CHAPTER-VII

SUMMARY AND FUTURE SCOPE OF THE WORK

The outcome of present investigations along with the future scope of the

investigation is discussed in this chapter. The electronic structure and structural phase

stability of AMX2 (A=Cu, Ag; M=AI, Ga, In; X=O. S, Se, Te) are studied using self-

consistent TB-LMTO method. The optical properties of the above compounds are also

investigated using FP-LMTO 'LMTART' method. A brief summary of the present

study is given below.

The structural stability of 3R and 2H polytypes of CuMO: (M=AI. Ga, In)

delafossite compounds are studied by calculating the electronic band structure as a

function of volume using TB-LMTO method. The total energies are computed as a

function of volume from which the equilibrium volume and bulk modulus are

obtained and compared with the available experimental data. Total energy

calculations show that 3R polytype of the delafossite is more stable than the 2H

polytype. However, in the case of CuGa02, 3R phase becomes stable at a pressure of

about 13 GPa. The energy difference between the 2H and 3R polytype of CuGa02 is

small, hence it is an indication that both the polytypes have equal stability in

accordance with the experimental observation at normal condition. The band structure

of the compounds shows the indirect band gap for both the polytypes. The band gap

for the compounds are estimated from the DOS and found to decrease from CuAlO2

to CuGa02 and then to Culn02. The calculated band gap values are in good

agreement with the earlier reported data. The electronic energy band and DOS at

ambient conditions are in good agreement with the earlier works. From the band

structure plots, one can find that the Cu 'd' like band and 0 'p' like bands are

dominating the valence band near the Fermi level. The M cation contributes more in

the upper part of the conduction band.

The optical properties of delafossite compounds are obtained by FP-LMTO

calculation. The onset of critical point or threshold energy value is meast~red from the

imaginary part of dielectric function, which is comparable with the calculated band

gap value of the compounds. The static dielectric constants and refractive index for

the compounds are calculated from the real part of dielectric function. 'Ihe static

dielectric constant value for 2H polytype is higher than the 3R polytypes, which is

due to their band gap value of the compounds. The value of refractive index is also

higher for 2H polytypes than the 3R polytype similar to static dielectric constant. The

calculated degree of anisotropy is negative and small for the above-referred

delafossite compounds. The birefringence of the materials depends on its anisotropy

property. Depending on the magnitude of the birefringence, the phase matching in

linear and non-linear optical interaction occurs. The calculated optical constants such

as static dielectric constant, refractive index and degree of anisotropy of the

compounds are in need of experimental data for verification.

The electronic structure, structural phase stability and optical properties of

AgM02 compounds are also studied. The calculated equilibrium volurnes From the

total energies for 3R and 2H-polytype of AgM02, are in agreement with the

experimental volume. To the best of our knowledge, the electronic band structures for

the 3R-polytypes of AgMO2 compounds are not available. The calculated bulk

modulus for the 2H and 3R- polytype are in need of experimental data for

comparison. The present work shows that 3R polytype is more stable than the 2H

polytype. The band s t ~ c t u r e s of AgMO2 show well-developed indirect band gap for

both the polytypes. The calculated energy band gap from DOS shows a decreasing

trend from AgA102 to AgGa02 and then to Agln02.

From the optical properties of these compounds, i t is found that the onset of

critical point or threshold energy value is comparable with the band gap value of the

compounds. Static dielectric constant for 2H- polytypes is slightly higher than the 3R

polytypes, which is mainly due to their smaller difference in energy band gap value of

the compounds. The refractive index also shows the same trend as that of static

dielectric constants. The calculated degree of anisotropy is found to be small and

negative for all the delafossite compounds. The calculated static dielectric constant

and refractive index of the compounds are in need of experimental data for

comparison.

The other part of the thesis deals with the electronic structure and high

pressure transitions of CuMX2 (M=AI, Ga, In; X=S, Se, Te) chalcopyrite compounds.

For the ambient bct phase, the total energies as a function of volume are calculated

and fitted with the Birch Murnaghan equation of state. The calculated equilibrium

volume and bulk modulus for compounds at ambient conditions are in good

agreement with experimental data.

Using energy dispersive X- ray diffraction technique. Roa el a1 observed

pressure induced phase transition from chalcopyrite to rock salt structure for CuAlSe2

compound. The total energies of CuAISe2 with fcc phase are calculated to undentand

pressure induced phase transition. It is found that the total energies of CuAISe2 show

the phase transition from bct to denser face centered cubic structure. The phase

transition of CuAlSe2 agrees well with the experimental results. The calculated cell

volume and bulk modulus for CuAISe2 are compared with experimental data, which is

less than the experimental value due to LDA. The calculated transition pressure is .

14.4 GPa, which agrees with the experimental value of 12.4 GPa.

To investigate the structural phase stability of CuAlS? and CuAITe2. the total

energies are calculated for possible fcc phase at different cell volumes. From the

present calculations, it is found that these compounds undergo phase transition from

bct to fcc and the transition pressure is about 18 GPa for CuAlS2 and 8.29 GPa for

CuAITe2. The theoretical results on structural phase transition of CuAIS2 and

CuAlTe2 are in need of experimental data for verification. The calculated volume and

bulk modulus of fcc structure of CuAIS2 and CuAITe2 are presented. The band

structure of these compounds is calculated with and without including 3d orbital of

Cu atom in the valence state, The band structure for the CuAIX2 compounds supports

the importance of 3d orbital of Cu atom. The DOS shows large downshift in the

energy gap when 3d orbital are included. The band structure for the bct phase shows

direct band gap and the calculated band gap value shows a decreasing trend from

CuAIS2 to CuAITe2. The calculated band gap underestimates the experimental value

due to LDA. The occurrence of non zero value of DOS at EF for the high pressure fcc

phase confirms the metallic nature.

For CuGaX2 compounds. the calculated equilibrium volume and bulk modulus

are in good agreement with the earlier experimental and reported data. The calculated

band gap values for the bct phase of CuGaX: are found to be in close agreement with

the earlier reported data.

Using energy dispersion technique, Werner et a1 observed the phase transition

in CuGaS2 from bct to NaCl structure at 16.9 - 22.5 GPa. In order to understand the high pressure phase transition of CuGaS2, total energies for the fcc phase are

calculated at different volumes and compared with that of bct phase. The fined total

energies confirm the experimental observation of phase transition. The calculated

bulk modulus for fcc phase is 100.82 GPa, which is in close agreement with the

experimental value of 94*15 GPa. The pressure at which transition occurs is

calculated from the equation of state. The transition pressure is about 27.93 GPa

which agrees with the experimental value of 16.9 -22.5 GPa.

The total energy calculations for CuGaSe* show the possibility of phase

transition under pressure. It is found that phase transition from bct to fcc occurs at

about 17.39 GPa. For the want of experimental data, the calculated cell volume and

bulk modulus for high pressure fcc phase of CuGaSe2 are not verified. Experimental

investigation is necessary to confirm this pressure induced structural phase transition.

Using high pressure X- ray diffraction methods, Mori et a1 predicted structural

phase transition from bct to d-Sc and then to d-Cmcm phase for CuGaTel. In the

present study, total energies for SC and d-Sc (cations are displaced from the original

position without breaking the symmetry) are calculated to check the existence of

d-Sc. The calculations show that the existence of disordered simple cubic at high

pressures is energetically not favourable when compared to ambient bct phase. To

ensure the appearance of d-Cmcm phase under pressure. the calculations are carried

out for primitive orthorhombic by displacing the atoms along the c- axis of the crystal.

The displacement is about 10% without breaking the crystal symmetry. Present

calculation shows the phase transition from bct to d-ortho at about 10.71 GPa. In

addition, the total energies are also calculated for the high pressure f'cc phase to check

the possibility of phase transition. The calculations show the phase transition at 20.5

GPa. The calculated cell volume and the bulk modulus are in need of experimental

results for verification.

The total energy calculations on CulnS2 and CulnSe2 show the structural

phase transition from bct to fcc phase, which is in good agreement with the

experimental observations of Tinoco el al. The calculated equilibrium volume and

bulk modulus for the bct phase are in good agreement with the experimental values.

In the case of CulnTe2 it was experimentally observed that it undergoes

structural phase transition from bct to d-Cmcm phase under pressure. The total

energies are calculated for d-Cmcm phase in a similar method adopted for d-Cmcm

phase of CuGaTe?. The total energy calculations are carried out by displacing the

atomic position by 10% along the c- axis. The calculations show the structural phase

transition from bct to d-orthorhombic at about 2.86 GPa, which is comparable with

the experimental value of 3.0 GPa. In order to check the possibility of further

s ~ I V C N ~ ~ phase transition, total energies are also calculated for fcc phase. The

compound undergoes the phase transition from bct to fcc at 10.44 GPa. The calculated

volume is 625.475 (a.111' and bulk modulus is 66.84 GPa. which are in need of

experimental data for verification. Band structures for bct and high pressure phases of

the above mentioned chalcopyrites are calculated. which show direct band gap for the

bct phase and metallic nature under pressure.

The optical properties for CuMX2 (M=AI, Ga. In; X=S. Se. Te) are studied for

ambient phase at equilibrium volume. The magnitude of peaks in the imaginary part

of dielectric function increases from CuMS2 to CuMSe2 and from CuMSe2 to

CuMTe2, which shows the importance of anions in the study of optical properties of

these compounds. The static dielectric constants for the compounds are calculated

from the real part of dielectric function. The calculated static dielectric constant

increases from S to Se and from Se to Te. The static dielectric constant increases as

the band gap value decreases for the compound, which agrees with the earlier work

done. The refractive index of the compounds increases from S to Te similar to static

dielectric constant i.e. from lower to higher atomic number. The degree of anisotropy

of the compounds is small and positive for all compounds except CuAIS2 and

CulnTez compounds. The calculated refractive index, degree of anisotropy and zero

crossing point shows the influence of anion in the optical properties of the

compounds.

The electronic band structure, structural stability and optical properties of

AgMXz (M=AI, Ga, In; X=S, Se, Te) compounds are studied. The equilibrium

volume and bulk modulus for the compounds are calculated and compared with the

experimental results. The electronic structure calculation for the high prrssurr fcc

phase of AgAlX2 is carried out to check the possibility of phase transition like other

chalcopyrites. The present calculation show that fcc structute is more stable than the

bct phase at high pressures. The equilibrium volume and bulk modulus for the high

pressure fcc phase of AgAIX2 compounds are in need of experimental data for

verification. The pressure and volume at which transition occurs are calculated from

the equation of state. The transition pressure for AgAIS2. AgAISe2 and AgAITe* is

5.27 GPa, 11.06 GPa and 7.18 GPa respectively.

In the case of AgGaX2. the structural stability and electronic structure are

calculated using TB-LMTO method. The calculated volume, bulk modulus and band

gap for the bct phase of the compounds are found to be in good agreement with the

available experimental and reported data. Using XAS technique Tinoco el a1

investigated the high pressure phase transition of AgGaS2. The phase transition from

bct to orthorhombic structure was predicted experimentally between 12 and 16.5 GPa.

In order to understand the structural phase transition in AgGaS2, the total energies are

calculated for the primitive orthorhombic structure. The fined value shows that the

primitive orthorhombic structure is energetically not favorable. So, total energies for

the base centered orthorhombic structure are calculated, which shows phase transition

at 7.34 GPa. The calculated transition pressure is less than the experimental value of

12 GPa. To examine any other possibility of phase transition apart from orthorhombic

phase, the total energies are calculated for the fcc phase. Present calculations show

that there is a possibility of structural phase transition from bct to fcc at a pressure of

about 16.07 GPa. The transition pressure value agrees with the experimental transition

pressure value of 17 GPa of the unknown phase. The calculated volume, bulk

modulus and transition pressure a n in need of experimental results for comparison.

Tinoco et a1 used XAS technique to investigate the phase transition in

AgGaSe2 com~ound. They observed that AgGaSel undergoes structural phase

transition from bct to orthorhombic and then to tetragonal and finally to some

unknown phase. Total energies for the orthorhombic phase are calculated similar to

AgGaS2 compound. The compound undergoes phase transition from bct to

orthorhombic at 27.75 GPa whereas the experimental value is 10 CPa. The

overestimation of transition pressure and volume may be due to the approximate

choice of symmetry group namely base centered orthorhombic. Resides the

orthorhombic structure, the total energies are calculated for the primitike tetragonal

structure to understand the experimental high pressure tetragonal structure. In the

present study, the phase transition occurs at a very high pressure of 67.5 1 GPa. Exact

crystallographic details of high pressure phases are required to solve these

discrepancies. Total energies for the compound with fcc structure show the phase

transition at about 30.52 GPa. The present theoretical phase transition value agrees

with the transition pressure value of experimentally determined unknown phase of the

compound.

High pressure X-ray diffraction measurements by Mori el a1 on AgGaTel

- predicted that the X-ray diffraction peaks of chalcopyrite coexist with P 4 under high

pressure. On further increase of pressure, it was observed that the X- ray diffraction

- peaks of P 4 and d-Cmcm coexist. Based on the coordination, it was fir~ally confirmed

that the high pressure phase is dCmcm phase. The present calculation is carried out

- on the basis o f experimental results. The total energy for the P 4 phase is calculated

and found that this phase is energetically not stable at ambient as well as at high

pressures. For disordered Cmcm phase. total energies are calculated for primitive

orthorhombic structure with 10% displacement o f atoms along c- axis. The prexnt

calculations show that phase transition from bct to d-ortho is at about 3.62 GPa, which

agrees with the experimental value of 5.4 GPa. Based on Qadri @I a1 experimental

observations, the total energies are calculated as a function o f reduced volume for the

high pressure fcc phase o f the compound. The present calculation confinns the

pressure induced structural phase transition for AgGaTe2 from bct to f'cc at about 6.95

GPa which is in good agreement with the experimental transition pressure value of

4i0.5 GPa. The calculated cell volume is 613.59 (a.u)' which i s also in good

agreement with the experimental value o f 622.573 (a.u)'.

The electronic structure and structural phase stability of AglnXl compounds

are performed using tight binding version o f LMTO. The equilibrium volume for the

bct phase is calculated by total energy calculation, which agrees with experimental

data. In order to understand the possibility o f phase transition from bct to fcc phase.

total energies are calculated for the compounds. The compounds are found to undergo

transition from bct to fcc at 17.5 GPa for AglnSz and 14.46 GPa for AylnSe2 and

4.289 GPa for AglnTe2 compounds. The calculated cell volume and bulk modulus and

the transition pressure values are in need of experimental results for verification. The

band structures for AgMXz (M= Al, Ga, In; X=S, Se, Te) compounds are calculated

for the bct phase. The band structure o f bct phase shows direct band gap similar to

C u M X l chalcopyrites. The non zero value of W S at EF under the application o f

pressure indicates the transition from semiconductor to metallic nature. The band gap

for the compounds are estimated from the DOS and compared with the available

experimental values.

The optical properties of AgMX2 are studied using FP-LMTO. The imaginary

and real part dielectric functions of the compounds are calculated. The threshold

energy value or onset of critical point for the compounds is calculated from the

imaginary part o f dielectric function. The static dielectric constant for the compounds

is calculated by averaging the parallel 61, and perpendicular components E l , , o f real

part dielectric functions. The refractive index is calculated and found to increase from

AgMS2 to AgMSe2 and from AgMSel to AgMTel. The static dielectric constant and

the refractive index show the influence of anions in the optical properties o f the

compounds. The degree o f anisotropy for the compounds is calculated and is found to

be small and positive except the AgAIS2, AgAISe2, AglnSl and AglnSe2. The zero

crossing point for the compounds is calculated which shows the decreasing trend from

S to Te i.e. from lower to higher atomic number.

The future scope of the present investigation of the above compounds is discussed

below.

I. In the case o f CuA102 and Culn02. the structural stability o f the compound is

studied by total energy calculation as a function of volume. Present results show that

3R polytype is more stable than the 2H. In CuGa02 compound it is found that the 3R

polytypes is found to be stable at around 13 GPa. The optical properties o f the

compounds namely static dielectric constants, refractive index and degree of

anisotropy are calculated which are in need of experimental data for verification.

11. The present investigation on the structural stability o f AgM02 shows that 3R

polytypes are more stable than the 2H polytypes. The calculated bulk modulus and

band gap are in need o f experimental data for comparison. The optical constants for

the compounds are calculated which are in need of experimental data for verification.

Ill. The pressure induced structural phase transition for CuAlXz (X= S, Se, Te) are

studied. The phase transition o f CuA1Se2 from bct to fcc agrees with the experimental

results. The predicted structural phase transition (bct to fcc) of CuAIS2, CuAlTe2 and

CuGaSez needs experimental investigation for verification.

High pressure experimental investigation on CuGaTez shows that it undergoes

transition from bct to d-Sc and then to d-Cmcm. In the case of d-Cmcm phase, the

calculations are carried out by considering primitive orthorhombic structure with

small displacement o f atoms along the c- axis. Present calculation supports the phase

transition from bct to disordered orthorhombic, whereas d- Sc phase is energetically

not stable. Experimental studies on CulnTe* show that it undergoes phase transition

from bct to d-Cmcm. The electronic structure calculation for d-Cmcm is carried out in

a manner similar to CuGaTe2 compound. The transition pressure and bulk modulus

agree with the experimental data. Detailed high pressure crystallographic date is

necessary to compare the present results.

IV. High pressure experimental data is needed to confirm the expected structural

phase transition in AgAIX2 and AglnX2 compounds. Present calculations show that

ternary chalcopyrite semiconductors prefer fcc phase under high pressure. The

existence of intermediate phases namely orthorhombic or d-Sc is mostly derived from

fcc structure. Hence, detailed high pressure crystallographic data is necessary to

verify the existence of fcc phase under high pressure.