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SELF-CONSISTENT PHONON CALCULATIONS IN SOLID NITROGEN
T. Wasiutynski
To cite this version:
T. Wasiutynski. SELF-CONSISTENT PHONON CALCULATIONS IN SOLID NITROGEN. Journal de Physique Colloques, 1981, 42 (C6), pp.C6-575-C6-577. �10.1051/jphyscol:19816167�. �jpa-00221245�
JOURNAL DE PHYSIQUE
Colloque C6, supplgment au n012, Tome 4 2 , ddcembre 1981
SELF-CONSISTENT PHONON CALCULATIONS IN SOLID NITROGEN
T . Wasiutynski
I n s t i t u t e o f Nuclear Physics, Krakow, Poland
Abstract.
-
Phonon c a l c u l a t i o n i n the self-consistent harmonio approximation were performed f o r temperature range 0-
40 X atzero pressure and f o r pressures range 0
-
10 kbars at i K. The parameters of the intermolecular p o t e n t i a l of the atom-
atom"6-expn form were optimised.
i, Model.
-
On the b a s i s of the e a r l i e r formulated s e l f - c o n s i s t e n t phonon approximation f o r the molecular c r y s t a l s / l / we studied s o l i d n i t r o g e n a t d i f f e r e n t temperatures and pressures. The approximation i s e s s e n t i a l l y the same as f o r the atomic o r y s t a l s /2/ r e g a r d l e s s the f a c t t h a t we have here t h r e e e x t r a r o t a t i o n a l degrees of freedom f o r each molecule. The harmonic equation of motion i s solved with t h e e f f e c t i v e p o t e n t i a l which is given by the convolution of the bare p o t e n t i a l with gaussian d i s t r i b u t i o n funotion. The width of the gaussian i s given by the inverse of the displ~ement-displacement c o r r e l a t i o n funotion. Sinoe the l a t t e r depends on the phanon f r e - quencies one has t o solve t h e equations s e l f c o n s i s t e n t l y ,A s the bare p o t e n t i a l V(r) we use the empirical atom-atom p o t e n t i a l o f the %-expn forms
Three empirioal parameters A, B and C were optimised i n order t o g e t t h e proper l a t t i o e constant a 5 5.66 g a t T 5 i 5 K, L a t t i c e energy U P 1.73 k c a l b o l e and the b e s t o v e r a l l agreement of the phonon fre- quenoies at q r 0 i n the cubic phase. The values of the parameters a r e l i s t e d i n t a b l e l together with the reoently published para- meters from the ab-initio c a l c u l a t i o n s /3/. Aa one oan see from t h a t t a b l e t h e two s e t s do not d i f f e r very much, The u n i t s are of k c a l kcal/mole and 8.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19816167
C6-576
Table i
JOURNAL DE PHYSIQUE
2. B s s a l t s .
-
The comparison of t h e c a l o u l a t e d and e x p e r i m e n t a l /4/phonon f r e q u e n o i e s i n ammi at q SE 0 f o r t h e w - H 2 i s shown i n
t a b l e 2.
Table 2 p r e s e n t o a l o a b - i n i t i o /3/
The temperature dependenoe o f t h e l a t t i o e c o n s t a n t aad two phonon modest one of t h e t r a n s l a t i o n a l and one of t h e r o t a t i o n a l o h a r a a t e r
C 383 361 A
128645 183770
Symmetry
4
Tg T
d ?
a r e shown on f i g u r e s 1 and 2, 5.8 LATTICE CONSTANT [A) 1
B 4.0 4.037
P r e s e n t o a l o u l a t i o n
38.1 42.8 51.8 48.5 51.7 57.3 75.3 Esperiment
To15 K /4/
32.3 36.3 59.7 46,8 48.4 54.0 69.4
I . I . t . I I S I
0 10 20 30 L0
TEMPERATURE ( K 1
ab-in1 t i o o a l o u l a t i o n /5/
39.5 48.5 70.3 48.8 48.4 55.5 72.0
TEMPERATURE [ K )
1: Temperature dependenoe of h t t i o e c o n s t a n t i n a-A2. Ex- p e r i m e n t a l p o i n t s from /6/.
2 t Temperature dependenoe e lowest E and Ta modes.
Experimental p o f n t s on E /1/
and on T, from /8/. g
Table 3 shows t h e comparison between c a l c u l a t e d and experimental phonon frequencies i n cl-' a t q r 0 f o r d i f f e r e n t p r e s s u r e s i n 6-Ha.
Table 3
3. Discussion.
-
The temperature dependenoe presented i n f i g u r e s 1 and 2 shows qUalitatiW3lg good agreement with t h e experimental data.One has t o n o t i c e , however, t h a t t h e oaloulated thermal expansion is bigger than t h e measured one. The opposite s i t u a t i o n takes place i n
t h e case of t h e temperature dependence of t h e r o t a t i o n a l mode E As a conclusion we oan say t h a t d i f f e r e n t anharmonic terms c o n t r i b u t e g*
t o t h e s e two phenomena. Another p o i n t with mentioning here is t h a t t h e intermolecular p o t e n t i a l derived for t h e oablo phase i s a l s o v a l i d f o r high pressure t e t r a g o n a l phase. Usaally t h i s i s t h e weak p o i n t because of t h e d i f f l o u l t i e s with p r e c i s e l y determining t h e r e p u l e i v e p e r t of t h e intermolecular p o t e n t i a l .
Beferenaes
/l/ T. Wasiutysbki, phys.etat.sol.(b)
/2/ T.R, Koehler, L a t t i c e dynamics of quantum c r y s t a l s i n t h e book uDynarnical p r o p e r t i e s of s o l i d " , vol.2, p.i, North Holland, 1974 /3/ 8.16 Berne, A. Van d e r Avoird, J.Chem.Phys. 2, 6107 ( 8 0 )
/4/ J"& Kjem8, O, Dolling, Phys.Rev. U, 1639 (1975)
/5/ T. Luty, A. Van d e r Avoird, R.& Berns, J,Chem.Phgs. a, 5305 ( 1980)
/ 6 / I i N . ICrupskii', A, I. Prokhatilov, A. I. Erenburg, Fiz.Niskhikh Temp. h, 359 (1975)
/7/ F, D. Medima, W.'B. Daniels , J. Chem. Phys. g4, 160 ( 1976) /8/ B.N. St. Louis, 0. Sohnepp; J, Chem. Phys, &, 5177 ( 1969)
/9/ Mk. Thiery , V, Chandresekkaran, J, Chem. Phys. 67, 3659 (1977).
Symmetry
A 2g
$U
p r 4 kbars exper /9/ c a l o
54.2 58.6
Q7,2 82.3
-
97-468.5 110.9
p m 5 kb-s exper /7/ c a l o
58.4 61.4
203.6 86.3
-
102.3-
71.9-
116.7p r 8.78 kbars exper /Q/ o a l o
64.0 72
114.4 Q9
i i 9
-
84.I 137
