RAIR spectra of CO2/H2O ices: theoretical prediction and

experimental results R. EscribanoR. Escribano, V.J. Herrero, B. Maté, O. Gálvez and , V.J. Herrero, B. Maté, O. Gálvez and

B. Martín-Llorente B. Martín-Llorente Instituto de Estructura de la Materia, CSIC, MadridInstituto de Estructura de la Materia, CSIC, Madrid

http://www.iem.cfmac.csic.es/departamentos/fismol/fmap/main.htmhttp://www.iem.cfmac.csic.es/departamentos/fismol/fmap/main.htm

andand Emilio Artacho,Emilio Artacho,

Department of Earth Sciences, University of Cambridge, UKDepartment of Earth Sciences, University of Cambridge, UK

Outline:Outline:

Continuation of previous talkContinuation of previous talk Ices of HIces of H22O/COO/CO22::

• Experimental method: RAIR measurementsExperimental method: RAIR measurements• Theoretical (solid state) calculations for Theoretical (solid state) calculations for

pure COpure CO22 crystals crystals

Summary of resultsSummary of results

Ices studiedIces studied H2O/CO2

Composition of the mixturesComposition of the mixtures H2O/CO2 : ~ 15:1

Preparation of the samplesPreparation of the samples

Sequential deposition (first H2O, then CO2)

Co-deposition

Inverse sequential deposition (first CO2, then H2O)

Sequential deposition over crystalline structures (first amorphous H2O, then annealed, then cooled to 80 K, then CO2)

Experimental setup RAIRS Experimental setup RAIRS

RAIRS : reflexion-absorption RAIRS : reflexion-absorption infrared spectroscopyinfrared spectroscopy

EEPP

SS

++

--

EE++

EEPP

SSEE--

dd

nn11

vacuum

nn22

nn11

ice, k22

nn metal, k33 33

p

pp

R

RAU

0

log

ps

ps

RR

RRAU

00

log

s

ss

R

RAU

0

log

Polarization s Polarization p Non polarized

Transmission vs Reflection-AbsorptionTransmission vs Reflection-AbsorptionSequential deposition (H2O, CO2)

reflection-absorption

3

transmission

S-polarizationP-polarization

A little bit of LO/TOA little bit of LO/TO……Molecular vibrations of a single crystal of arbitrary shape:

H = H(0) + H’

H(0) : molecular vibrations of uncoupled molecules

H’ : long-range dipole-dipole interactions, Hij

e.g.: mol. 2 vibrating in mode interacting with mol. 3 of all other cells vibrating in mode

Use of D tensor:Use of D tensor:

ji

jijiikrij

rr

rreH

3,,

*

5,,

* .).)(.(3

x y

jijiyj

xyij

xiij DkDH

,,,, *))((*)(

ikr

xyyxxy e

rr

rrkD

35

3)(

D depends only on the structure of the lattice and shape of the sample, but not on internal molecular properties or molecular orientation; when the shape is of ellipsoid of revolution, D can be calculated numerically

H’ =

Solving the equation Solving the equation of motion:of motion:

H = H(0) + H’

H(0) : uncoupled molecules → ω0

H’ : dipole-dipole interactions → ωn α

220

2n Ω

Qμ

εV4π

ωω

If dimensions of crystal (typically ~ nm) are much smaller than wavelength of incident radiation (1000 cm-1 <> 104 nm), then only factor that influences Ωα is shape of the crystal.

Usual experimental conditions:Usual experimental conditions: In most IR transmission measurements, incident radiation field lies in plane

of substrate; if sample is thin film, then only TO vibrations can be seen (molecular vibrations in the plane of the film), never LO (perpendicular to that plane).

Similarly, in RAIR experiments on thin films, only TO vibrations are seen in S polarization (no LO-TO splitting). In this case, the metal surface selection rule (MSSR) also applies.

μ’→ωTO

μ’→ωLO

absorption at ωTO only for normal incidence transmission

absorption at ωTO and ωLO and many frequencies in between

Polycrystalline sample with many crysytallite shapes

If direction of propagation of incident radiation is not normal but tilted then LO and TO can be seen both in transmission and in P polarization RAIR spectra

absorption at ωTO and ωLO

Other experimental conditions:Other experimental conditions:

Co-deposition (H2O+CO2)

Sequential crystalline

S-polarization

P-polarization

Summary of experimental resultsSummary of experimental results

RAIR spectra provide information on physical characteristics of sample

On all depositions (80K), CO2 tends to form slabs, with two peaks on P-polarization spectra: ~2343 cm-1 (TO), 2380 cm-1 (LO), and only one on S-polarization spectra: ~2340 cm-1 for 3 band

After warming (105K), the CO2 in slabs is fully desorbed, but a fraction remains with no crystalline structure: one peak at ~2340 cm-1 for both polarizations

This fraction is located inside the water ice and remains until heating up to the water phase change temperature (~165K), except for sequential crystalline deposition, for which all CO2 is desorbed at 105K

Theoretical calculations of pure CO2 crystals:

SIESTA program“Spanish Initiative for Electronic Simulations of Thousands of Atoms”

Brief description:•Optimization of geometrical structures of periodic systems•Calculation of force constants in the harmonic potential approximation•Calculation of vibrational modes of the crystal•Prediction of “stick” spectrum (frequency and intensity of each normal mode)•Description of normal modes in terms of atomic Cartesian displacements•Prediction of LO/TO splitting

COCO22 crystal crystal

Cubic, face centered, a=5.624Å

Crystal with weak van der Waals forces among molecules

Vibrational modes /cm-1:

Exp. Description

73,90,130 librational

655,660 2 bending

1387 1 sym stretch

2345 3 asym stretch

Calculated Calculated frequenciesfrequencies

(LO/TO splittings (LO/TO splittings in bracketts)in bracketts)

12CO2(LO/TO) Int

602.8 0.07

602.9 0.07

603.0(0.4) 0.07

603.4 <10-3

603.5 <10-3

608.3 0.12

608.3 0.11

608.4(16.0) 0.11

1296.8 0

1296.9 0

1296.9 0

1296.9 0

2293.3 0

2304.7 1.04

2304.7 1.04

2304.7(29.4) 1.04

Summary of theoretical results

Theoretical DFT calculations on pure CO2 ice reproduce observed crystal symmetry and structure and predict vibrational frequencies with ~6% red-shift in worst case

LO-TO splitting is also predicted slightly smaller than observed

Future plans

Studies of other binary mixtures: H2O/CH3OH,

H2O/NH3, H2O/N2O,…

Studies of ternary systems: H2O/CH3OH/CO2

Ab initio or DFT calculation of amorphous solids

Funding agencies:Funding agencies: CAM, FSE for studentshipCAM, FSE for studentship CSIC: studentship for UA with University of Jaén, CSIC: studentship for UA with University of Jaén,

Juan de la Cierva Program, PIF 200550F0051 Juan de la Cierva Program, PIF 200550F0051 “Hielocris”“Hielocris”

Spanish Ministry of Education, Project FIS2004-Spanish Ministry of Education, Project FIS2004-00456, Sabbatical grant00456, Sabbatical grant

The Madrid groupThe Madrid groupMolecular Physics of Atmospheres and PlasmasMolecular Physics of Atmospheres and Plasmas

Miguel Angel Moreno

Belén Maté

Kenty Ortega

Oscar Galvez

Verónica Verdejo

Isabel Tanarro

Beatriz MartínIsabel Méndez

Víctor Herrero

Parameter Parameter ΩΩαα

crystal2

31

3512

122α121α312

2α1αα rdrd

r

).r(rnr)(rn3

r

)(r).n(rn

V41

assuming normalized nα(r1) functions such as:

crystal

2α 1drn

V1

COCO22 spectra spectraCube (8x8x8)

Needle (32x4x4)

Slab (16x16x2)

Calculated spectra

Signorell, JCP 2003

Transmission vs Reflection-AbsorptionTransmission vs Reflection-Absorption

Sequential deposition (H2O, CO2)

(1) transmission 3

S-polarization P-polarization(2) Reflection-absorption

33

Sequential deposition (H2O, CO2)

Solving the equation of motionSolving the equation of motion

α

220

2n Ω

Qμ

εV4π

ωω

ωn also called ωLO , ω0 = ωTO

Ωα (varies between 0 and 1)

ωLO ≥ ωTO (almost) always

H = H(0) + H’

H(0) : uncoupled molecules → ω0

H’ : dipole-dipole interactions → ωn

If dimensions of crystal (typically ~ nm) are much smaller than wavelength of incident radiation (1000 cm-1 <> 104 nm), then only factor that influences Ωα is shape of the crystal:

Spherical crystals: Ωx = Ωy = Ωz = 1/3 and all vibrations ωn = 1/3 (ωLO+2 ωTO)

Thin films: Ωx = Ωy = 0 (for polarization parallel to surface of film), Ωz = 1 (for polarization perpendicular to surface of film); and then two absorptions are seen at exactly ωTO and ωLO.

Tensors R and S:Tensors R and S:

For spectroscopic activity, kFor spectroscopic activity, k~0 and summation ~0 and summation for D becomes:for D becomes:

xyxyyx

xyxyxy SR

aaRD

233

4

3

4

where R depends on crystal structure (cubic, orthorrombic, …) but not on wavevector k, and S conveys the contribution from the sample surface polarization charge, and depends on the shape (slab, needle,…) of the sample but not on the structure of the crystal.

For ellipsoids of revolution:

200

010

001

21

3a

gS with g=0 for sphere, -8π/3 for slab,

4π/3 for long needle

Oblate or prolate crystals:Oblate or prolate crystals:

μ’→ωTO

μ’→ωTO

μ’→ωLO

μ’→ωLO

absorption at ωTO only for normal incidence transmission

absorption at ωTO and (ωLO+ ωTO)/2

SIESTA (cont’d.)SIESTA (cont’d.)

Technical details of the method:• Energy optimization algorithm: conjugate gradient• DFT: Perdew-Burke-Ernzenhof generalized gradient• Pseudopotentials: Troullier-Martins with partial core• Basis Set: variationally optimized (MV Fernández-Serra)

double-zeta with polarization• Grid mesh cutoff: 300 Ry fineness• K-sampling: 6 Å• Force constants calculated numerically, 0.01 Å step• Born charges: 5 x 2 x 2 sampling in reciprocal space

… fairly strict relaxation parameters required to achieve high symmetry of the crystal

COCO22 crystal crystal

Cubic, face centered, a=5.624Å

Crystal with weak van der Waals forces among molecules

Vibrational modes /cm-1:

Exp. Calc. Description

52-90(9) translational

73,90,130 90-121(8) librational

655,660 604,608(8) 2 bending

1387 1298(4) 1 sym stretch

2345 2294(1) 3 asym stretch

2306(3)

Dispersion curves Dispersion curves 3

ResultsResults

560 580 600 620 640 660 215022002250230023502400

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

550 600 650 21502200225023002350

0.00

0.02

0.04

0.06

0.08

0.10

0.12

without LOTO correction

Abs

orba

nce

Wavenumber, cm-1

with LOTO correction

Wavenumber, cm-1

Summary RAIR spectra provide information on physical characteristics of

sample On all depositions (80K), CO2 tends to form slabs, with two

peaks on P-polarization spectra: ~2343 cm-1 (TO), 2380 cm-1 (LO), and only one on S-polarization spectra: ~2340 cm-1 for 3 band

After warming (105K), the CO2 in slabs is fully desorbed, but a fraction remains with no crystalline structure: one peak at ~2340 cm-1 for both polarizations

This fraction is located inside the water ice and remains until heating up to the water phase change temperature (~165K), except for sequential crystalline deposition, for which all CO2 is desorbed at 105K

Theoretical DFT calculations on pure CO2 ice reproduce observed crystal symmetry and structure and predict vibrational frequencies with ~6% red-shift

LO-TO splitting is also predicted slightly smaller than observed