-Mayer potential, given as




er 
2
C and


BAexprb  

. Here “e” is
electronic charge, “r” is the nearest neighbour distance,
“b” is the hardness parameter and “A” is the strength
parameter.
According to lattice dynamics developed by Leibfried
and Ludwig [11] & Mori and Hiki [12], lattice energy
changes with temperature. Hence, the addition of vibra-
tional energy contribution to static elastic constants, one
gets second and third order elastic constants (CIJ and CIJK)
at required temperature.
0 Vib0Vib
IJIJ IJIJKIJK IJK
CCC and CCC (5)
where superscript 0 has been used to denote SOEC and
TOEC at 0 K (static elastic constants) and superscript
Vib has been used to denote vibrational part of SOEC
and TOEC at a particular temperature. The expressions
of and are given in our previous pap er [2].
IJ
CIJK C
2.2. Orientation Dependence of Ultrasonic
Velocities
When sound wave propagates through a crystalline me-
dium, there is three mode of propagation: one longitudi-
nal acoustical (LA) and two transverse acoustical (TA).
Thus, there exist three types of velocities as one long itu-
dinal (VL) and two shear (VS1 and VS2). These velocities
depend on the direction of propagation of wave [13]. The
expressions for direction dependent ultrasonic velocities
in cubic crystals are as follows:
Along <100> crystallo graphic direction;
11 44
LS1S2
C
V ; VV
dd






C
(6)
Along <111> crystallo graphic direction;

33 D. SINGH ET AL.
11124411 1244
LS1S2
C2C4C CCC
V ; VV
3d 3d

 





(7)
Along <110> crystallo graphic direction;
11 12444411 12
LS1S2
CC2C CCC
V; V; V
2dd d

 





(8)
The ultrasonic ve locities can be worked out using cal-
culated values of second order elastic constants. The
Debye average veloc ity (VD) is useful for information of
Debye temperature and thermal relaxation time of the
materials. The following expressions have been used for
evaluation of Debye average velocity [13].
1/3
D33
LS1
1/3
33 3
LS1S2
along 100
11 2
V;
and111direction 3VV
11 11
;along110direction
3VVV




 



  




  




 

 
 

 

(9)
2.3. Orientation Dependence of Ultrasonic
Grüneisen Parameters
A number of anharmonic properties of solids are fre-
quently expressed in terms of Grüneisen parameters that
are expressed in quasiharmonic approximation as diverse
weighted averages of Grüneisen tensor of the first order:

j1
ii
q



 

 . For example, the thermal ex-
pansivity is relative to the specific heat weighted
j
qq
C
 
 
q,i,i,iq,i
C, which is thermal
Grüneisen parameter
 . The shear (ultrasonic) Grüneisen
parameter can be suitably expressed by thermal conduc-
tivity weighted averages of the product jj



 [14].
Brugger derived expressions for the components of
Grüneisen tensor in terms of second- and third- order
elastic constants of an anisotropic elastic continuum [15].
These relations permit the above weighted average to be
reliably calculated from elastic and thermal data. The
comparison of ultrasonic attenuation and non-linear pa-
rameters evaluated with help of them, justifies the ex-
pression of Grüneisen parameters [16]. Formulae of
Grüneisen parameters along different crystallographic
directions are given in literature [17].
3. Results and discussion
The second- and third- order elastic constants (SOEC and
TOEC) have been evaluated using two basic parameters i.e.,
lattice parameter and hardness parameter. The lattice pa-
rameters [6-10] for AmN, AmP, AmAs, AmSb and AmBi
are 4.825 Å, 5.432 Å, 5.592 Å, 6.003 Å and 6.076 Å re-
spectively and the values of hardness parameter are 0.293 Å,
0.301 Å, 0.302 Å, 0.303 Å and 0.271 Å for AmN, AmP,
AmAs, AmSb and AmBi respectively. The computed re-
sults of temperature dependent SOEC and TOEC are listed
in Table 1. We found no experimental/theoretical result of
SOEC and TOEC of these materials directly in existing
literature. So, we have compared our results with NaCl-type
rare-earth monochalcogenides [18].
It is clear from the Table 1 that, out of nine elastic
constants, four (i.e., C11, C44, C112 and C144) are decreas-
ing and other four (i.e., C12, C111, C166 and C123) are in-
creasing with the temperature while C456 is found to be
unaffected. The increase or decrease in stiffness con-
stants is due increase or decrease in atomic interaction
with temperature. If inter-atomic distance increases or
decreases with temperature then interaction potential
decreases/increases, which causes decrease or increase in
stiffness constants. This type of behaviour has been
found already in other NaCl-type materials like gadolin-
ium and cerium monopnictides [18,19]. The comparison
justifies our calculations of second and third order elastic
constants. There are no elastic data as a function of tem-
perature for these compounds in literature. Most simple
theories are able to get a reasonable estimate of elastic
constants at room temperature only by using experimen-
tal parameters. Table 1 depicts that AmN has highest
valued SOEC and TOEC in contrast to other monopnic-
tides. Hence mechanical influence of AmN is better than
AmP, AmAs, AmSb and AmBi.
The stability of a cubic crystal is exp ressed in terms of
elastic constants as:
111211 12
T44S
C2C CC
B0, C0 and C0
32


 .
CIJ are the conventional elastic constants, BT is the bulk
moduli. The quantities C44 and CS are the shear and
tetragonal moduli of a cubic crystal. Estimated values of
bulk, shear and tetragonal moduli for AmN, AmP, AmAs,
AmSb and AmBi at room temperature are presented in
Tables 1-2 that satisfies the above stability criterion for
these materials.
The ultrasonic velocity is a key factor to characterize
the properties of material. It is directly related to SOEC
and density of that particular material as shown in Eqs.
(7-9). The evaluated velocities for longitu dinal and shear
waves are presented in Table 3 and the Debye average
velocities are shown in Figures 1-3.
It can be seen that the velocities of the chosen materi-
als along longitudinal and shear waves increase with
increase in temperature. The Debye average velocity of
these materials is found to increase with temperature. It
is also observed th at it is large along <111> direction and

D. SINGH ET AL.
34
Tabl e 1. Second- and third- order elastic constants of AmY at the temperature range 100 K to 500 K in the unit of 1011 Dyne/cm2.
Material Temp (K) C11 C
12 C 44 C 111 C 112 C 123 C 144 C 166 C 456
100 7.15 2.40 2.51 –104.4 –9.87 3.52 4.05 –10.29 4.02
200 7.30 2.31 2.52 –109.8 –9.56 3.01 4.08 –10.32 4.02
300 7.50 2.21 2.53 –110.6 –9.23 2.50 4.11 –10.35 4.02
400 7.71 2.11 2.54 –111.5 –8.90 2.00 4.14 –10.39 4.02
AmN
500 7.93 2.02 2.55 –112.5 –8.60 1.49 4.16 –10.43 4.02
100 5.28 1.32 1.41 –85.84 –5.35 1.86 2.37 –5.72 2.35
200 5.42 1.24 1.41 –86.31 –5.05 1.37 2.39 –5.74 2.35
300 5.59 1.16 1.42 –87.09 –4.74 0.88 2.41 –5.76 2.35
400 5.77 1.07 1.42 –87.98 –4.42 0.39 2.42 –5.79 2.35
AmP
500 5.96 0.99 1.43 –88.92 –4.10 –0.10 2.44 –5.81 2.35
100 4.94 1.16 1.24 –81.50 –4.68 1.61 2.12 –5.04 2.10
200 5.08 1.08 1.25 –82.02 –4.38 1.12 2.13 –5.05 2.10
300 5.31 1.00 1.25 –83.60 –4.07 1.07 2.15 –5.08 2.10
400 5.43 0.92 1.26 –83.83 –3.75 0.14 2.16 –5.10 2.10
AmAs
500 5.61 0.84 1.26 –84.77 –3.43 –0.35 2.18 –5.12 2.10
100 4.33 0.88 0.96 –73.87 –3.50 1.16 1.66 –3.84 1.65
AmSb 200 4.47 0.80 0.96 –74.50 –3.19 0.66 1.68 –3.86 1.65
300 4.66 0.72 0.96 –75.97 –2.86 0.15 1.69 –3.87 1.65
400 4.80 0.65 0.97 –76.25 –2.56 0.33 1.70 –3.89 1.65
500 4.97 0.58 0.97 –77.19 –2.25 0.13 1.71 –3.91 1.65
100 5.10 0.76 0.86 –93.99 –2.90 0.83 1.56 –3.38 1.55
200 5.28 0.67 0.86 –94.83 –2.46 0.12 1.57 –3.39 1.55
300 5.48 0.58 0.86 –95.96 –2.02 –0.60 1.58 –3.40 1.55
400 5.69 0.48 0.87 –97.25 –1.57 –1.32 1.59 –3.41 1.55
AmBi
500 5.89 0.39 0.87 –98.45 –1.13 –2.03 1.60 –3.43 1.55
Table 2. Bulk moduli (BT) and tetragonal moduli (CS) of
AmY at room temperature in the unit of 1011 Dyne/cm2.
Material BT C
S
AmN
AmP
AmAs
AmSb
AmBi
3.97
2.63
2.44
2.04
2.21
2.64
2.22
2.16
1.97
2.45
is small along <100> direction (Figures 1-3). Due to
lack of experimental data of these materials for ultra-
sonic velocities of AmY, we compare our with other B1
structured materials like semiconductors [20], rare-earth
monochalcogenides [21,22] and metallic alloys [23]. The
order and nature of ultrasonic velocities and Debye av-
erage velocity is found to be same. It is clear from Table
3 that the computed values of ultrasonic velocities are
highest in case of AmP. So we can say that the propaga-
tion of sound waves through AmP will be better than that
of other chosen materials. Hence our approach to com-
pute SOEC and TOEC is logical.
SOEC and TOEC are used to obtain Grüneisen pa-
rameters and average squares of the Grüneisen parame-
ters along <100> direction for longitudinal wave over 39
modes and for shear wave 18 modes; along <110> direc-
tion for longitudinal wave over 39 modes, for shear wave
polarized along <001> direction over 14 modes and for
shear wave polarized along <110> direction over 20 mo-
des and along <111> direction for longitudinal wave over
39 modes and for shear wave polarized along <110 > d irec-
tion over 14 modes. The temperature dependent averaged
ultrasonic Grüneisen parameters and averaged squares of
the Grüneisen parameters are presented in Table 4. The
value of average Grüneisen parameters is the highest for
Figure 1. Debye average velocity versus temperature along
<100> direction.

35 D. SINGH ET AL.
Figure 2. Debye temperature versus temperature along
<111> direction.
Figure 3. Debye average velocity versus temperature along
<110> direction.
Table 3. Ultrasonic velocities (in 105 cm/s) of AmY along different crystallographic directions in the temperature range 100 K
- 500 K.
Materials Directions Velocity 100 K 200 K 300 K 400 K 500 K
<100>
<111>
AmN
<110>
VL
VS1 = VS2
VL
VS1 = VS2
VL
VS1
VS2
2.284
1.353
2.312
1.329
2.305
1.353
1.862
2.308
1.355
2.312
1.351
2.311
1.355
1.909
2.339
1.357
2.314
1.378
2.320
1.357
1.964
2.372
1.360
2.317
1.406
2.331
1.360
2.020
2.405
1.363
2.321
1.434
2.342
1.363
2.076
<100>
<111>
AmP
<110>
VL
VS1 = VS2
VL
VS1 = VS2
VL
VS1
VS2
2.325
1.199
2.145
1.346
2.188
1.199
2.015
2.355
1.201
2.146
1.378
2.199
1.201
2.069
2.392
1.204
2.101
1.410
2.211
1.204
2.131
2.430
1.206
2.153
1.432
2.225
1.206
2.193
2.469
1.208
2.157
1.475
2.238
1.208
2.254
<100>
<111>
AmAs
<110>
VL
VS1 = VS2
VL
VS1 = VS2
VL
VS1
VS2
2.177
1.092
1.973
1.261
2.023
1.092
1.905
2.209
1.094
1.976
1.293
2.035
1.094
1.961
2.259
1.097
1.979
1.325
2.048
1.097
2.036
2.284
1.098
1.983
1.357
2.061
1.098
2.081
2.321
1.100
1.986
1.388
2.074
1.100
2.140
<100>
<111>
AmSb
<110>
VL
VS1 = VS2
VL
VS1 = VS2
VL
VS1
VS2
2.083
0.979
1.815
1.207
1.883
0.979
1.860
2.117
0.981
1.818
1.240
1.896
0.981
1.918
2.162
0.982
1.821
1.273
1.909
0.982
1.987
2.194
0.984
1.824
1.306
1.923
0.984
2.039
2.233
0.986
1.828
1.337
1.936
0.986
2.099
<100>
<111>
AmBi
<110>
VL
VS1 = VS2
VL
VS1 = VS2
VL
VS1
VS2
2.079
0.854
1.682
1.204
1.786
0.854
1.917
2.115
0.855
1.684
1.239
1.799
0.855
1.976
2.154
0.857
1.687
1.274
1.814
0.857
2.038
2.195
0.858
1.689
1.307
1.828
0.858
2.100
2.195
0.859
1.689
1.307
1.828
0.859
2.100

D. SINGH ET AL.
36
Table 4. Ultrasonic Grüneisen parameters of AmY along different crystallographic directions in the temperature range 100 K
- 500 K.
Material Grüneisen parameters 100 K 200 K 300 K 400 K 500 K
Ultrasonic longitudinal wave propagates along <100>
AmN
AmP
AmAs
AmSb
AmBi
<ji>
<(ji)2>
<ji>
<(ji)2>
<ji>
<(ji)2>
<ji>
<(ji)2>
<ji>
<(ji)2>
0.459
1.768
0.453
1.976
0.455
2.048
0.455
2.207
0.463
2.670
0.444
1.674
0.437
1.863
0.436
1.923
0.436
2.067
0.441
2.507
0.429
1.576
0.419
1.751
0.416
1.791
0.417
1.947
0.421
2.360
0.414
1.487
0.403
1.651
0.402
1.701
0.399
1.824
0.402
2.230
0.400
1.407
0.389
1.561
0.387
1.608
0.383
1.725
0.385
2.119
Ultrasonic shear wave propagates along <100> and polarized along <100> direction
AmN
AmP
AmAs
AmSb
AmBi
<(ji)2>
<(ji)2>
<(ji)2>
<(ji)2>
<(ji)2>
0.120
0.119
0.120
0.122
0.129
0.118
0.118
0.119
0.121
0.128
0.116
0.117
0.117
0.120
0.128
0.115
0.116
0.117
0.119
0.127
0.113
0.115
0.116
0.119
0.127
Ultrasonic longitudinal wave propagates along <111>
AmN
AmP
AmAs
AmSb
AmBi
<ji>
<(ji)2>
<ji>
<(ji)2>
<ji>
<(ji)2>
<ji>
<(ji)2>
<ji>
<(ji)2>
–0.689
2.167
–0.710
2.275
–0.719
2.333
–0.737
2.456
–0.789
2.859
–0.660
1.994
–0.677
2.072
–0.683
2.112
–0.698
2.209
–0.747
2.565
–0.630
1.825
–0.644
1.883
–0.646
1.896
–0.663
1.999
–0.708
2.309
–0.603
1.676
–0.615
1.720
–0.619
1.743
–0.630
1.807
–0.672
2.091
–0.577
1.546
–0.588
1.577
–0.591
1.596
–0.601
1.648
–0.641
1.906
Ultrasonic shear wave propagates along <111> and polarized along <110> direction
AmN
AmP
AmAs
AmSb
AmBi
<(ji)2>
<(ji)2>
<(ji)2>
<(ji)2>
<(ji)2>
1.9468
2.286
2.3838
2.6036
3.2101
1.881
2.202
2.290
2.499
3.098
1.810
2.117
2.187
2.416
2.998
1.744
2.039
2.120
2.317
2.912
1.683
1.969
2.048
2.242
2.842
Ultrasonic longitudinal wave propagates along <110>
AmN
AmP
AmAs
AmSb
AmBi
<ji>
<(ji)2>
<ji>
<(ji)2>
<ji>
<(ji)2>
<ji>
<(ji)2>
<ji>
<(ji)2>
–0.774
2.302
–0.760
2.488
–0.761
2.569
–0.760
2.758
0.765
3.361
–0.748
2.154
–0.730
2.324
–0.729
2.392
–0.724
2.565
–0.726
3.143
–0.720
2.007
–0.699
2.168
–0.691
2.214
–0.689
2.404
–0.687
2.951
–0.694
1.875
–0.671
2.031
–0.667
2.089
–0.657
2.243
–0.652
2.786
–0.669
1.758
–0.644
1.911
–0.639
1.967
–0.628
2.114
–0.619
2.645
Ultrasonic shear wave propagates along <110> and polarized along <001> direction
AmN
AmP
AmAs
AmSb
AmBi
<(ji)2>
<(ji)2>
<(ji)2>
<(ji)2>
<(ji)2>
0.126
0.104
0.101
0.095
0.088
0.122
0.101
0.098
0.093
0.087
0.119
0.099
0.095
0.091
0.086
0.115
0.097
0.094
0.089
0.084
0.112
0.095
0.092
0.088
0.083
Ultrasonic shear wave propagates along <110> and polarized along <110> direction
AmN
AmP
AmAs
AmSb
AmBi
<(ji)2>
<(ji)2>
<(ji)2>
<(ji)2>
<(ji)2>
2.852
3.037
3.524
3.865
4.820
2.749
3.236
3.372
3.693
4.634
2.638
3.097
3.201
3.553
4.467
2.531
2.968
3.089
3.388
4.324
2.432
2.851
2.968
3.261
4.206

D. SINGH ET AL.
37
5. Acknowledgements
AmN along <100> direction and the lowest for AmBi
along <111> direction for longitudinal waves, while av-
eraged square Grüneisen parameters is the highest for
AmBi along <110> direction in which shear wave polar-
ized along <110> direction, and the lowest for AmBi in
which shear wave polarized along <001> direction as
shown in Table 4. Hence we can say that AmN is the
best for longitudinal wave propagation along <100> di-
rection and AmBi would be the best for shear wave
propagation. It is found that obtained values of
Grüneisen parameters and average squares of the
Grüneisen parameters are decreasing with the tempera-
ture. This is due to adjustment of SOEC and TOEC for
different modes. This type of nature is also found in
other B1 structured materials like rare-earth monochal-
cogenides [21,22,24], semiconductors [20] and metallic
alloys [23]. It establishes that properties of these materi-
als are very similar to either a semiconductor or metals.
We are extremely grateful to Prof. S. K. Kor, Prof. R. R.
Yadav, Dr. Giridhar Mishra, Mr. S. K. Verma, Mr. Me-
herwaan Rathore, Mr. Sanjay Upadhyaya & Mr. Kajal
De, University of Allahabad; Prof. B. P. Singh, Prof.
Rekha Agarwal, Mrs. Neera Bhutani & Dr. P. K.
Yadawa, ASET, New Delhi; Dr. A. K. Tiwari, BSNVPG
College, Lucknow; Dr. Priyanka Awasthi, DMO,
Lucknow; Dr. Akhilesh Mishra, DST, New Delhi; Dr. A.
K. Gupta, NIOS, Noida; Dr. D. K. Singh, GIC, Jalaun;
Dr. A. K. Yadav, Ambedkar University, Lucknow; and
Mrs. Shivani Kaushik, NIMS University, Jaipur for
many useful helps like reading the manuscript, discus-
sion and knowledgeable suggestions during the prepara-
tion and revision of the manuscript.
6. References
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4. Conclusions
On the basis of analysis of above result, we can say that:
1) We have used the Coulomb and Born-Mayer poten-
tial having two basic parameters i.e., lattice parameter
and hardness parameter to compute SOEC and TOEC.
Evaluated values of SOEC and TOEC have been com-
pared with available B1 structured materials, which are
near to agreement, hence our approach to calculation
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3) SOEC and TOEC have been used to find out the ul-
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bye average velocity and Grüneisen parameters in AmY.
4) Ultrasonic velocity is found to be highest for AmN
along all chosen direction, so AmN will be most suitable
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doi:10.1063/1.345208
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along <100> direction and AmBi is the best for thermal
purposes, because Grüneisen parameters are most sensi-
tive to temperature.
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Due to absence of experimental information on ultra-
sonic properties of these monopnictides, no straight
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Grüneisen parameters, we conclude that current approach
is justified and obtained results will be usefu l for finding
various theoretical, experimental investigations like ul-
trasonic attenuation, non-linearity parameters, ultrasonic
measurements, polarizing microscopy, solid state NMR,
SEM, TEM; and for scientific world and society.
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D. SINGH ET AL.
38
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