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Synthesis and Characterization of
Ytterbium Diiodide Hydrates

presented by

BoYoung Kim

has been accepted towards fulfillment

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SYNTHESIS AND CHARACTERIZATION

OF YTTERBIUM DIIODIDE HYDRATES

BY

BoYoung Kim

A THESIS
Submitted to
Michigan State University
in partial fulfillment of requirements
for the degree of

MASTER OF SCIENCE

Department of Chemistry

1988

5079242.

ABSTRACT

SYNTHESIS AND CHARACTERIZATION
OF YTTERBIUM DIIODIDE HYDRATBS

BY

BoYoung Kim

The previously unreported ytterbium diiodide hydrates,
YbIZ.HéO and YbI2.2H20 have been prepared. Both hydrates
possess orthorhombic symmetry; Lattice parameters for
YbI2.H20 and Yb12.2H20 are: a = 16.012(5) A, b = 8.140(2) A,
c = 4.5079(9) A ; and a = 13.025(5) A, b = 10.455(5) A, c =
4.507(3) A, respectively.

The monohydrate YbIZ.H20 was prepared by a solvent
procedure, and the dihydrate YbI2.2H20 by a solid-vapor
procedure. These hydrates have been characterized by
powder X-ray diffraction, IR, NMR, and elemental and water
analyses. The ytterbium diiodide hydrates are compared and

contrasted with analogous alkaline earth and lanthanide

dihalide hydrates.

ACKNOWLEDGMENT

I wish to thank Professor Harry A. Eick for his
guidance, and support throughout this study. I appreciate
advice of my guidance COImnittee, Dr. C.K. Chang, and Dr.
T.J. Pinnavaia. I also gratefully" acknowledged Dr. S.A.
Hodorowicz who helped in TGA-DTA measurement and in powder
X—ray diffraction studies.

I thank to Dr. L.D. Le for his help with the solid
state NMR work. Thanks go to Dr. R.H. Schwendeman, H.H. Nam
and H.R. Kim for their aid in the YbIZ.H20 FT IR work.

Financial support is gratefully acknowledged from the
National Science Foundation DMR 83-00739 and from the
department of chemistry, Michigan State University.

Finally, I appreciate my parents and my husband,

Jineun, for their patience, encouragement and support.

This work was partially supported by the
Department of Energy Office of Basic Energy
Sciences, the National Science Foundation
(CHE-9816108), and the American Chemical

Society Petroleum Research Fund.

iii

Chapter Page
CHAPTER ONE: INTRODUCTION ........................... 1
A. Preparatory and Structural Background ........ 1
CHAPTER TWO: EXPERIMENTAL .......................... 12
A. _Chemicals ................................... 12

B. Synthesis Equipment ......................... 14

C. Synthesis Procedures ......................... 14

1. Anhydrous ytterbium diiodide ............ 14_

2. Ytterbium diiodide monohydrate .......... 17

3. Ytterbium diiodide dihydrate ............ 20

D. Elemental and Water Analyses ................ 21

1. Ytterbium ............. _ .................. 21

2. Iodine .................. ................ 21

3. Water ................................... 21

E. Instruments ................................. 21

1. Powder X-ray diffraction ................ 21

2. Infrared ................................ 22

3. NMR ..................................... 22

CHAPTER THREE: RESULTS ............................. 24
A. Anhydrous Ytterbium Diiodide ................ 24

B. Ytterbium Diiodide Monohydrate .............. 26

C. Ytterbium Diiodide Dihydrate ................ 32
CHAPTER FOUR: DISCUSSION ........................... 35
A. Synthesis ................................... 35

B. Powder X-ray Diffraction .................... 39

C. Infrared .................................... 44

D. NMR ......................................... 47

E. Elemental and Water Analyses ................ 48
Future Work .......................................... 50
References ........................................... 51

TABLE OF CONTENTS

iv

Tables

I

II

III

IV

VI

VII

VIII

IX

XI

LIST OF TABLES

Page
Lattice parameters, space groups and colors of
lanthanide trihalide hexahydrates ............... 3
Lattice parameters and symmetries of
selected lanthanide dihalide hydrates ........... 8
Lattice parameters and symmetries of
selected alkaline earth halide monohydrates ..... 9
Chemicals used for synthesis work .............. 13
Observed and calculated interplanar d—spacings
and intensities for anhydrous YbI2 ............. 25
Observed and calculated interplanar d-spacings
and observed intensities of YbIZ°H20 .......... 28
Observed and calculated interplanar d-spacings
and observed intensities of YbIZ'ZHZO .......... 33
Elemental and water analysis results ............ 34
Vapor pressure of selected species .............. 36
Comparison of the structure types of some
lanthanide dihalides with those of alkaline
earth dihalides ................................. 43

Comparison of the IR frequencies of water with
those in YbIz‘HZO .............................. 46

LIST OF FIGURES

Figure Page

1 Schematic representation of anhydrous Yblz
synthesis apparatus ............................ l6

2 Apparatus used for the synthesis of YbIZ'HZO ..19
3 Infrared spectrum of YbIZ'HZO ................. 30

4 NMR spectra of YbIZ°H20 at 250C -— 750C ........ 31

vi

CHAPTER ONE: INTRODUCTION
A. Preparatory and Structural Background

Lanthanide elements form a number of hydrates which
belong to diverse structure types. Some methods for the
preparation of lanthanide halide hydrates have been reported
in the literature and are discussed below. The chloride and

bromide halide hydrates have been studied extensively.
1. Lanthanide trihalide hydrates

The general preparatory procedure for hydrated
lanthanide trichlorides (MCl3‘xH20; M = lanthanide) is
dissolution of the lanthanide oxides in concentrated
hydrochloric acid with subsequent precipitation of the
hydrate upon removal of the acid.

The thermal decomposition of MC13°xH20 (x = 6,7) has
been investigated with Differential Thermal Analysis (DTA)
by numerous workers [1-5]. Wendlandt found that the heavier
lanthanide (from Eu to Lu) trichloride hexahydrates begin to
lose water of hydration in a slow stream of air in the

temperature range 650C to 950C [2]. He also found that as

fl}

the basicity of the cation decreases, igeL, as the cationic
radii decrease in size, the possibility of forming
intermediate hydrates increases. When the trichloride
hexahydrate was heated at 360°C — 425°C in air, the metal
oxidechloride, the quantity of which increased as the
basicity’ of the cation decreased, was found to be the
product.

Ashcroft and Mortimer studied the thermal decomposition
of the trichloride hydrates MC13’xH20 using a Bufferential
Scanning Calorimeter (DSC) [6]. Decompositions carried out
in [a nitrogen atmosphere at relatively low temperatures,
around 280°C, gave the anhydrous trichloride as the final
product. They found three intermediate hydrates (x = 3, 2,
1) for M = La, Ce, Pr, Nd, Eu, and Gd, and two (x = 4, 1)
for M = Sm, Tb, Er, Tm, Yb, and Lu.

The trichloride hexahydrate structures have been
characterized by single crystal X-ray diffraction. Graeber,
et al. demonstrated that MC13°6H20 phases were describable
with monoclinic symmetry ,space group P2/n and two molecules
in a cell [8], as shown in Table I. The structure contains
the 8-coordinate complexes [MC12(OH2)6] that one third of
the chlorine atoms form no bonds with metal atom.

The MC13'7H20 structure was determined by Brouty and .
Herpin [7]. They reported for this heptahydrate triclinic
symmetry, space group P1, 2 = 2, amd a cell that contains

the 9-coordinate complex [MC12(OH2)7].

Table I. Lattice parameters,space groups and colors of
lanthanide hexahydrates.

Compound Color Space Lattice Parameters Ref
Group a(A) 9(3) g(A) B(°)
Smel3°6820 Yellow PZ/n 9.67 6.55 7.96 93.67 [8]
EuCl3‘6Hé0 Colorless PZ/n 9.68 6.63 7.96 93.67 [8]
GdCl3’6H20 Colorless PZ/n 9.64 6.53 7.93 93.67 [8]
TbCl3'6H20 Colorless P2/n 9.63 6.51 7.89 93.67 [8]
DyCl3'6HZO Yellow P2/n 9.61 6.49 7.87 93.67 [8]
HoCl3‘6H20 H. Y. Pz/n 9.58 6.47 7.84 93.67 [8]
ErCl3’6H20 L. P. PZ/n 9.57 6.47 7.84 93.67 [8]
TmCl3'6H20 Green Pz/n 9.55 6.45 7.82 93.67 [8]
NdBr3'6H20 Blue P2/n 10.073 6.785 8.212 93.52 [10]
GdBr3°6H20 White PZ/n 10.014 6.753 8.149 93.43 [10]
TbBr3 6HZO White PZ/n 10.000 6.744 8.139 93.35 [10]
DyBr3’6H20 White P2/n 9.969 6.733 8.102 93.30 [10]
HoBr3’6H20 P. Y. P2/n 9.937 6.717 8.085 93.32 [10]
ErBr3'6HZO Pink P2/n 9.925 6.700 8.073 93.33 [10]
TmBr3‘6HZO White P2/n 9.920 6.698 8.056 93.44 [10]
YbBr3 6HZO White PZ/n 9 920 6.693 8.046 93.43 [10]
LuBr3 6H20 White P2/n 9.902 6.678 8.024 93.42 [10]

H. Y.= Honey Yellow L. P.= Light Pink P. Y. = Pale Yellow

The synthesis procedure for the lanthanide tribromide
hydrates is similar to that for the trichloride hydrates.
Mayer and Zolotov indicated [9] that tribromide monohydrates
could be obtained as an intermediate phase during thermal
decomposition of tribromide hexahydrates in air. They
hypothesized that the decomposition proceeds according to

the steps detailed in (l):

MBr3.6H20-’>MBI3.H20-->MBr3-->MOBr-->M203 (1)

M = Pr, Nd, Sm and Eu

Monohydrates were not observed with the heavier lanthanide
elements; the hexahydrates decomposed directly through the

oxidebromide according to (2):

MBr3‘6H20-->MBr3 + MOBr-->MOBr-->M203 (2)

M = Gd, Tb, Dy, Ho, Er, Tm, Yb and Lu

In addition, it is interesting to note that the U, Np, and
Am tribromide hexahydrates were prepared as evidenced by the
mass increase of the appropriate anhydrous tribromide upon
exposure to oxygen-free water vapor in an inert atmosphere.
The structural properties of lanthanide tribromide
hexahydrates were discussed by Brown, et al. [10]. All of
the tribromide hexahydrates are isostructural with the
trichloride hexahydrates; they exhibit monoclinic symmetry,

space group P2/n, with two molecules per unit cell. The

space group, lattice parameters, and colors of these
hexahydrates are summarized in Table I.

Due to the intrinsic chemical instability of triiodide
hydrates to undergo spontaneous decomposition to
oxideiodides and HI, it is difficult to prepare the
lanthanide triiodide hydrates. As a consequence they are

only characterized to a limited degree.
2. Lanthanide dihalide hydrates

Several lanthanide dihalide hydrates (MX2°xH20, x s Cl,
Br, I) have also been reported. Their lattice parameters and
symmetries are summarized in Table II. Although SmIz°H20 is
reported in the table to be orthorhombic, lattice parameters
could not be found.

Europium dichloride dihydrate was characterized by
Hasse and Brauer [11]. They’ prepared EuC12'2H20 from a
solution of Eu203 in dilute hydrochloric acid by employing
amalgamated zinc for reduction of Eu3+ followed by
precipitation with concentrated hydrochloric acid.

They found that EuC12°2H20 ”belongs to the monoclinic
crystal system, space group C2/c, with z = 4 (see Table II).
It is obvious that the atomic arrangement of EuC12°2H20 is
nearly the same as that of SrClZ’ZHZO which has square
antiprismatic coordination for the metal ions. They
described that coordination shell of the Eu2+ ion as

probably consisting of two hemispheres, one of four chlorine

atoms and the other of four water molecules arranged to form
the coordination number of 8.

Haschke and Eick prepared the dihalide monohydrates,
MXZ’HZO, (M = Sm, Eu; X = Br, I) for samarium and europium
by vapor phase hydration of the anhydrous phase [12-14].
Powder X-ray data showed that the SmBr2°H20 phase was
indexable on orthorhombic symmetry .with systematic
extinctions consistent ‘with. space group ana. They“ also
discovered an intermediate hydrate, EuBrZ‘HZO, when an
anhydrous EuBr2 specimen hydrolyzed in a powder X-ray
diffraction camera [13]. This hydrated dibromide phase-was
isostructural with SrBrz’HZO (and presumably with
SmBrz'HZO), and was indexable on orthorhombic symmetry,
space group ana.

The diiodide monohydrates, SmIz'HZO and EuIZ'HZO, have
been identified [14,15]. Wang investigated the hydration of
Smlz [15]. A hydrated anhydrous SmI2 specimen was obtained
with water absorbed on silica gel serving as the hydrating
reagent. The powder X-ray diffraction pattern showed this
SmIz'HZO phase to be indexable as B-Sm12 which is
orthorhomic and isomorphous with EuIZ.

EuI2°H20 was obtained by hydration of anhydrous Eulz
with atmospheric moisture when a specimen was not rigorously
isolated from the atmosphere. This monohydrate phase showed
orthorhombic symmetry and is isostructural with BaClZ’HZO,

space group anm.

3. Alkaline earth halide hydrates

Lattice parameters and symmetries of selected alkaline
earth dihalide hydrates are summarized in Table III. Because
of their similar size and like charge the divalent
lanthanide halides behave similarly to the alkaline earth
halides. The crystallographic data presented in Tables II
and III show the presence of structural similarities between

MX2.H20 (M = Sr, Ba, X = Cl, Br, I) and LnX2.H20 (Ln = 8m,

Table II. Lattice parameters and symmetries of selected
lanthanide dihalide hydrates

EuC12.HZO Orthorhombic 10.86 8.80 4.16 [19]

EuClz.ZHZO Monoclinic 11.66 6.40 6.69 105.37 [11]

SmBr2.H20 Orthorhombic 11.43 9.18 4.32 [12]
EuBr2.HZO Orthorhombic 11.46 9.20 4.29 [13]
SmIZ.HZO Orthorhombic [15]

EuIZ°HZO Orthorhombic 12.37 9.67 4.48 [14]

Table III. Lattice parameters and symmetries of selected alkaline
earth halide hydrates

BaClz'HZO Orthorhombic 11.094 4.500 9.054 452.0 [18]
BaBrz’HZO Orthorhombic 11.643 4.604 9.438 505.9 [18]
BaIZ'HZO Orthorhombic 12.494 4.772 10.014 597.1 [18]
SrClZ'HZO Orthorhombic 10.881 4.162 8.864 401.4 [18]
SrBrZ’HZO Orthorhombic 11.464 4.295 9.229 454.4 [18]
SrIZ’HZO Orthorhombic 12.474 4.495 9.741 546.2 [18]
CaClZ’ZHZO Orthorhombic 5.893 7.469 12.070 531.3 [16]

CaIZ'4HZO Monoclinic 6.825 7.846 9.637 110.47 509.1 [17]

CaI2'6.5H20 Monoclinic 6.755 8.162 17.878 107.76 2426.8 [17]

10

4. Spectroscopic studies

Infrared spectrocopy
In general, lattice water exhibits vibrational

frequencies at 3550 - 3200 cm-1

(antisymmetric and symmetric
—OH stretching) and at 1630 - 1600 cm”1 (HOH bending).
Lattice water also shows "libration modes" in the low-
frequency region because of rotational oscillations of the
water molecule. These rotations are restricted by
interactions with neighboring atoms [23].

Lutz and Christian studied by infrared spectroscopy-the
iSotypic alkaline earth halide monohydrates, MX2°H20, with
M = Sr and Ba and X = Cl, Br, and I [22]. They found that
the water molecules are asymmetrically bonded in the

chloride and bromide hydrates and symmetrically bonded in

the case of the iodide hydrates.

NMR spectroscopy

Nuclear magnetic resonance spectroscopy has become a
useful tool for the study of the atomic arrangement and the
electron charge distributions in a given specimen.

It is a highly characteristic feature of NMR that
spectral lines of liquids are much narrower than those of
solids. This substantial difference in line broadness arises
from the static anisotropic interactions present in solids.

In liquid specimens these interactions are averaged by the

isotropic motions of the nuclei.

11

A good example to illustrate this difference in line
broadness is the 1H-NMR linewith of water and ice. The
resonance line of ice has a width of the order of 105 Hz
whereas that of liquid water is but a few Hz [43].

Line broadness in solids results from magnetic dipolar
and Fquadrupolar interactions and from chemical shift
anisotropy. Due to the restricted molecular motions present
in solids, but not in liquids, the anisotropic interactions
are not averaged out in time. In powdered samples these
interactions give rise to NMR line broadening. To overcome
this problem the Magic Angle Sample Spinning (MASS)
technique was developed by Andrew, et a1. [37] in 1959. It
is capable of partially suppressing the anisotropic
broadening.

Numerous NMR hydrate studies have been reported since
Pake’s first study in 1948 of the proton resonance absorption
lines of the hydrated crystal, CaSO4'2H20_ [24]; Pake
determined the distance between hydrogen nuclei in the water
molecules of hydration and the orientation of the line
connecting the proton pair in the water molecule. The
analysis of broad proton NMR absorption curve of the powder
CaSO4’2H20, was also described to show that structural

information about the water molecule could be obtained.

I!»

CHAPTER TWO: EXPERIMENTAL

A. Chemicals

Chemicals used in.1flua synthesis experiments described

in this work are listed in Table IV.

12

Table IV.

Chemicals used for syntheses

Compound
or
Element

Manufacturer

—-_—_-—————nun——--_-—-——————-——-——-————.—a—-~-—---——--—--———u———

Ytterbium
metal

Mercury
iodide
Methyl
alcohol

Acetone

Dimethyl
ether

Diethyl
ether

Calcium
hydride

Benzo-
phenone

Nitric
acid

Silver
nitrate

Ferric
ammonium
sulfate

Ammonium
thiocaynide

Analytical reagent
grade

99.82
Anhydrous GR

Analytical reagent
grade

Analytical reagent
grade

Analytical reagent
grade

952

ACS/reagent grade

99.92

Analytical
reagent
grade

Cerfified ACS
grade

Research Chemicals.
Phoenix, AZ

Mallinckrodt
St.Louis, MO

EM Science
Cherry Hill, NJ

J.T. Baker Chemical Co
Phillpsburg, NJ

Matheson
Mallinckrodt
St.Louis, MO

EM Science
Cherry Hill, NJ

Fisher Scientific
Springfield, NJ

EM Science
Cherry Hill, NJ

Sargent-Welch
Skokie, IL

Mallincrodt

St.Louis, MO

Fisher Scientific
Springfield, NJ

__-____--—___—-_________-_-__-____--_-___-_—__—_--_—---_.

14

B. Synthesis Equipment

A high vacuum line which can be pumped to 10’7 - 10'5
Torr must be used for the synthesis of ytterbium diiodide
monohydrate. The liquid-nitrogen-trapped vacuum line used in
this work consisted of a mercury diffusion pump, a CENCO
roughing pump, and an all glass manifold as described by
Shriver [26].

All manipulations of reactants and products were
carried out in a glove box. The argon atmosphere of this box
was continuously recirculated and purged of water with

molecular sieves and of oxygen with heated BASF catalyst.
C. Synthesis procedures
1. Anhydrous ytterbium diiodide

Metal chips were cut from a block of_ytterbium kept in
the glove box. Weighed pieces of Yb chips and Hg12 in the
molar ratio of 1:8 were placed in the lower bulb of a two
bulb Pyrex reaction vessel.

The Pyrex vessel was removed from the glove box,
connected to the vacuum line, and evacuated to 10"3 Tbrr.
The vessel was shaken gently to facilitate removal of
trapped gases, sealed, and cut from the vacuum line at the
end of second bulb with a hand torch.

The sealed Pyrex vessel was situated into a tubular

Fir,

15

furnace for 7 days as is shown in Figure 1 and maintained at

a temperature of 365°C.
When mercuric iodide was removed from the reaction bulb
by sublimation, the green anhydrous ytterbium diiodide

remained. The absence of water' was verified. by infrared

analysis.

diiodide synthes aaaaaaaaaaaa

 

 

17

2. Ytterbium diiodide monohydrate

Ytterbium diiodide monohydrate was prepared in the
apparatus shown in Figure 2. This H-shaped apparatus was
cleaned before use in the following manner: It was first
rinsed with an acid solution which contained 33% HNO3, 5%
HF, and 60% H20, then filled with aqua regia and allowed to
sit overnight. The aqua regia was removed and the apparatus
then rinsed with distilled water several times. It was then
dried in an oven.

Ytterbium (diiodide monohydrate synthesis experiments
were attempted with three solvents: methyl alcohol, dimethyl
ether, and acetone.

An elaborate purification procedure was developed for
the solvent ultimately used. That procedure is described
here.

About 75 ml of dimethyl ether was stirred for 24 h over
0.5 g of CaH2 in a round flask situated in a dry ice bath to
removelzmoisture, then. distilled under high ‘vacuum (10-5
Torr), frozen with liquid nitrogen, and evacuated. It was
necessary to repeat these stir-freeze-pump cycles several
times, then distill the dimethyl ether into a pre-evacuated
bottle which contained Na-K alloy (1:3) and benzophenone..
When the color of the solution remained violet-blue,
indicative of the absence of moisture, the ether was
distilled into the H-shaped reaction vessel.

A weighed amount of powdered anhydrous ytterbium

l8

diiodide was placed in chamber (a) [see Figure 2] through
the Fisher-Porter stopcock. The same molar amount of water
was purified by freeze and thaw cycles and distilled into a
5 mm o.d. glass ampoule which was then sealed. The sealed
water ampoule was also introduced into chamber (a).

About 20 ml of purified dimethyl ether was then
distilled into chamber (a) of the H-shaped reaction vessel
which had been pre-evacuated to 10'6 Torr to dissolve the
anhydrous ytterbium diiodide. The apparatus was removed from
the vacuum line and kept at a temperature lower than the
boiling point of dimethyl ether (~250C) in an isopropyl
alcohol-dry ice bath (-40°C).

The water ampoule was broken by several freeze-shake-
thaw cycles. As the water reacted with the ytterbium
diiodide, the color of the dimethyl ether solution changed
from green to white. The solution was then filtered through
the coarse frit in the H-vessel from chamber (a) into
chamber (b). Finally, the white solution in chamber (b) was
pumped to dryness by evacuating the H-vessel to 10"5 Torr on
the high vacuum line. A bright greenish-yellow powder later
demonstrated to be ytterbium diiodide monohydrate remained.
Powder X-ray diffraction confirmed that the powder was a new

phase.

19

Figure 2. Apparatus used for the synthesis of ytterbium
diiodide monohydrate.

 

 

 

 

 

 

 

20

3. Ytterbium diiodide dihydrate

Ytterbium diiodide dihydrate was prepared by the
hydration method described by Kwapisz [27]. A weighed amount
of anhydrous ytterbium diiodide situated in a pyrolytic
graphite boat was placed in a Pyrex tube in the glove box.
The Pyrex tube was removed from the glove box, connected to
the vacuum line, and evacuated. A quantity of cupric sulfate
weighed according to equation (3) to give the appropriate

molar ratio of water was inserted into a silica boat.

5Yb12(s)+ 2[CuSO4‘5H20](s) —-> 5[Yb12°2H20](s) +2CuSO4(s)

(3)

The tube was filled with argon, and as the gas flowed
through the Pyrex tube, the silica boat was introduced. The
tube was then evacuated to 10"3 Torr. During the hot weather
in summer, the hydration reaction was conducted in a
refrigerator (4°C) over a period of 2 weeks.

As time passed, the color of the anhydrous ytterbium
diiodide changed from green to [dark green. The change of
mass of each. reagent indicated that anhydrous ytterbium
diiodide was hydrated by the cupric sulfate, and that
ytterbium diiodide dihydrate was produced. X-ray powder

diffraction confirmed that the product was identical to that

prepared by Kwapisz.

21

C. Analysis

1. Ytterbium

Ytterbium metal content was determined by gravimetric
procedures. A 6N HNO3 solution was added to the sample
confined in a platinum crucible to remove iodine, direct

ignition at 950°C produced the sesquioxide.

2. Iodine

The product was analyzed for iodine by' the Volhald
method [28] in acid medium. In this process an excess of
standard silver nitrate was added to the solution and. the
excess Ag+ was back-titrated with a standard potassium
thiocyanate solution. A 40% ferricammonium sulfate solution

served as indicator.

3. Water

Water analyses was conducted by Galbraith Laboratories,

Inc., by the Karl Fisher water analysis method.

22

D. Instruments

1. Powder X-ray Diffraction
The hydrated products were characterized by powder X-

ray diffraction analysis. Interplanar d-spacings were
determined with an evacuated Guinier camera (114.6 mm
diameter) by' using CuKal .radiation Lt a1 = 1.54050 A).
Silicon powder (a = 5.43082(3) A) was employed as an
internal standard. Paraffin oil and ScotchR tape served to
protect the silicon-sample inixture from further reaction
with moisture.

For the anhydrous ytterbium diiodide specimens, powder
X-ray diffraction was carried out with the sample confined

in 0.3 mm o.d. sealed Lindemann glass capillaries.
2. Infrared

IR spectra were recorded with a BOMEM model DA3

Fourier-transform infrared spectrometer between 4000 cm"1

and 800 cm'1 at 3 cm'1

resolution. The sample which was
mixed with nujol and pressed between NaCl plates was

maintained under vacuum during analysis.
3. NMR

NMR spectra were measured with the powdered sample in a

sealed 5 mm o.d. NMR tube at 250 MHz on a Bruker WM-250

 

 

23

Spectrometer. The 16 step phase-cycled spin-echo [29] NMR
procedure was used for removal of base line distortion due
to ringing of the transmitter/probe circuits and dead time

of the receiver. Two 90 degree pulses (P1 = 9.5 and P2 = 9.5

microsec), two delay times (D1 = 50 and D2 = 44 microsec)
and recycle times (10 microsec) were used. Temperatures at

which the measurements were taken varied in the range of

250C and 75°C .

CHAPTER THREE: RESULTS

A. Anhydrous ytterbium diiodide

The powder X—ray diffraction pattern of the anhydrous
YbIZ prepared by reaction with excess HgI2 with Yb showed
about 20 reflections which could be ascribed to a hexagonal
cell with a = 4.504(3) A and c = 6.970(5) A.

Interplanar d-spacings and intensity values ' for
anhydrous YbIz prepared' in this study together' with the
values calculated by the program POWD12 [35] with the

positional and thermal parameters reported for Cd12 by

Wyckoff [30] are given in Table V.

24

25

Table V. Observed and calculated interplanar
d-spacings and intensities of anhydrous YbI2

h k l Iobs Icalc dobs(A) dcalc(A)
0 0 1 M 31.8 6.53 6.972
1 0 0 VW 1.9 4.037 3.900
0 O 2 VW 1.4 3.476 3.486
1 0 1 VS 100.0 3.343 A 3.404
1 0 2 S 59.0 2.597 2.599
1 l 0 M 40.0 2.228 2.252
1 1 1 W 12.1 2.138 2.143
1 0 3 w 24.2 1.997 1.996
2 0 1 W 20.2 1.878 1.877
2 0 2 VW 8.9 1.703 1.702
2 1 1 W 18.8 1.444 1.442
1 1 4 VW 18.2 1.379 1.378
3 0 0 W .7.5 1.301 1.300
2 0 4 VW 0.1 1.301 1.299
2 1 3 VW 0.1 1.247 1.245
2 2 0 VW 4.7 1.127 1.126
1 0 6 VW 2.3 1.110 1.114
2 2 1 VW 2.3 1.110 1.114
2 2 2 w 1.069 1.111
3 1 l W 1.069 1.111

* VS,very strong;$,strong;M,medium;w;weak;
VW,very weak.

26

B. Ytterbium diiodide monohydrate

It was indicated previously (Chapter two,sec 2.) that
several synthesis attempts were made with methyl alcohol,
acetone, and dimethyl ether. The results obtained with each
solvent are presented here.

The green Yblz powder produced bubbles when it contacted
the water-methanol solvent. As it reacted gas evolution
persisted and a green solution resulted. When diethyl ether
was added to the methyl alcohol solvent to precipitate
Yb12°H20, a yellow precipitate formed; its color changed to
white.

When acetone was used as solvent, the Yb12 dissolved
readily at room temperature to form a dark violet solution.
The Violet color probably results from ionization of the
iodide ion in the acetone solution and its subsequent
complexation with acetone. When the acetone was removed under
vacuum by heating about 20 minutes with a heat gun, the green
powder appeared again. By powder X-ray diffraction it was
verified that the green powder was anhydrous YbIZ.

In other experiments with the YbIZ-acetone solution the
acetone solvent was removed slowly by inserting into liquid
nitrogen the end of the chamber of the H-shaped vessel that
did not contain the specimen. AS the acetone was removed
slowly, the violet color disappeared and the yellow powder
again formed. Prof. Dr. Hodorowicz determined the water of

hydration by DTA-TGA and demonstrated that the yellow powder

27

was YbIZ'IOHZO. This DTA-TGA result shows that it is
possible to form higher hydrates of divalent ytterbium
iodide.

The powder X-ray pattern of YbIZ'HZO was characteristic
of an orthorhombic cell with the lattice parameters;
a = 16.012(5) A, b = 8.140(2) A, and c:== 4.5080(9) A. The
interplanar d-spacings were indexed and the parameters
refined by the programs ITO9 [33] or TREOR [34]. In Table VI
the observed interplanar d—spacings and correspOnding
intensities and the calculated d-spacings of YbIZ‘HZO are
presented. Every reflection is indexed and the figure-of-
merit is 29.0 [46]. Extinctions are consistent with space

28

Table VI. Observed and calculated interplanar
d-spacings and observed intensities of

YbI2.H20

o o
h k l Iobs dcalc(A) dexp(A)
2 0 0 VS 8.006 8.018
1 1 0 VS 7.256 7.247
2 1 0 M 5.708 5.722
3 1 0 W 4.463 4.474
0 2 0 VW 4.070 4.080
4 0 0 VW 4.003 4.007
0 1 1 VW 3.945 3.944
1 1 1 W 3.829 3.833
4 1 0 M 3.592 3.594
2 1 1 VS , 3.537 3.535
3 2 0 W 3.236 3.238
3 1 1 W 3.172 3.173
O 2 1 S 3.021 3.021
4 O 1 8 2.993 2.993
1 2 1 VW 2.969 2.971
4 2 0 8 2.854 2.855
2 2 1 S 2.826 - 2.826
4 1 1 M 2.809 2.809
1 3 0 VW 2.675 2.675

3 2 l W 2.629 2.631

 

29

The infrared spectrum of YbI2°H20 was recorded to help
characterize the environment of the water molecule.inIZ°H20
exhibits the infrared spectrum shown in Figure 3. The
principal features of this infrared spectrum are the bands
between 1600 cm"1 and 3600 ‘ cm‘l. Figure 3 shows bands at
3430 cm"1 and 1610 cm'1 which result from the O-H asymmetric
stretching and HOH bending modes of the water molecule,
respectively.

Solid-state powder static proton NMR spectra of
YbIZ'HZO are shown in Figure 4. Spectra from 25°C and 750C
are compared, and the effects of temperature on -the
appearance of the NMR spectra are illustrated in Figure 4.

The results of the elemental and water analyses are

tabulated in Table VIII.

 

30

 

.ON:.NHQW wo Esuuowmm cmHMHHGH .m Guzman

7.2 u
8.2. ooeu comm oooe

P — .

00m
F

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

BONVIIIWSNVHI

31

Figure 4. NMR spectra of Yb12.H20 at 25°C -- 75°C.

 

 

75°C

 

 

 

 

 

32

C. Ytterbium diiodide dihydrate

Several attempts were made in summer months to prepare
YbIz'ZHZO with CuSO4'5H20 as the hydrating agents in
anticipationthat Yb12°2H20 would be the product. However,
anhydrous YbIz formed a different hydrate at room
temperature in the Pyrex reaction vessel. When the reaction
was carried out for tWo weeks in the refrigerator (4°C) in
summer, the YbIz surface became dark green, but a yellow-
colored solid had formed beneath it. X-ray powder
diffraction showed the surface to be YbIZ’ZHZO, with other
unidentified compounds present in the lower part of the
product. This inhomogeneous product apparently results from
the differential absorption of water by the anhydrous YbIz.
As might be expected, YbIZ'ZHZO was produced on the surface
with a lower hydrate beneath the surface.

According to the program ITO9 [33] the d-spacings of
this dark-green colored hydrate are indexable on
orthorhombic symmetry with a figure-of-merit of 22.9. The
observed and calculated d-spacings and the observed
intensity data for Yb12°2H20 are presented in Table VII. The
lattice parameters were refined by program APPLEMAN [36]:
a = 13.024(5) A, b = 10.455(5) A, and c = 4.507(3) A.

Metal and iodine analysis data of ‘the dihydrate are:

presented in Table VIII.

 

33

Table VII. Observed and calculated interplanar
d-spacings and observed intensities of

Yb12.2H20
h k l Iobs dca1c(z) dobs(X)
1 1 o 5 8.153 8 160
2 o 0 5 6.512 6.496
0 2 0 VW 5.228 5.228
1 2 o 5 4.851 4.846
2 2 o 5 4.077 4.075
3 l 0 vw 4.010 4.010
1 1 1 VW '3.945 3.948
0 3 0 vs 3.485 3.488
0 2 1 W 3.414 3.413
3 2 0 M 3.340 3.347
1 2 1 M 3.302 3.299
4 o 0 VW 3.256 3.255
2 2 1 vs ‘ 3.023 3.022
3 1 1 W 2.996 2.997
4 2 0 VW 2.764 2.766
3 3 0 5 2.718 2.718
1 3 1 vw 2.697 2.699
3 2 1 5 2.684 2.683
4 3 0 VW 2.397 2.383

4 2 1 VW 2.359 2.359

 

34

Table VIII. Elemental and water analysis results

compound Yb(Z) 1(2) water(1)

YbI2°H20 cal. 38.90 57.05 4.05
exp. 38.95(4) 58.85(7) 4.05(29)

YbIZ°2H20 cal. 37.38 54.83 7.78

exp. 38.33(3) 53.90(8)

 

CHAPTER FOUR: DISCUSSION
A. Synthesis

Anhydrous ytterbium diiodide

Anhydrous Yblz was prepared by chemical reaction (4) in

an excess of HgIZ.
Yb(s) + HgIZ(l)-—-> YbIZ(s) + Hg(l) (4)

Hg212 was also a probable product. No effort was made
to separate the Hg from either the excess of HgI2 or from
Hg212 that may have formed. The vapor pressure data of each
reaction component as shown in Table IX substantiate that
HgIZ should be separable quantitatively by sublimation from
YbIZ.

Oxidation of ytterbium by Hglz took place easily:
ytterbium metal is a powerful reducing agent, (Yb+3 + 3e"
———> Yb, E0 = -2.27 v ) (Yb+3 + e‘ ———> Yb+2, E0 = -1.21 V)
This large reduction potential coupled with the large vapor
pressure difference between Hg and HgI2 and YbI2 assured

quantative reduction [47]

35

 

36

Table IX. Vapor pressure of selected compounds at various

temperatures
Compound Vapor Pressure Temp Ref
CaSOA'ZHZO 0.005 mg/l 25°C [41]
Cuso4 1.4 mg/l 25°C [41]
ngz 100 Torr 262°C [41]
Hg 100 .Torr 262°C [41)
YbI2 1.9xlo‘16 Torr 260°C [47]

2 Torr 790°C

 

37

Ytterbium diiodide monohydrate

Although, methyl alcohol, ethyl alcohol, acetone,
dimethyl ether, and diethyl ether were considered as
solvents for the synthesis reaction, dimethyl ether proved
to be the solvent of choice.

Methyl alcohol whose boiling point is 64.50C was chosen
initially for the preparation. It was thought that this
solvent could be removed easily and that it would not react
with YbIZ. However, with dimethyl ether as solvent
significantly more pure YbIz°H20 could be prepared than was
obtained with either methyl alcohol or acetone. Accordingly,
this solvent has proved to be the best found to date for the
preparation of YbIZ'HZO. The fact that dimethyl ether must
be kept at a temperature below its boiling point, -25°C,
somewhat complicates the synthesis procedure. From the IR
spectrum it is clear that dimethyl ether did not form
complex with YbIz. Some of the problems encountered in this
YbIz’HZO synthesis procedure are decomposition of the
solutions during synthesis because of impurities not removed
or leakage in the high vacuum system, air sensitivity of the
components, the length of time required for the synthesis
procedure, and purification of the solvent.

However this method also has some advantages. The
exceedingly high'vapor pressure of dimethyl ether allows'
very easy solvent removal and its low dielectric constant

tends to increase the YbI2°H20 yield.

38

Ytterbium diiodide dihydrate

This preparation was attempted first via a sodid-vapor
procedure in a Pyrex reaction vessel by Kwapisz [27]. He
prepared a ytterbium diiodide hydrate specimen which he
thought was the monohydrate, but which was later demonstrated
to be the dihydrate, YbI2°2H20.

Some of the problems encountered in this synthesis
procedure ‘were selection. of a suitable hydrating agent,
variable reaction time with respect to the environment, low
thermodynamic stability of the product, and production of an
inhomogeneous layered product.

Kwapisz prepared YbI2'2H20 according to equation (5).

5Yb12(8) + 2[CUSO4.5H20](S) --> 5[Yb12.2H20](S) + 2CUSO4(S)

(5)

He found that with CuSO4°5H20 as a hydrating agent one or
two water molecules could readily be donated for this
Yb12°2H20 synthesis. CaSO4°2H20 *was initially’ used. as a
hydrating agent by Kwapisz, but with it the YbIZ did not
evidence any hydration whatsoever. Since the residual. H20
vapor in dried air for CaSO4 is 0.005 mg/liter and that for
anhydrous CuSO4 is 1.4 mg/liter [41], the absence cf
hydration with CaSO4°2H20 is readily understandable. The
partial pressure of H20 in the reaction environment must be
controlled. carefully' to avoid production of higher ‘YbIz

hydratesprior to completion of the desired hydration

 

 

39

reaction.

Several generalizations of YbIz'ZHZO synthesis
experiments made by the solid - vapor method indicate the
following:

First, the formation of YbIZ'ZHZO was complete within 7
days at room temperature. Since the H20 tensimetric pressure
of the hydrating agent is greater in summer than in winter,
the hydration reaction proceeds more rapidly in summer than
in winter.

Second, the vapor pressure of water required for
hydration must either equal or be slightly less than that of
CuSO4'5H20 since hydration can be achieved.

Third, YbI2'2H20 must possess greater thermodynamic
stability than does the monohydrate since monohydrate was
never observed in a product prepared by this procedure.
However, this dihydrate may be metastable toward either

further hydration or hemihydration.

B. Powder X-ray diffraction

Anhydrous ytterbium diiodide

The standard deviations of the parameters derived from
the observed reflections by localLy written programs were
very small, typically less than t 0.005 A an indication
that the parameters are well determined. This good fit is
considered evidence that YbIZ exhibits the hexagonal

symmetry CdIZ-type structure. The CdIZ—type structure is the

   

40

only reported structural form for YbIZ. This structure
consists of a layer-like atomic arrangement and exhibits in
its physical properties the characteristics of layered
compounds [38].

The CdIZ layered structure in the crystal can be viewed
as hexagonal close-packing of iodine ions with the small
cadmium ions nested in the octahedral holes between every
two layers of iodine ions. To maintain stoichiometry half of
the octahedral holes must be vacant. These vacancies result
in the two adjacent layers of iodine atoms being held
together by van der Waal’s forces.

According to Asprey and Kruse [38] Yblz does not exibit
the polytypism so characteristic of the CdIZ-type structure.
With the atomic positibnal and thermal parameters reported
by Asprey and Kruse, the reflection intensities could be
calculated. by' the jprogram. POWD12. The agreement. between
calculated and observed intensities for YbIz as shown in
Table V substantiates that the metal ions occupy'the 1a
positions and the iodide ions the 2d positions in the space

group.

Ytterbium diiodide monohydrate

The symmetry of YbIZ‘H2O is the same as those of
SrClZ'HZO, MBrz'HZO (M = Sm, Eu,and Sr), and EuIZ'HZO. The
lattice parameters observed for the YbI2.H20 are: Q can be
as big as by a factor of approximately 1.5 of the above

related divalent halide monohydrates, and p and Q are

 

 

41

consistent with those reported previously for the divalent
halide monohydrates, as is illustrated in Table II and Table
III.

The YbIZ'HZO unit cell volume of 587.63 A3 can be
regarded as the summation of the volume of anhydrous YbIZ,
61.2 A3, and that of H20, 36.74 A3, derived from the
structure of solid water [30]. This summation would imply
that the cell contains six YbIZ'HZO moieties, or that z = 6.

It was thought initially that EuIZ.H20 structure (z=4)
expected to be the structure type for Yb12.H20 with Yb atom
substituted for Eu atom. The lattice parameter a which is
calculated from the hypothetical cell containing six
Eu12.H20 moieties is 18.05 A. The EuBr2.H20 structure (2 =
4) was also considered. The lattice parameter a, 17.19 A, is
calculated from the hypothetical large cell containing six
EuBr2.H20 moieties. On the basis of these above calculations
it is clear that the calculated lattice parameter a, 17.19
A, from the EuBr2.H20 structure is closer to the lattice
parameter a, 16.012 A, of the observed present
investigation, Yb12.H20. Thus it is suggested that the best
struCturral model for the Yb12.H20 would entail, probably,
EuBr2.H20 ‘with. positional coordinates transformed. t0"the

large cell.

Numerous attempts were made to calculate a theoretical
powder pattern for YbIZ‘Hzo by using positional parameters
of related hydrates which have the same space group,

P212121, and reasonably similar values Of z, with estimated

42

thermal parameters. For example, CeOSO4'H20 and TiOSO4°H20
were used as model structures. For these calculations the
ytterbium atom was situated in the cation site, one X
occupied the O atom site, and the second X occupied the S
atom site. The water molecule occupied its established
position. Lattice parameters for YbIZ'HZO were used for the
calculation. run“; of the theoretical intensities matched
the observed pattern. ' The CRYSTDAT data base was also
searched for an appropriate structural model for YbIQ'HZO;
this search was not fruitful [42].

As was discussed. earlier (Chapter one, sec 3) _the
lanthanide(II) and the alkaline earth halides form similar
hydrates. Since the radius of Ca2+ with coordination
number 8 is 1.26 A and that of Yb2+ 1.28 A [32], there
should be structual similarities between CaXz and Lnxz (Ln
= Yb and adjacent elements, Tm and Lu; X= Cl, Br, I). Thus,
their halide hydrates would be expected to Show some similar

structure types as is evident in Table X.

43

Comparison of the structure types of some lanthanide

dihalide with those of alkaline earth halides

Table X.

M\X Cl

Sm PbClZ(9)a
CaF2(8)

Eu PbC12(9)
CaF2(8)

Tm SrIZ(7)

Yb SrIZ(7)

Ba PbClZ(9)
Fe2P(9)
CaF2(8)

Sr PbC12(9)
CaF2(8)

Ca SrI (7)
CaC 2(6)
a-Pb02(6)

a
PbC12(9)

SrBr2(8)

SrBr2(8)
PbC12(9)

SrIZ(7)
CaC12(6)

CaC12(6)

PbC12(9)

PbC12(9)

,SrBr2(8)

CaC12(6)

a-Pb02(6)

Ti02(6)

a-Pb02(6)
T102(6)

_ a
m EuI2(7)

PbC12(7)

m-EuIZ(7)
PbC12(9) Sr12(7)

CdI2(6)

CdIz(6)

.PbC12(9)
FeZP(9)

PbClZ(9)
SrI2(7)

CdI2(6)

[39]

[39]

[39]

[39]

 

44

Ytterbium diiodide dihydrate

The symmetry of YbIZ'ZHZO, orthorhombic by the program
ITO9, is the same as those of SrClz‘HZO, MBrZ'HZO (M:= Sm,
Eu, Sr). The unit cell volume of 613.81 A3 can be regarded
as the summation of the volume of YbIZ, 61.2 A3, derived
from the unit cell volume of anhydrous YbIZ, and that of
H20, 35.8 A3, derived from the structure of solid water.
When these volumes are compared to that of the dihydrate, it
is apparent that the unit cell contains four Yb12°2H20
moieties, or that z = 4.

Several attempts were made to calculate theoretical X-
ray powder diffraction patterns of YbI2'2H20 by using
positional and thermal parameters of related hydrates which
have the same space group, anm. None of the theoretical
intensities matched the observed pattern. The CRYSTDAT data
base was also searched for an appropriate structural model

for YbI2'2H20; this search was not successful.
C. Infrared spectra

YbI2°H20 exhibited the infrared spectra shown in
Figure 3. The O-H stretching frequency of the water observed
at 3325 cm"1 is shifted to a lower wavenumber than that of
free water because the rigidity of the crystalline lattice
constrains the H20 molecule. This observation suggests that
the hydroxy group is probably weakly hydrogen-bonded to the

anion. However, if only weak hydrogen-anion bonds are

 

 

45

present, the shifting of the O-H stretching modes is more
influenced by the nature of the metal ions than by the
strength of hydrogen bridges [22]. In general, lattice water
molecules are trapped in the crystalline lattice either by
weak hydrogen-bonds to anions or by weak ionic bonds to the
metal ions. On the basis of literature data, the structures
of the iodide monohydrates are more symmetric with respect to
the H-bonds than those of the tmomide and chloride
monohydrates. This behavior was predicted previously [22].
For example, iodide monohydrates possess C2V symmetry,
whereas bromide and chloride monohydrates do not. From the
appearance of two uncoupled O—H stretching modes, the water
molecules in the latter two monohydrates are unsymmetrically
bonded, with a symmetry lower than sz. These modes are also
shifted to lower wavenumbers because the rigidity of the

crystalline lattice constrains the H20 molecule.

 

 

46

Table XI. Comparison of IR absorption frequency of
water with that in YbIZ'HZO.

Free H20(cm—l) Crystal H20(cm_l) Assignment
3430 . 3435 ”asym stretch
3325 3330 ”sym stretch
1610 1620

47

D. NMR

In this work the available MASS-NMR instrument could not
be used because of a malfunctioning contact and its
relatively slow spinning speed (2-5 kHz). In order to achieve
line narrowing of very wide homogeneous proton NMR lines, a
very high spinning speed (about 20 kHz) is required. Also, if
the line shape is Gaussian, the static NMR line width is
directly related to the second moment, M, according 'to the

Van Vleck equation (6):

2 (6)

M = 0.180 ( Av1/2 )
where 1301/2 is full width at half-height [44]. Therefore,
the STATIC NMR technique had to be utilzed.

The line width and the second moment can be used to
characterize tflue broad featureless absorptions obtained in
solid-state proton NMR studies. The second moment, M, of

nuclear spin, I, is the sum of M(hetero) and M(homo) as

follows:
M(hetero) = (l/3)yzzyg2f125(s+1)'i[(1-3COSZQfi)2/I_fi:] (7)
J, '6 Jo
M(homo) = (3/4)714I12I(I+1) .Efi[(1-3COSZ0;*)2/r:] (8)
4 . 4

where I and S are nuclear spins, y is the magnetogyric ratio
of spin I or S, 0 is the angle between the field direction

and the internuclear vector, r, and h is h/2n (h = Plank's

48

constant). Any rapid molecular motion will tend to partially
average the dipolar interactions (i.e., the angular parts of
the above equations), so that the second moment will appear
to be decreased below its rigid lattice value. spin-spin
relaxation time (T2) will then increase. In particular, at
the melting point or above the onset of molecular
motion,thesecond moment drops to a relatively small value.
The hydrate spectra shown in figure 5 are markedly
temperature - dependent. There is a large decrease in the
second moment parameters at 750C, an indication that water
molecular? motion. is ‘taking’ place» As the temperature_ is
raised from 250C, hindered rotational and vibrational motion
of water molecules increases and free rotational motion of

water probably occurs between 650C and 750C.

E. Elemental and water analysis

Ytterbium diiodide monohydrate

The standard deviation of duplicate Karl Fisher water
analyses of YbIZ’Hzo indicated that the average water
content. agreed well with the theoretical value. Elemental
ytterbium and iodide analyses agreed with the expected

formula, YbIZ‘HZO.

Ytterbium diiodide dihydrate

Metal and iodine analyses indicate that the ytterbium

49

and iodine content exhibit good agreement with values
calculated for a dihydrate. However, water analysis by the
Karl Fisher method was inconsistent with that expected for a
dihydrate product. It is presumed that the product became

hydrated further either during analysis or transfer.

SUGGESTIONS FOR FUTURE WORK

The single crystal of YbIZ°H20 should be prepared by
the solvent procedure for a better understanding of the
properties of hydrates by single crystal X—ray diffraction
procedures. It is necessary that high quality crystal be
used, therefore the crystallization techniques must be
improved.

A thermal decomposition study of YbIz'HZO by TGA-DTA is
needed for qualitative identification. TGA-DTA has become a
useful analytical tool that enables one to determine phase
transitions of hydrates.

Solid-state NMR studies of YbIZ'HZO should be achieved
by the Magic Angle Spinning technique to obtain structural
information.

The YbI2'2H20, which was prepared by only the solid-
vapor procedure, might be synthesized by the solvent
procedure. By varing the water stoichiometry, various other
hydration numbers might be determined and a phase diagram

constructed.

50

10.

11.

12.

13.

14.
15.

16.

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