phase diagrams of the elements i\\m lawrence kai

$: PHASE DIAGRAMS OF THE ELEMENTS i\\m LAWRENCE Kai$
TO«L- 51902

PHASE DIAGRAMS OF THE ELEMENTS

David A. Young

&

September 11, 1975

aiS Prepared for U.S. Energy Research & Development

1 Administration under contract No. W-7405-Eng-48

i\\m LAWRENCE K a i LABORATORY

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UCRL-51902


David A. Young

MS. date: September 11, 1975

OlSTRIBUTt0M npTu,5 revivor IStWUMtTED

Contents

Abstract 1 Introduction 1 Phase Dlagraas 3

Hydrogen 3 Helium 4 Lithium 5 Berylliua - 6 Boron , 7 Carbon 7 Nitrogen 8 Oxygen 10 Fluorine 10 Neon 11 SodiuD 11 Magnesium 12 Aluminum 12 Sil icon 13 Phosphorus 13 Sulfur 14 Chlorine 16 Argon 16 Potassium 16 Calcium 17 Scandium 17 Titanium la Vanadium IS Ch.'omium . . . . < IB Manganese 19 Iron 20 Cobalt 20 Nickel 21 Copper '. 21 Zinc 21 G«lllu» 21!

- i l l -

Germanium 22 Arsenic 23 Selenium 23 Bromine 24 Krypton 24 Rubidium 24 Strontium 24 Yttrium 26 Zirconium 26 Niobium 27 Molybdenum 27 Technetium 27 Ruthenium 27 Rhodium 27 Palladium 27 Silver 28 Cadmium 28 Indium 28 Tin 28 Antimony 29 Tellurium 30 Iodine 31 Xenon 31 Cesium 31 Barium 33 Lanthanum 34 Cerium 24 Praseodymium 35 Neodymium . 36 Promethium 37 Samarium 37 Europium .- 38 Gadolinium 39 Terbium 39 Dysprosium 40 Holmlum 40

-iv-

Erbium 41 Thulium 41 Ytterbium 41 Lutetlum 43 Hafnium 43 Tantalum 43 Tungsten 44 Rhenium 44 Osmium 44 Iridium 44 Platinum 44 Gold 44 Mortury 45 Thallium 45 Lead 46 Bismuth 46 Polonium 48 Astatine 48 Radon ~ 48 Francium 48 Radium 48 Actinium 48 Thorium 48 Protactinium 48 Uranium 49 Neptunium 50 Plutonium 50 Aroericium 52 Curium 54 Berkellura 54

References 55 Append!* A: The Space Lattices 64

-v-


Abstract

A summary of the pressure-temperatur« phase diagrams of the elements is presented, with graphs of the experimentally determined solid-solid phase boundaries and melting curves. Comments, including theoretical discussion, are provided

for each diagram. The crystal structure of each solid phase is identified and discussed. This work is aimed at encouraging further experimental and theorerir»l research on phase transitions in the elements.

Introduction

Phase diagrams are useful as compact summaries of large amounts of experimental data. As such thay provide an important challenge for theory, since accurate computation of phase transitions typically requires a very high degree of accuracy in so l id - and l iquid-state theoretical models. To date there have been very few f irst-principles calculations of one-component pressure-temperature phase diagrams.

The experimental study of phase boundaries has led Co the discovery of such unexpected phenomena as isostructural phase transitions and melting curve extreraa. A qualitative theoretical understanding of these phenomena has been achieved, and work 1B continuing in this area. The s i g nificance of these phenomena if that

they may be quite common at ultrahigh pressures where the atomic she l l structure exhibits stepwise breakdown.

Another aspect of phase diagrams that has attracted much attention i s the recurrence of patterns in the diagrams of closely related elements. This has been used successfully in predicting the structure*? and propert ies of high pressure phases. Thus, certain phase transitions observed at relatively low pressure provide important clues about the behavior of materials at much higher pressure. Deeper theoretical understanding of observed phase behavior w i l l thereby allow quantitative prediction of properties of materials at much higher pressures where experiments are d i f f i cult to perform. It may also be

hoped chat an adequate theory of phase diagrams for elements w i l l promote the more complex task of describing phase behavior in compounds and multi~component systems.

This report i s aimed at encouraging theoretical and experimental research on phase transit ions. I t i s a summary of the experimental data obtained to date on the phase diagrams of the elements. Only so l id and liquid phases are shown; the l iquid-vapor boundary i s not considered here. The temperature abscissa i s always referred :o zero Kelvin in order to i l lustrate, the true s i zes of the various f ie lds of phase s t a b i l i t y . Commonly occurring sol id phases are labelled with abbreviations: bcc » body-centered cubic (two atoms per unit c e l l ) , fee • face-centered cubic, hep - hexagonal close packed, and dhep - double hexagonal. Other sol id phases are identif ied according to the 14 l a t t i c e types l i s t e d in Appendix A. Dashed l ines in the figures indicate extrapolations or poorly determined phase boundaries.

For each element where data are available, a phase diagram i s 3hoi.n

and one or more paragraphs of comments are provided. When appropriate, the comment? Include information on the la tes t theoretical understanding of Che phase diagram. Cursory descriptions of complex crystal structures found among the elements are included in the comments. For detai l s of structures, however, che reader should consult Donohue's The Structures of the Elements.

The bibliography i s not exhaustive, since only the most recent papers are c i ted . However, the reader can eas i ly work back froo the reference? in the recent papers to the ear l i er ones. The gveat bulk of the work cited here was done since 1960. Two other useful surveys of phase diagrams for the elements

2 3 e x i s t , ' but they are already beginning to be dated by continuing research. Very recently, J. F. Cannon has published a c r i t i c a l review of the behavior cf the

4 elements at high pressures. Cannon's review and the present one cover much the same ground, and i t i s hoped that these surveys w i l l f i l l the gap l e f t by ten years of active research.

- 2 -

Phase Ditgrams

HYDROGEN

The phase diagram of hydrogen

i s shown in Fig. I. Solid and liquid hydrogen are composed of diatomic molecules interacting according to van der Waals and electric-quadrupole forces. Solid hydrogen and deuterium in thermodynamic equilibrium ( i . e . . , para-H, and ortho-D,) crysta l l i ze with the molecules centered on hep l a t t i c e s i t e s . The molecules are essent ia l ly freely rotating. For ortho-rich H. or pars-rich D». the stable s tate at zero Kelvin i s cubic, with the molecules centered on an fee l a t t i c e and presumably ordered, with axes pointing along body diagonals.

As the cubic l a t t i c e is warmed to about 2 K, a f irst-order transition (probably marfcensitic, involving the motion of planes of molecules) to the hexagonal phase occurs* Further warming then apparently leads to an order-disorder transit ion. This occurs as the l ibrating molecules begin to rotate freely. The temperature of the crystallographic transition i s a function of pressure and concentration of spin s t a t e s .

The phase boundary indicated by the das.i.«d l ine in Fig. 1 i s for 70% o-H-, which has been measured to 5.3

2

J

n — • — i — • — \ — I HYDROGEN L^fCubic)

1 I

Hexogono!

0 20 40 60 Temperature - K

Fig. 1. The phase diagram of hydrogen.

kbar. Theoretical calculations suggest that pure o-D» and P~H_ should have transitions to rotationally ordered cubic l a t t i c e s at zero Kelvin and compressions corresponding to pressures of a few tens of kilobars. Recently there has been great interest in theoretical arid experimental investigations of the insulator-to-metal phase transition in hydrogen,

which is exepcted to occur in the 9

megabar range. The three molecular solid isotopes melt in a regular sequence, and the melting curves

S

have been determined to 3.5 kbar. 10

11,12

HELIUM

The phase diagram of helium is shown in Figs. 2-6. The cohesive energy of solid and liquid helium is entirely due to very weak van der Waals forces. Because of the strong quantum effects observed in the solid and liquid phases, the phase diagram of helium has been extensively studied and worked out in detail."* Both isotopes 3 and 4 are liquid at T " 0 and p = 0 as the result of aero point motion. Under pressure, both liquids solidify. At zero Kelvin and pressures above 0.1 kbar, both solids are hep and show a transition to fee around 15 K and above 1 kbar. (Figs. 2 and 5) In Tie, a bec phase appears below 0,1 kbar and the melting pressure has minimum at 0.32 K (Fig. 3). In He, the bec field is very small, and is replaced by hep at the lowest temperatures (Fig. 6). The melting curve of He has a very flat minimum at 0.78 K. This curve has been extended to 14 kbar, at which pressure the melting temperature is 7? K.

3 In He the normal Fermi liquid

persists down to a temperature of 1 mK, where a transition to recently discovered superfluid phases occurs

13 (Fig. 4). The boundary separating the normal Fermi liquid from the A and B su?erfluid phases represents a second-orn>;c phase transition, like

10 20 30 Temperature ~ K

Fig. 2. The phase diagram ot helium - 3 .

0.25

0.20

-S 0.15 -

£ 0 .10=

0.05 -

2 4 Temperature - K

Fig. 3. The phase diagram of helium - 3 .

0.05

0.04 -

0.03 -

^ 0.02

0.01 -

-i | i | i | r

HELIUM-3

- bcc (Solid) —

. . - A liquid Y " /

-B liquid /

_ /Fermi liquid

-, j / , 1 , 1 ,

0.05

0.04 -

-3 0.03

8 0.02

0.01 -

0.001 0.002 0.003 Temperature - K

The phase diagram of helium - 3 .

0

Fig. 5.

10 20 30 Temperature - K

The phase diagram of helium - 4.

. 1 i • i |n—r

HELIUM-4 1

—r

_ hep 1 —

- bcc / -

1 ,

i

Liquid 11 1

1 1

' 1

-. i , i \ . i 1

Fig. 6.


The phase diagram of helium - 4 .

tha t in He. The A-B phase boundary i s a f i r s t - o r d e r phase t r a n s i t i o n , and i t j o ins the Fermi l i qu id at a t r i -c r i t i c a l po in t . The A and B f lu ids are thought to be superf luids that r esu l t from weak coupling of fermions s imi la r to that found in superconductors. In He the normal f lu id ( I ) undergoes a second-order t r a n s i t i o n (A-transi t ion) to a superf luid phase ( I I ) , which a r i s e s from the Bose-Einstein condensation as i t i s modified by the He-He pa i r i n t e rac t ions (Fig. 6 ) .

LITHIUM

The phase diagram of lithium is shown in Fig. 7. Upon cooling to

-5-

80 - 1 ' 1 ' LITHIUM -

- O -

60 -

40

- Liquid 1

20 - jf V -

n ep :

. _ u _

bcc /

1 . 1 / ,

-


Fig. 7. The phase diagram of lithium.

about 80 K, l i th ium changes from bcc to a close-packed (cp) s t r u c t u r e . The iden t i ty of t h i s s t ruc tu re (or s t ruc tu res ) i s not yet agreed upon. This i s a mar tens i t ic t r ans i t i on with a considerable temperature h y s t e r e s i s . The change in t r a n s i t i o n temperature

with pressure i s very smal l , as 14

me'isurements to 3 kbar have shown. Stager and Drickamer have found a sharp drop in res i s tance at 70 kbar and 296 K, which i s shown by the c i r c l e in Fig. 7. The s t ruc tu re of the high pressure phase i s not known. The melting curve of l i th ium has been determined to 60 kbar. The melting temperature becomes near ly constant a t t h i s p ressure ,

which suggests tha t a melting point maximum wi l l occur a t a somewhat greater p ressure .

BERYLLIUM

The phase diagram of beryll ium i s shown in Fig. 8. Beryllium has a t r a n s i t i o n from hep to bcc j u s t before melt. The bcc phase i s about P% more dense, giving r i s e t o the negative slope of the phase boundary. The hep-bec phase boundary has been determined to 60 kbar. The same study yielded two other res i s tance anomalies belcw 1000 K that appear to correspond to f luc tua t ions in the hexagonal c/a l a t t i c e r a t i o , ra ther than to genuine phase t r a n s i t i o n s .

500 1000 1500 2000 Temperofure - K

Fig. 8. The phase diagram of beryllium.

-6-

S t a t i c high pressure res i s tance 18 measurements by Marder showed a

d iscont inui ty a t 93 kbar and 293 K, but other inves t iga tors have been

19 unable to repeat th i s r e s u l t . The melting curve has been determined to 60 kbar.

a t pressures above 100 kbar and temperatures near 2000 K, but the probabi l i ty of sample contamination in th i s work was l a rge . Boron

22 expands very s l i g h t l y upon melting 23

near 2350 K, which implies a melting curve with pos i t ive s lope. The melting curve has not been d i r ec t ly measured.

Solid boron i s covalently bonded. The phase diagram i s e s s e n t i a l l y unknown. Many different c r y s t a l s t ruc tu re s of boron have been described in the l i t e r a t u r e * but t h e i r re la t ionsh ip to one another i s unclear. Furthermore, contamination of boron with metals and the formation of boron-rich borides has a s trong effect on the c rys ta l s t r u c t u r e . I t i s suspected tha t many of the s t r u c tures reported for pure boron are in fact those c- bor ides .

Sol id i f ica t ion of l iquid boron y ie lds the "S-rhombohedral" s t r uc tu r e with 105 atoms per uni t c e l l and 16 d i s t i n c t atomic pos i t i ons . This very complex s t ruc tu re can be resolved in to groups of linked lcosahedra of boron atoms. I t i s l ike ly to be the s t ab le phase at low pressures .

S t a t i c high pressure res i s tance measurements up to 250 kbar show no

20 evidence of phase t r a n s i t i o n s . 21

Wentorf reported a new boron polymorph of unknown structure obtained

-7-

CARBON

The phase diagram of carbon is shown in Fig. 9. This phase diagram has been the subject of much experimental work owing to the problem of producing artificial diamonds.

Liquid


Fig. 9. The phase diagram of carbon.

However, the very high temperatures and pressures involved have made the measurement of the phase boundaries extremely d i f f i c u l t , and the phase diagram cannot be sa id to be firmly es tab l i shed .

Graphite, the s tab le phase a t low pressures , has hexagonal l a t t i c e symmetry. Graphite consis ts of plane sheets of covalently bonded atoms. The sheets are bonded to each other by weaker van der Waals forces. The high pressure diamond phase i s cubic, with e ight atoms per uni t c e l l . Each atom i s covalently bonded to four neighbors located at the corners of a te trahedron.

Because diamond i s metastable at room temperature and pressure , the free energy difference between graphite and diamond can be computed from measured thermodynamic da ta , and the graphite-diamond phase boundary can

24 be es tab l i shed . This has been done with reasonable accuracy up t o 1200 K. and 40 kbar. Beyond t h i s , the ac tua l transformation of graphite to diamond in t rans i t ion-meta l matrices has been

24 carr ied out . These measurements extend the phase boundary to 80 kbar. The dashed l ine i s a l i nea r ex t rapola t ion of the lower-temperature r e s u l t s . Together with the melting curve, t h i s y ie lds a graphi te -diamond-liquid t r i p l e point near 100 kbar and 3500 K.

Shock wave experiments up to a fdw hundred kbar c lear ly show the graphite-diamond t r a n s i t i o n , but t h i s i s dominated by nonequilibrium ef fec ts and the i n i t i a l s t a t e of the graphi te .

26 The s igni f icance of shock data

ind ica t ing a new phase a t yet higher pressure i s s t i l l uncer ta in . Very recen t ly , Vereshchagin's group has observed a t r a n s i t i o n from the diamond to a meta l l i c phase a t pressures of

27 approximately 1 Mbar. They a l so observed tha t the t r a n s i t i o n pressure drops with increasing temperature, which i s s imi la r t o the behavior of the semiconductor-to-metal t r a n s i t i o n s in s i l i c o n and germanium.

The melting temperature of graphi te shows a maximum near 5000 K and 50 kbar according to recent

28 work. Uncertaint ies in the temperature measurements are l a rge . Melting of diamond has not been reported, but the melt ng curve i s assumed to have a negative slope by analogy with s i l i c o n .

NITROGEN

The phase diagram of ni trogen i s shown in Figs . 10 and 11 . Nitrogen in the so l id and l iqu id phases i s composed of diatomic molecules weakly bonded to each other by van der Waals and electr lc-quadrupole forces.

29 Three so l id phases are known. In

8 --

•' • 1 ' 1 / NITROGEN

1 '--

1 1

Tetragonal

-

1 ^ S \ Hexagonal (0 )

-

- Cubic / ( a ) / -

-i . / i 1 ^T 1

Liquid

1 i

-

4 -

2 -


Fig. 10. The phase diagram of nitrogen.

100 120

The phase diagram of nitrogen.

the cubic a phase, the molecules are centered on an fee lattice with the molecular axe* pointing along body diagonals. This ordering is presumably stabilized by quadrupolar forces. At 36 K, the cubic phase transforms to a hexagonal phase in which the molecules are centered on an hep lattice and are thought to be rotatlonally disorderad. The Y phaae is a tetragonal structure with two molecules par unit call. The molecules are packed In shsats with the molecular axes all aligned and lying In

-9-

the plane of the sheet . The d i rec t ion of the molecular axis s h i f t s by 90° from one sheet to the next. The s o l i d - s o l i d phase boundaries have been determined to about 10 kbar

(Fig. 10) been dete (Fig. 11)

30 The melting curve has been determined to about 25 kbar

2i

OXYGEN

The phast diagram of oxygen i s shown in Fig. 12. Oxygen in the so l i d and l iqu id phases i s composed of diatomic molecules weakly bonded by van der Waals and e l e c t r i c -quadrupole forces. Three so l id phasa are known. The monoclinic a phase

i s ant i ferroiragnet ic , due to the ordering of the spins in the t r i p l e t ground s t a t e . A t r a n s i t i o n to the rhomb oh edra l 0 phase, which i s paramagnetic, takes place a t 24 K. This t r a n s i t i o n i s de f in i t e ly f i r s t order , although mar tens i t l c . Another t r a n s i t i o n to the cubic Y phase, a lso paramagnetic, takes place with la rge volume change at 44 K. This phast. shows some ro t a t i ona l d i sorder . All of these phases may be regarded as close packed with d i s t o r t i ons i n t r o duced by the non-spherical molecules. The so l id - so l id phase boundaries have

been determined to a few kbar 32 The melting curve has a lso been determined

33 to 3.5 kbar.

10 n —i—'—i—'—i—'—r

OXYGEN

Monoclinic/ Rhombohedral ( a ) / ( ,

J-Z-J L 20 40 60

Temnertiture - K

FLUORINE

The phase diagram of fluorine is shown in Fig. 13. Fluorine in Che solid and liquid is composed of diatomic molecules weakly bonded by

S;

1.5 - ' 1 1 1 ' FLUORINE

1 ' -

J 1.0 J

Pres

sure

-

0.5

0

- Monocli 1 , 1

Cubic

nic(a) / / / i *

, 1 1,1

1 1 IT| 1 1 1 1


Fig. 12. The phnsa diagram of oxygen. Fig. 13. The phase diagram of fluorine.

-10-

van der Waals and electric-qttadrupole forces. At low temperatures f luorine i s tnonoclinic with a s t ruc tu re very s imilar to a -0 2 - At 46 K a t r ans i t i on with a large volume change takes place to cubic g-£luorine. This phase i s i s o s t r u c t u r a l with Y-0-, and the l a t t i c e i s ro ta t iona l ly d i s ordered. The s imi la r i ty between B-F 2 and y-Oo i s seen in the close agreement in the t r ans i t i on temperatures and the melt temperatures in the two elements. The a-$ phase boundary in Fig. 13 W a s determined from the AH

and AV of t r ans i t i on 5,34 The melting curve has been determined to only a few ba r s .

NEON

The phase diagram of neon is shown in Fig. 14. Neon in the so l id and l iquid s t a t e s i s composed of atoms weakly bound by van der Waals forces. Solid neon i s fee. The malting curve has been determined to 10 k b a r . 3 6

SODIUM

The phase diagram "f sodium is shown in Fig. 15. Below 36 K, sodium is hep. At 36 K a martensitic phase change leads to a bec structure which persists up to melt. The phase boundary separating the two phases

50 100 Temperature - K

Fig. 14. The phase diagram of neon.


Fig. 15. The phase diagram of sodium.

-11-

has not been reported, but the densit ies are so nearly equal that the i n i t i a l value of dl/dp should be close to zero, as indicated in Fig. IS. Static high pressure measurements in the sol id up to 600 kbar reveal no phase changes. The melting curve has been determined to 80 kbar.

MAGNESIUM

The phase diagram o f magnesium i s

shown i n F i g . 16 . S o l i d magnesium i s

hep . R e s i s t i v i t y and x -ray measure

ments on magnesium under s t a t i c h igh

pressure show indications of a sluggish phase transition near 100 kbar. The structure of the high pressure phase i s undetermined. The melting curve has been determined to 40 kbar' and the results have been corrected to the atmospheric-pressure melting point In Fig. 16.

37

38

ALUMINUM

The phase diagram of aluminum i s

shown In F i g , 17 . S o l i d aluminum i s

f e e . S t a t i c h igh preaaure measure

ments tentatively indicate a part ial 39 transformation to hep at 205 kbar.

The melting curve haa been determined 40 to 60 kbar.

40

2 30

I -10

i | i i I i | i i i i | i i MAGNESIUM

hep

Ql I I I

Liquid

[ I I i I I I I 500 1000 1500

Temperature - K

Fig. 16. The phase diagram of magnesium.

80

60

S 40h n

2 0 -

i i i | i i i i | i i i i ALUMINUM

fee f Liquid

L 0 U J

• • i • * ! • 500 1000 1500

Temperature - K

Fig. 17. The phase diagram of aluminum.

-12-

SILICON

The phase diagram of s i l i con i s shown in Fig. 18. Normal so l id s i l i con i s covalently bonded semiconductor with the cubic diamond s t r u c t u r e . S t a t i c high pressure measurements show a sharp drop in r e s i s t i v i t y near

41 200 kbar. Subsequent x-ray work showed th i s phase to have the t e t r a -

42 gonal white t i n s t r u c t u r e . Here each atom has four nearest neighbors and two next nearest neighbors lying s l i g h t l y far ther away. The accurate determination of the phase boundary i s complicated by i t s s e n s i t i v i t y to shear s t r e s s e s . In addi t ion , recovery of s i l i con compressed above 100 kbar has yielded a complex cubic form with

43 16 atoms per uni t c e l l . This uncertainty in the phase diagram i s indicated by a dashed l i n e in Fig. 18. At low pressures , so l id s i l i con melts to a more-dense meta l l ic l iqu id . The melting curve Has been measured to 200 kbar, and a c lear -cu t t r i p l e

44 point occurs a t ISO kbar. Shockwave experiments a l so show phase t r ans i t i ons i n the 100-200 kbar

45 region, but t h e i r prec ise nature

250

i s unknown.

PHOSPHORUS

The phase diagram of phoaphorua I s shown in Fig. 19. Of Che various a l lo t rop ic form of phosphorus that

2 0 0 -

.3150

100

50

i i i i | i i i i | i i I i | i i SILICON

Tetragonal (white tin)

• ' •

500 1000 Temperature •

1500

Fig. 18. The phase diagram of silicon.

30

£ 2 0 -

Jiof-

T ' I ' ' ' PHOSPHORUS

Ortho rhombic Liquid


1500

FiE. 19. The phaae diagram of phosphorus.

-13-

46

have been prepared, black phosphorus appears to be the most stable phase at atmospheric pressure. Black phosphorus has an orthorhombic structure consisting of puckered layers of covalently bonded atoms.

At room temperature and about 50 kbar, black phosphorus undergoes a phase change to a rhombohedral lattice, isostructural with arsenic. A further transition near 110 kbar to a simple cubic structure was also

46 observed. The rhombohedral lattice is a simple distortion of the simple cubic, and thus the phase transition is easily reversible. Conductivity studies indicate that the cubic phase

47 is metallic. Solid-solid phase boundaries have not been determined. The melting curve of othorhombic black phosphorus has been determined to about 20 kbar

SULFUR

48,49

The phase diagram of sulfur is shown in Fig. 20. The literature on the allotropy of sulfur presents the most complex and confused situation of all the elements. Solid sulfur under room conditions is composed of covalently bonded S„ rings that interact with each other through van der Waals forces. Below 360 K at atmospheric pressure sulfur has an ortho-rhombic lattice with 128 atoms (16

molecules) per unit cell in a very complex arrangement. Above 360 K, the solid is monoclinic, with 48 atoms (6 molecules) per unit cell. The orientations of two of the six molecules in each unit cell are disordered.

There is much disagreement about the structures of the high pressure phases and the phase boundaries separating them. The phase diagram shown in Fig. 20 is due to Vezzoli, et al. ~ The phase boundaries in the solid were detected by means of volumetric, optical, and electrical-resistance techniques.

The phase transitions are often difficult to detect, as indicated by the dashed boundaries in Fig. 19. The large number of phases can be understood as a series of stepwise conformational changes in the S g rings with changes in temperature and pressure. The structures of the phases other than the well-known I and 11 have not been worked out, although there is evidence that phase XII is monociinic, with closely packed helical chains of atoms

similar to the selenium and tellurium 53 rfructures. Resistance measurements

on sulfur compressed to 400 kbar showed no transition to a metallic

.. 54 scate. The melting curve shows a number

of definite cusps attributed to the

-14-

T SULFUR

40 -

I Monocltnic II

Fig. 20. The phase diagram of eulfur.

-15-

intersection of solid-solid phase boundaries. In addition, Vezzoli

52 et al. have discovered a number of "phases" (indicated by letters) in the liquid using DTA techniques. These regions in the liquid appear to be different polymeric states resulting from the breakup of the Sg rings. The nature of the transitions joining the liquid phases is not clearly understood. The lower portion of the melting curve given by Vezzoli £t_ al. has been independently confirmed.

CHLORINE

The phase diagram of chlorine is shown in Fig. 21. Chrlorine in the solid and liquid states exists as

.s

i — i — r -CHLORINE

T

4 -

Orthorhombic Liquid


Fig. 21. The phase diagram of chlorine.

d i a t o m i c m o l e c u l e s bonded t o n e i g h b o r s

by van d e r Waals f o r c e s . S o l i d

c h l o r i n e h a s an o r t h o r h o m b i c s t r u c

t u r e , composed of a p p r o x i m a t e l y

c l o s e - p a c k e d l a y e r s o f m o l e c u l e s . The

m e l t i n p c u r v e h a s been d e t e r m i n e d t o

7 k b a r .

ARGON

The phase diagram of argon is shown in Fig. 22. Argon in the solid and liquid is composed of atoms weakly bonded by van der Waals forces. Solid argon is fee. The melting curve has

31 been determined to 26 kbar.

POTASSIUM

The phase diagram of potassium is shown in Fig. 23. Solid potassium is bcc. No martensitic transition of the

30

-§20-

10-

-— | ! i ' • • ' i •

ARGON /-

-fee

•

— f Liquid

1 , 1 . 1 "


400

Fig. 22. The phase diagram of argon.

-16-

80 -1 ' 1 POTASSIUM

- • I ' " -

1 60

i 1 _

1 40 j: tfc bcc 1 20

n i , ,y , •

0 200 400 600

Temperature - K

Fig. 23. The phase diagram of potassium.

kind occurlng in Li and Na i s found

in potassium upon cooling to 5 K.

However, Stager and Drickamer found

two res i s tance anomalies a t 280 kbar

and 360 kbar a t 77 K. These t r a n s i

t ions were not observed at 296 K.

The authors suggest that the more

dramatic second t r a n s i t i o n i s analo

gous to the low temperature t r ans i t i on

in Li and Na. The melting curve of

potassium has been determined to

80 k b a r . 1 6

40

30

o 20

10

500 1000

Temperature -

1500

Fig. 24. The phase diagram of calcium.

measurements at 77 K showed a sharp rise in resistance near 140 kbar and a subsequent sharp drop near 400

58 kbar. These data were ascribed to two rather sluggish phase transitions, first cu . semimetallic, then to a metallic phase. These data are in rough accord with later Soviet

59 work. The melting curve of calcium has been determined to 40 kbar.

CALCIUM SCANDIUM

The phase diagram of calcium is shown in Fig. 24. Under room conditions calcium i* fee. Near 700 K at one atmosphere it undergoes a transition to a bcc structure. The phase boundary has been measured to 30 kbar. High pressure resistance

Scandium is hep at atmospheric pressure. Static high pressure resistance measurements at room temperature showed no evidence of a phase change to 140 kbar. Shock wave measurements by Carter, e_t_ al_. showed a kink in the u -u curve at

s p -17-

approximately 350 kbar. This was

ascribed to a sluggish low pressure

s o l i d - s o l i d phase change. No kink

was found in the shock v?ave work of

Gust and Royce. Scandium melts a t

1812 K. The melting curve has not

been reported.

TITANIUM

The phase diagram of titanium is shown in Fig. 25. At room temperature and pressure titanium is hep. A transformation to a bec phase occurs near 1150 K. The phase boundary has been determined to about 110 kbar, where a triple point occurs. The low temperature, high pressure ui phase may be regarded as a distorted bec lattice with hexagonal symmetry. This structure has three atoms per unit cell and two distinct types of atomic positions.

Shock wave experiments show a strong break in the u -u curve for

s p titanium, indicating a phase change occurring at 175 kbar. The nature of this phase transition has not been determined. Titanium melts at 1941 K. The melting curve has not been reported.

VANADIUM

Vanadium is bcc. No solid-solid phase transitions have been reported. Vanadium melts at 2178 K. The melting curve has not been reported.

CHROMIUM

The phase diagram of chromium i shown in Fig. 26. Pure chromium is antiferromagnetic below 311 K and paramagnetic above this temperature. Although there has been some controversy about various allotropes of

sure

- k

bar

s §

J 111111111

- Hexagonal : (w) i

7 " l " " l " " -

/ TITANIUM J

bcc : ~ hep

*. i i i 1 • • i ' 1 111 11 1 11

mp J

U-iquid; i V i i i i*

500 1000 1500 2000 2500

Temperature - K

Fig. 25. The phase diagram of titanium.

8 o

3 6

I 2 0

T T 1111II11 1 1 I I 1111 CHROMIUM

1 | I I I 1

V ^ - ' T e t r a g o n a l

^ O r r h o i h o m b i c Liquid -

. J_

bcc

11 1 • i i i 1 i • i i 1 • i i

mp

• 1 \, , , ' 500 1000 1500 2000 2500

Temperature - K

Fig. 26. The phase diagram of chromium.

-18-

chromium, it Is probable that the paramagnetic phase is simple bcc up to the melting point. Below 311 K, the paramagnetic phase transforms to an antiferromagnetic phase by a first-order phase transition. This phase is in a spin-density wave state In which the polarization is perpendicular to the wave vector. This magnetic state is inconsistent with the retention of full cubic symmetry, and the lattice instead takes on a very slight orthorhombic distortion of the bcc lattice.

At 123 K, another first-order tr sition occurs to a new antiferromagnetic spin-density wave state in which the polarization and wave vectors are parallel. This phase has a small tetragonal distortion of the bcc lattice. The lattice distortions in the magnetic phase are too small to be detected with present x-ray techniques. The phase boundaries have been determined to 8 kbar. ' Static pressure measurements at room temperature to 55 kbar show no other phase changes. Chromium melts at 2148 K. The melting curve has not been reported.

MANGANESE

The phase diagram of manganese

i s shown in Fig. 27. There are four

a l l o t r o p e s , a l l of cubic symmetry.

The a form has a complex body

70

50

40

_8 30

8 20

10

I I I I I I 1 I I I I l — I I I I MANGANESE

Liquid

Cubic ( a )

0|_i—i—i—i—L_ 0 500 1000 1500

Temperature - K

Fig. 27. The phase diagram of manganese.

centered cubic l a t t i c e with 58 atoms

per uni t c e l l and 4 d i f ferent types

of atomic pos i t i ons . At atmospheric

pressure near 1000 K, a t r a n s i t i o n

occurs to the fi form, thought to have

20 atoms per uni t c e l l and 2 types of

atomic p o s i t i o n s . Near 1370 K a

t r a n s i t i o n to the fee Y phase occurs ,

and near 1520 K a fur ther t r a n s i t i o n

to the bcc 6 phase occurs. The 'phase

boundaries and the melting curve have 71 been determined to 40 kbar.

-19-

IRON

The phase diagram of iron is shown in Fig. 28. The phase diagram and especially the melting curve of iron is of great interest because of the problem of the state of the earth's core and the origin of the geomagnetic field. Under room conditions iron is ferromagnetic and has a bcc structure. At 1044 K it passes through the Curie point and near 1200 K it transforms to the fee phase. The bcc phase once again becomes stable before melting. Above 100 kbar, the bcc phase transforms to a nonferromagnetic hep phase. The

ct-y, ct-e, and y~e phase boundaries 72 have been determined to 200 kbar.

The y-& transition and the melting curve have been determined to 52 kbar, where they meet in a triple

73 point. The melting curve of the Y phase has been extended about 5

73 kbar beyond the t r i p l e po in t .

COBALT

The phase diagram of cobalt is shown in Fig. 29. At room temperature cobalt is hep. At a temperature depending on the sample grain size, a sluggish phase change to fee occurs. For large crystal grains the transformation temperature is 661 K. The phase boundary has been measured to 50 kbar. Cobalt melts at 1765 K. The melting curve has not been reported.

500 1000 1500 2000 Temperature - K

60

_ 50

I 40 £ 30

1 20 * 1 0 -

0

111 I I I 111 ] 11 1 I 11 I I I ( I 11 I

COBALT

hep J fee L ' q u i d "

mp

11 i i I i I I i 11 i i ) I i i t i I i i i i 0 500 1000 1500 2000 2500

Temperature - K

Fig. 28. The phase diagram of i ron . Fig. 29. The phase diagram of cobal t .

-20-

The phase diagram of nickel i s shown in Fig. 30. Solid n icke l i s fee. The melting curve has been determined to 80 kbar. '

80

0 60 -Q

i 4 0

1 20 at

0.

" " I " " I " 1 ' I 1

NICKEL

fee /Liquid

i I . . . . I i i • , I i ill i I . , , , 500 1000 1500 2000 2500

Temperature - K

Fig. 30. The phase diagram of n i cke l .

COPPER

The phase diagram of copper is shown in Fig. 31. Solid coppfer is fee. The melting curve has been

75 determined to 65 kbar.

ZINC

The phase diagram of zinc i s shown in Fig. 32. Solid zinc has a d i s to r ted hep l a t t i c e , with the c /a r a t i o considerably grea te r than i d e a l . Under p ressure , t h i s ratio shows unusual f luc tua t ions , but no c lear -cu t so l id - so l id phase changes are found up to 200 kbar. The melting curve has been determined to 60 kbar.

80

60

£ 40

20

I—1—I I 1 COPPER

fee

| Liquid

I • • • / • I ! "0 500 1000 1500

Temperature - K

Fig. 31. The phase diagram of copper.

80 7 ' 1 ' 1 '

ZINC | i | i •

J 60 - / ~ | 40

£ 20

hep / : f Liquid

/ °( I . 1 . 1 / , 1 . * °( 2C 10 400 600 8( 10 1000 12C Temperature - K

Fig. 32. The phase diagram of z inc.

- 2 1 -

GALLIUM

The phase diagram of gallium is shown in Fig. 33. Solid gallium at atmospheric pressure has an ortiio-rhombic structure with eight atoms per unit cell. Each atom in this structure has one nearest neighbor and six other near neighbors somewhat farther away. At atmospheric pressure gallium melts just above room temperature, and the melting temperature initially decreases with increasing pressure. Gallium II is probably body centered tetragonal. The high-temperature gallium-III phase is a complex orthorhombic lattice with 40 atoms per unit cell. The phase boundaries, including the melting

curve, have been determined to ,. ,. 78,79 75 kbar.

GERMANIUM

The phase diagram of germanium is shown in Fig. 34. Solid germanium under room conditions is a semiconductor with the cubic diamond struc-

60 ture. Above 100 kbar shock wave and electrical resistance measure-

41 ments indicate the appearance of a new phase. This phase is metallic, with the tetragonal white tin structure. There remains some uncertainty concerning new phases obtained from

81 quenching experiments. The cubic-tetragonal phase boundary and the

80

60

L ' !

2

I 40

2 0 -

' I • I ' GALLIUM

TZ\

Orthorhombic ( I I I )

Orthorhcmbic (M

I I I 0 100 200 300 400

Temperature - K

Fig. 33. The phase diagram of gallium.

250

200

-§ 150

| 100

* Tetragonal . (white tin)

| I • I i | I i I GERMANIUM

Liquid

•_ Cubic 5 0 1 - (diamond)

• • • i l i t i i i . X i . i l 500 1000 1500 Temperature - K

Fig. 34. The phase diagram of germanium.

-22-

http://ilitiii.Xi.il

netting curve have been determined up 44 to 200 kbat.

ARSKNIC

The phase diagram of arsenic la shown in Fig. 35. Ac atmospheric pressure arsenic crystallizes in Che prtnltlvc rhoabohedral laccice characteristic of the group VB elements- High pressure resistance measurements shoved no anomaly up Co

82 200 kbar. However, arsenic that had been compressed to ISO kbar showed a tetragonal structure, which

S3 may represent a high pressure phase. The melting curve has been determined up to 60 kbar.

60

40

£ 3

i 20

1 ' ' I ' ' ' ARSENIC

Rhombohedral Liquid

-iJ_ 0 500 1000 1500

Temperature - K

Fig. 35. The phase diagram of arsenic.

SELENIUM

The phase diagram of selenium is shown in Fig. 36. Solid selenium at lou pressure has a hexagonal crystal structure composed of covalently bonded helical chains of atoms. In this state selenium is a semiconductor. Near 130 kbar, a resistance discontinuity is observed, and selenium becomes a metallic conductor. * An attempt to determine the structure of this high pressure form was

87 unsuccessful. The melting curve has been determined Co 60 kbar. It shows a clear maximum in temperature.

60

40

20 -

I ' I ' I ' ! SELENIUM

Hexagonal

I I I / I 0 200 400 600 800 1000 1200

Temperature - K

Fig. 36. The phase diagram of selenium.

-23-

BROMINE

The phase diagram of bromine Is shown In Fig. 37. Solid bromine Is composed of diatonic molecules held together by weak van der Haals forces. The solid has an orthorhombic structure, analogous to chlorine. Indirect evidence for a phase transition in solid bromine at 35 kbar has

91 been reported, but no details of the phase boundary or the structure of the new phase are available. The melting curve has been determined to , „ „ 56,89 10 kbar.

KRYPTON

The phase diagram of krypton is shown In Fig. 38. Solid and liquid krypton consist of atoms bonded by weak van der Waals forces. The solid Is fee. The melting curve has been

36 92 determined to 12 kbar. '

RUBIDIUM

The phase diagram of rubidium Is shown in Fig. 39. At low pressures solid rubidium is bcc. Bundy and Strong found a sharp resistance jump

93 near 75 kbar and room temperature. Stager and Drickamer found a sharp rise In resistance near 200 kbar at two temperatures. Soviet work confirmed the 75 kbar transition, but found the next transition near 135-

140 kbar rather than 200 kbar. 5 9

The lower transition is Indicated in Fig. 39 by a dashed line. These transitions are thought to correspond to those observed in cesium at low pressure. The upper transition Is likely to be due to a shift In the electronic configuration of the rubidium atoms. The melting curve has been determined to 80 kbar. The melting temperature appears to be approaching a maximum near 80 kbar.

STRONTIUM

The phase diagram of strontium is shown in Fig. 40. Under room conditions strontium is metallic with an fee structure. With increasing pressure at room temperature or below, strontium becomes semi-

94 metallic. Hear 35 kbar, a phase transition to the metallic bcc structure occurs. The unusual change from a more efficient to a less efficient packing with increasing pressure appears to be due largely to the electronic transitions mentioned. Beyond the 3S kbar transition, strontium shows metallic conductivity with no indication of further transitions up to 500 kbar. The fcc-bcc phase boundary intersects the p = 0 axis at 830 K. This boundary and the meltiig curve have been determined to 40 kbar.

-24-

10

2 _ OrthorhombTc

BROMINE

2

O j - - 1 I . I

80

60

ji I £ 40 3

i 20

"HP ' ~T RUBIDIUM

0 100 200 300 400 Temperature - K

200 tfia 600 Temperature - K

Fig. 37. The phase diagram of bromine. F i 8 - 3 9 - *>« P h a s e diagram of rubidium.

12

10

r 4

2


Fig. 38. The phase diagram of krypton.

-25-

-

1 ' 1 ' 1 KRYPTON

- r

- fee / Liquid

I |

r |

i •

,. l / , 1 . 1 1

50

40

2 30

£ 2 0 -

10

11 i i | i i I i | i i i i | I STRONTIUM

bec / Liquid

I J U 0 500 1000 1500

Temperature - K

Fig. 40. The phase diagram of s trontium.

YTTRIUM

Solid yttrium at low pressure is hep. Above 110 kbar, yttriur.

95 becomes a superconductor, A itudy of the pressure dependence of the transition temperature indicates the presence of several superconducting

96 modifications. However, these modifications are not thought to have different crystal structures, but rather arise from slight changes in band structure.

Static resistance measurements to 250 kbar shew no phase transition

97 anomalies. Shock-wave experiments by Gust and Royce showed a kink in Che the u -u curve at 280 kbar. The s p authors suggested that the kink indicated the stiffening of the solid as inner electron cores overlapped. Carter, e_t _ai. saw a kink in tk& u -u curve at 370 kbar and suggested s p a sluggish low pressure transition as an explanation. Yttrium melts at

63 1775 K. The melting curve has not been reported.

ZIRCONIUM

The phase diagram of zirconium

i s shown in Fig. 41. Zirconium under

room conditions Is hep. under com

pression i t transforms to the hexagonal

w phase isostructural with u-titanium.

This i s a distorted bec phase. Near

1140 K at atmospheric pressure the

hep phase transforms to bcc. The

tr ip le point joining the three phases

occurs near 60 kbar and 1000 K. The

phase bounds.-ies have been uorked out

to 70 kbar. Vereshchagln observed

a sharp change of slope in the resist

ance as a function of pressure near

100 kbar, but what this means i s 97

unclear. A shock-wave study of

zirconium showed a sharp break in the u -u curve at 260 kbar, which pre-

s P 66 sumably indicates a phase change. Zirconium melts at 2123 K. 6 3 The melting curve has not been reported.

80 i i i i | i i i > | i i i i | i r

ZIRCONIUM n | n i _

" Hexagonal ! -

60 : y -

£ 40 3 - -*?

1 hep bcc

20 -Liquid

n 1 ill I 1 1 1 M

mp\

ul I iL I -"0 500 1000 1500 2000

Temperature - K

Fig. 41. The phase diagram of zirconium.

-26-

KI0BIW1 RUTHENIUM

Solid niobium is bcc. No resistance anomalies have been found

97 below 250 kber. Niobium melts at 2741 K. The melting curve has not been reported.

Solid ruthenium in hep. Compression to 400 kbar at room tespera-

99 tur* showed no change of phase. Ruthsnium melts at 2SS3 K. 6 3 The melting curve has not been reported.

MOLYBDENUM RHODIUM

The phase diagram of molybdenum is shown in Fig, 42. Solid molybdenum is bcc. An approximate melting curve

98 has been determined to 90 kbar.

TECHNETIUM

The phase diagram of rhodium i s

shown in Fig. 43. Solid rhodium i s

fee. The melting curve has been

approximately determined to 80

k b a r . 3 8 ' 7 4

Solid technetium is hep. 63

Technetium melts at 2443 K. The melting curve has not been reported.

100

80 -

I 60t-

40

20

0.

i—•—i—'—r MOLYBDENUM

bcc

J Liquid

J i 1000 2000 3000

Temperature - K

Fig. 42. The phase diagram of molybdenum.

Solid palladium i s fee . P a l l a d i

um melts a t 1825 K. The melting

curve has not been reported.

100

1000 2000 3000

Temperature - K

Fig. 43. The phase diagram of rhodium.

-27-

SILVER

The phase diagram of silver Is shown In Fig. 44. Solid silver Is fee. Compression to 300 kbar at room temperature shows no evidence of a phase change. The melting curve has been determined to 65 kbar.

CADMIUM

The phase diagram of cadmium Is shown In Fig. 45. Solid cadmium Is hep. Compression In the 100-200 kbar range shows small anomalies In the resistance and hexagonal c/a ratio, and a sluggish phase transition has

37 been suggested as an explanation. Independent resistance measurements

to 250 kbar showed no strong 97 anomalies. The melting curve has


INDIUM

The phase diagram of indium i s

shown In Fig. 46. Solid indium i s

body centered te t ragona l . Compression

at room temperature t o 300 k ar shows

no ind ica t ion of any phase changes.

The melting curve has been de te r

mined to 80 k b a r . 7 8

The phase diagram of t i n i s

shown in Fig. 47. Below 290 K at

Temperature - K

0 200 400 600 800 Temperature - K

Fig. 44. The phase diagram of s i l v e r . Fig. 45. The phase diagram of cadmium.

-26-

80

| 6 0 -

i "o i

20

1 1 1 1 1 1 1 iNDIUM

: / -

: / -

— Tetragonal / -/ Liquid -

I 1 J l / i 1 I 1 -


800

Fig. 46. The phase diagram of indium.

100

80 I i 60

40 -

2 0 -

Tetragonal (white tin)

Cubic •^(diamond)

0 200 400 600 800 Temperature - K

Fig. 47. The phase diagram of t in .

atmospheric pressure, t in i s cubic diamond l ike s i l i con and germanium. Above this temperature t in has the tetragonal white t in structure with four atoms per unit c e l l . In this structure each t in atom has four nearest neighbors at the vertices of a flattened tetrahedron. Two more neighbors l i e s l ight ly farther 3way.

The diamond-to-white-tin boundary has been determined to about

102 50 K and 10 kbar. At room temperatute near 90 kbar, the white t in transforms to a body-centered tetragonal structure with two atoms per unit c e l l . The boundary joining the two phases has been approximately determined to 95 k b a r . 1 0 3 ' 1 0 4 Tht melting curve has also been determined . , , , . 103,104 to 75 kbar. *

ANTIMONY

The phase diagram of antimony is shown in Fig. 48. Solid antimony under room conditions is rhombohedral, isostructural with arsenic. At room temperature, antimony has two phisa transitions, one near 70 kbar and one near 85 kbar (circles). 1 0 5 The 70-kbar transition is sluggish and apparently has a very small volume change. The phase II structure is simple cubic, which corresponds to the elimination of the low pressure

-29-

100

80

• 6 0

a>

20

0

I i | I i I i | i i i i | I ANTIMONY

° \ Tetragonal

- v \ («o

- \sn Rh'ombohedral \

I I I

Liquid

1 • ' ' ' ' '

500 1000 1500

Temperature - K

Fig. 48. The phase diagram of antimony.

rhombohedral d i s t o r t i o n . Hie t r a n s i tion, a t 85 khar i s wore s t rongly marked, with not iceable volume and res i s tance changes. The s t ruc tu re of phase I I I i s uncer ta in , but recent worfe suggests a te t ragonal s t ruc tu re

analogous to that found in arsenic a t high p ressures . Phase I I I shows

82 good me ta l l i c conduct iv i ty . The melcing curve has been determined to 70 kbar. ' Two cusps, ind ica t ing t r i p l e p o i n t s , have been found, one at 3.9 kbar, and the other a t 57 kbar. Stishov and Hkhomlrova assumed that the two t r i p l e poin ts corresponded to the two room temperature t r a n s i t i o n s , as indicated in Fig. 48.

TELLURIUM

The phase diagram of tellurium is shown in Fig. 49. Solid tellurium under room conditions is a semiconductor, with a hexagonal structure composed of covalently bonded helices packed together. This structure can be regarded as a distortion of the simple cubic lattice. Near 40 kbar at room temperature (circle), a transition to a metallic phase occurs. The structure of this phase has not

108 yet been determined. Near 70 koar at room temperature (circle), a fur ther t r a n s i t i o n to a rhombohedral

108 l a t t i c e occurs . This phase i s i s o s t r u c t u r a l with 3-polonium. Studies of superconductivity a t high pressures ind ica te poss ible new

80

60

; 40

20

TELLURIUM T

" ^ Rhombohedral (III) S S

s ll V

Hexagonal

-i L J_ J L E "0 200 400 600 800

Temperature - K

J i g . 49. The phase diagram of te l lur ium.

-30-

109 phases a t s t i l l higher p res su res .

The so l id - so l id phase boundaries and

the melting curve have been de te r

mined to about 70 kbar. A de f in i t e

maximum in the melting temperature

i s found near 10 kbar.

IODINE

The phase diagram of iodine is shown in Fig. 50. Solid iodine at low pressures is composed of diatomic molecules in an orthorhombic lattice, isostructural with solid bromine and chlorine. No clearly defined phase transition has been found at moderate pressures, but an x-ray study of the solid to 60 kbar showed a continuous shifting of x-ray

112 reflections. This was interpreted as a shifting of the orientations of

the diatomic moleculea within the orthorhombic unit cell.

At higher pressures, above 100 kbar, the resistance of iodine drops

113 rapidly to a metallic value. Here It is thought that the I„ molecules dissociate into an atomic metallic structure. It is not clear whether this is a continuous or an abrupt transition. Shock wave experiments on iodine show a strong break in the plot of u vs u D at approximately 700 kbar.H4 Given a transition to the metallic phase at a much lower pressure, this break is likely to represent a phase transition from one metallic phase of iodine to another. The melting curve has been determined to 50 kbar. '

XENON

50 -

u 4 0 -o M

g 3 0 -

a i 20-

1 0 -

n ' i • r IODINE

Orrhorhombic

0L-0 200 400 600 800 1000

Temperature - K

Fig. 50. The phase diagram of iodine.

The phase diagram of xenon is shown in Fig. 51. Solid and liquid xenon are composed of atoms bonded

by weak van der Waals forces. Solid xenon is fee. The melting curve has


CESIUM

The phase diagram of cesium is shown in Fig. 52. Cesium has been intensively studied because of its unusual properties. Solid cesium at atmospheric pressure is bcc. At

-31-


Fig. 51. The phase diagram of xenon.

60

50

>.. 40 1 .a: r £ 30

K 10

0

. • " T '' ' 1

CESIUM

- IV / • -— f c c ^ L ~"

- fee \

-bcc

J •

1 l / l Liquid -


Fig. 52. The phase diagram of cesium.

room temperature the bcc phase t r a n s forms to fee at 23 kbar. Further compression y ie lds two more phase t r ans i t i ons only about 1 kbar apart near 42 kbar. The f i r s t new phase i s also fee , but the s t ruc tu re of the second (IV) has not yet been de te r mined. The s o l i d - s o l i d phase boundaries have been determined, ' and they show very weak temperature depenlence, except that the upper fee phase apparently disappears a t low temperatures.

The i s o s t r u c t u r a l fcc-fcc t r a n s i t ion occurs with a 9% volume change, and has exci ted much cu r io s i t y . The f i r s t t h e o r e t i c a l attempt a t an explanation proposed tha t the t r a n s formation represents a s h i f t from 6s

to 5d character of the conduction 120 band. Although details of this

theory have been criticized, it is widely agreed to be qualitatively correct.

A further sluggish t r a n s i t i o n in so l id cesium occurs near 125 kbar, accompanied by a large increase in

5° r e s i s t ance . This phase (V) exh ib i t s superconductivity and i t has been suggested tha t the phase i s t r a n s i t i o n - m e t a l - l i k e , with increased d-electron character, 95

The melting curve of cesium has been worked out to 55 k b a r . 1 1 7 , 1 1 8

Two melting temperature maxima occur near the bcc-fcc transition. The

-32-

decreasing melting temperature of the close-packed fee phase i s due to the density of the l iquid increasing beyond that of the s o l i d . This phenomenon has been ascribed to the smearing out in the l i qu id of the sharp e lec t ron ic t r a n s i t i o n observed in the s o l i d . Thus the volume cont rac t ion in the l i qu id can be thought of as a smoothly varying change in. r e l a t i v e concentration of two e lec t ron ic spec ies , whereas in the so l id t h i s change takes place a l l a t once. The melting curve of phase IV once again takes on a normal appearance.

i i i i I i r i i I 11 i i i n BARIUM

Liquid

1 ' • ' ' * ' ' ' ' * • '

0 500 1000 1500 Temperature - K

Fig. 53. The phase diagram of barium.

BARIUM

The phase diagram of barium is shown in Fig. 53. Solid barium at atmospheric pressure is bcc. At room temperature, a well-marked phase

122 transition occurs at 55 kbar. The high pressure phase has been

123 determined to be hep. There is disagreement over the trajectory of the bec-hep phase boundary, since DTA measurements show dp/dT > 0

125 while resistance measurements show dp/dT < 0. Additional evidence supports the first possibility, which is shown in Fig. 53. A second phase transition to a phase (III) of unknown structure has also been reported. * Stager and

Drickamer found a further transition at 144 kbar and room temperature, and inferred from a detailed study that this was a melting transition. Later work indicated a solid-

129 solid transition instead. A further transition at 240 kbar was found at 77K, presumably to yet another solid phase. The melting curve has been determined to about nn it. 124,125,128 , „. 90 kbar , * * and three melting-curve maxima appear. I t seems l ike ly that e l ec t ron ic phase changes s imilar t o those observed in

130 cesium are occurring i n barium.

-33-

LANTHANUM

The p h a s e d i a g r a m of l a n t h a n u m

i s shown i n F i g . 5 4 . Lanthanum

exhib i t s three so l id phases a t atmospher ic p ressure . From 0 to 580 K, the s t ab le phase i s dhcp. At 580 K, a pftase t r a n s i t i o n to an fee phase occurs with a decrease in volume.

The dhep-fee phase boundary has been 131 worked out to 24 kbar. At 1130 K,

a t r a n s i t i o n to a bec phase occurs , and melting occurs near 1200 K. E l e c t r i c a l r e s i s t ance measurements made to 250 kbar sfiow a smalt r e s i s t ance anomaly near 100 kbar, which may indica te a phase t r a n s i t i o n .

Ttyo s e t s of shock wave ©.xperi-ments show kinks i n the u e-u_, curve s p for lanthanum a t 250 kbar*2 ^ a 225 kbar 61 The first report ascribes the fcinfc to xenon core repuls ions ,

40 I I | I I I I | I I LANTHANUM I

62

r-|-r-r

Ll'qui'd'

I I I I, 500 1000 1500 Temperchjre - K

Fig. 54. The phase diagram of lanthanum.

while the second ascr ibes i t to the in t e r sec t ion of the Hugoniot and the melting curve. The fcc-bcc boundary and the melting curve have been determined to near ly 40 kbar.

CERIOM

The phase diagram of cerium is shown in Fig. 55. This unusual diagram has been intensively studied. At zero Kelvin and atmospheric pressure, cerium is fee. Between approximately 100 K and 45'J K, a dkep phase is stable. Between 450 (c and 1000 K, the fee phase is again stable, with the difference that the Y phase is ferromagnetic while the a phase is paramagnetic. A bec phase then intervenes just before melting. The dhcp phase disappears at low

pressures. 133

80

1 60

40,

20

I • | I I I I | I I I I | T CERIUM

Orthorhombic 1

U (a) dhcp

Liquid _ |

1_L 7) L ' f a c c

' • ' " • • • • I I I 0 500 1000 1500

Temperature - K

Fig. 55. The phase diagram of cetium.

-34-

The unique feature of the cerium diagram is the isostructural a -*• y

phase transition, which ends in a critical point estimated from

134 resistance measurements to lie at 17.5 kbar and 550 K. A considerable theoretical effort has been made to explain the a •* y phase transition and critical point. The earliest theories assumed that the transition represented a promotion of the localized 4f electron to the delocal-i2ed 5d band. 135 Later theories modified this by assuming only a

135 partial 4f derealization . Such models imply a definite increase in the number of conduction elections as the pressure is Increased. But this is contradicted by positron-annihilation experiments that indicate no change in the number of

135 conduction electrons. In general it could be said that the y -*• a transition results from the Interaction of the 4f and conduction electrons, but the precise model of this interaction is disputed.

Further compression of cerium leads to another phase transition in the 50-60 kbar range. The new phase (a 1) has been determined to be orthorhoiribic, isostructural with

137 a-uranium. The phase boundary has been determined over a r e l a t i v e l y short temperature range, but i t i s i n t e r e s t i ng that extrapolat ion of the

rx-y phase boundary and ct-a* phase boundary leads to points very near one another on the melting curve. Stager and Drickamer reported a fur ther possible phase change near

138 160 kbar a t room temperature. Two s e t s of shock wave data give d iscor-

1 f c 61,62 _ dant r e s u l t s . In one case , a kink in the u -u curve was found at

61 s p 480 kbar and ascribed to melting. In the other case, no kink was « * 6 2

found. The melting curve of cerium has

134 been determined to 70 kbar. The remarkable feature i s a minimum In the melting temperature around 33 kbar. Jayaraman explains the minimum in terms of isotherms s imi la r i n shape to the s u p e r c r i t i c a l isotherms observed in the v i c in i t y of the

134 l iquid-vapor c r i t i c a l po in t . These isotherms r e f l ec t the rapid decrease in the s i ze of the cerium atoms in the so l id phase as the pressure i s increased.

PRASEODYMIUM

The phase diagram of praseodymium i s shown in Fig. 56. Normal so l id praseodymium I s dhep. A room-temperature t r a n s i t i o n to an fee phase occurs a t 40 kbar ( c i r c l e ) . The t ra jec tory of the dhep-fee phase boundary i s d i f f i c u l t to follow

139

-35-

~r i i i | i i i i | m i |"i i 80 PRASEODYMIUM

60 1 -1

40 - \ fee 1 _

20

_L

\ 1 Liquid "

dhcp\ 1 ~ \ y b c e •

V . I #. . . 1 , . 500 1000 1500

Temperature - K

Fig. 56. The phase diagram of praseodymium.

because i t i s extremely sluggish and apparently qui te sens i t ive to Impur i t ies . An approximate value for the zero-pressure t r ans i t i on temperature i s 833 K. ** Resistance measurements to 500 kbar show severa l anomalies above tha t a t 40 kbar, and suggest two more high-pressure phases of unknown s t ruc tu re

138 above Che fee phase. Two s e t s of shock-wave experiments

show kinks in the u -u curve for 8 P 62

praseodymium at 300 kbar and 270 kbar. The f i r s t report ascr ibes

62 the kink to xenon-core r epu l s ions , while the second t en ta t ive ly ascr ibes i t to an e lec t ron ic rearrangement In the l i q u i d . A bec phase appears before melt . The bcc-fcc phase

boundary and the melting curve have 131 — been determined to 70 kbar.

NEODYEtCH

The phase diagram of neodymium i s shown in Fig. 57. Under room conditions neodymium i s dhep. High pressure tf-ray s tud ies at room temperature show a t r a n s i t i o n to the

139 fee phase near 50 kbar ( c i r c l e ) , This t r a n s i t i o n i s very d i f f i c u l t to de tec t , and the in te r sec t ion of the phase boundary with the p » 0 a jds , although suspected, could not be

140 directly measured. Instead, a temperature of 960 K is inferred from a generalized rare earth phase diagram,

80 -

1UX Resistance measurements

£ 60 -

r 20

0

1 -\ I T ] T T T T ' | 1 \ » l-JTTT-• " NEODYMIUM

-/

-~

\ f " / '

/ / Liquid

~ dh=p \ Lc ™

_L, 1 1 . 1 1 1 1 \ l J 1 I • !..!__) 0 500 1000 1500

Temperature - K

Fig. 57. The phase diagram of neodyroium.

-36-

61

on neodymium up to 600 kbar showed anomalies in the 100-200 kbar region at d i f ferent temperatures, which could correspond to another high-

138 pressure phase t r a n s i t i o n . Two se t s of shock-wave experiments

show kinks in the u -u„ curve for s p neodymium at 280 kbar and 250 kbar. The f i r s t report ascr ibes the kink to

62 xenon-core repuls ions , while the second i den t i f i e s i t with melting. A bcc phase appears before melt . The bcc-fcc phase boundary and the melting curve have been determined to 60 kbar.

PROMETHIUM

Promethium I s dhcp at room 142 temperature and pressure . Prom

ethium has not been extensively worked with because the element i s unstab7i , and the most-easily avai lable isotcpe has a h a l f - l i f e of 2.6 years . The melting temperature i s 1315 K. No high-pressure work has been reported.

SAMARIUM

The phase diagram of samarium i s shown in Fig. 58. Under room condit ions samarium has a close-packed s t ruc tu re of rhombohedral symmetry. The arrangement of close-packed layers in th i s s t ruc tu re i s ababcbcac,

80 1 1 1 1 | 1 I 1 1 | 1 1 I I | I l SAMARIUM

1 60 dhcp -

1 V

1 4 0 I bee -5 X

c£ X X , .

20 _ Rhombohedral s x l (Siti) 1 / "

n • • • • ! • • i • 1 • 1 /Liquid"

ill A 1 l_ 0 500 1000 1500

Temperature - K

Fig. 58. The phase diagram of samarium.

henceforth ca l led "Sm-type." Res is t ance measurements to 600 kbar a t room temperature show anomalies near 50 kbar and 160 kbar that might correspond t o phase t r a n s i t i o n s 138 The

62

dhcp phase appears in samarium near 40 kbar and 623 K ( c i r c l e ) .

Two s e t s of shock wave exper i ments show kinks in the u s-Up curve for samarium a t 310 kbar*>2 and 270 kbar. The f i r s t report ascr ibes the kink to xenon-core repulsions while the second i d e n t i f i e s i t with melting. A phase assumed to be bcc appears before melt- An in f l ec t ion in the bcc- to-close-packed-sol id phase boundary i s assumed to represent the

131 Sra-type-dhcp-bcc t r i p l e po in t . The bcc-sol id phase boundary and the melting curve have been determined to

131 60 kbar.

•37-

EUROPIUM

The phase diagram of europium i s shown in Fig. 59, Solid europium at atmospheric pressure i s bcc. Below 88.6 K, europium i s ant iferromagnetic , with a h e l i c a l arrangement of sp in s , and i t becomes paramagnetic above th i s temperature. The t r a n s i t i o n has been

144 determined to be f i r s t order , which means that the bcc l a t t i c e i s very s l i g h t l y d i s to r t ed in the magn e t i c phase, as in the case of chromium. The pressure dependence of the t r a n s i t i o n has been determined to

145 90 kbar. I t has been suggested that as the l a t t i c e becomes less compress ib le with increasing p ressure , the f i r s t - o r d e r t r a n s i t i o n simply stops at about 20 kbar and gives way

144 to a pure second-order transition. S t a t i c high-pressure res i s t ance

measurements show a sharp change near 150 kbar and room temperature, which probably corresponds to an e lec t ron ic phase t r a n s i t i o n 138 The t r a n s i t i o n pressure appears to decrease with

138 temperature. Three s e t s of shock wave experiments show anomalies in

61,62,146 the u - u , curve. s 6 1 *

Carter ej; jal. found a d iscont inui ty in the u -u curve at 106 kbar, and sug-s p gested tha t t h i s corresponds to the in t e r sec t ion of Hugoniot and melting curve. Gust and Royce found anomalous behavior in the 180-360 kbar range and suggested a sluggish

phase transformation. Bakanova 146 e t a l . found a kink in the u -u s p

curve at 386 kbar and ascribed t h i s to an e l ec t ron i c rearrangement.

It Is possible that the anomalies in the shock data correspond with the

138 resistance anomaly which has been ascribed t o a d i v a l e n t - t r i v a l e n t e l ec t ron ic phase t r a n s i t i o n . According to t h i s theory, the anomalously divalent europium becomes more r a r e - e a r t h - l i k e aa the pressure inc reases . The europium melting curve has been detei-mined to 70 . , 147,148 . fc

kbar. A temperature maximum appears near 30 kbar . The close analogy between the behavior of europium and barium has been pointed out .

0 500 1000 1500 Temperature - K

Fig. 59. The phase diagram of europium.

-38-

GADOLINIUM

The p h a s e d i a g r a m of g a d o l i n i u m

i s shown i n F i g . 6 0 . Under room

c o n d i t i o n s g a d o l i n i u m i s h e p . A

t r a n s i t i o n t o t h e s a m a r i u m - t y p e p h a s e

o c c u r s a t a b o u t 25 k b a r ( c i r c l e ) a t 149 room t e m p e r a t u r e . The h c p - S m - t y p e

p h a s e bounda ry h a s n o t b e e n d i r e c t l y

d e t e r m i n e d . R e s i s t a n c e measurements 60 138

t o 500 k b a r show no a n o m a l i e s . *

Two s e t s o f shock wave e x p e r i

ments show k i n k s i n t h e u - u c u r v e s 6 2 p

f o r g a d o l i n i u m a t 260 k b a r and 345 k b a r . The f i r s t r e p o r t a s c r i b e s

t h e k i n k t o x e n o n - c o r e r e p u l s i o n s ,

w h i l e t h e s econd i d e n t i f i e s i t w i t h an

e l e c t r o n i c t r a n s i t i o n i n t h e s o l i d .

A b c c p h a s e a p p e a r s b e f o r e m e l t , and

a k i n k i n t h e b e c - h e p p h a s e b o u n d a r y

was t a k e n t o be h c p - S m - t y p e - b c c t r i p l e 131 p o i n t . The m e l t i n g c u r v e h a s b e e n

„ ~_4 ^ . / n , L 1 3 1 , 1 4 8 d e t e r m i n e d t o 40 k b a r .

TERBIUM

The phase diagram of terbium is shown in Fig. 61. Under room conditions terbium is hep. A resistant anomaly indicating a transition has been reported at 27 kbar (circle), and the high pressure phase has been determined to be the Sm-type. Resistance measurements to 500 kbar show smooth behavior and no clear

• | i • | 1 -

GADOLINIUM _ 40 1 -

1 •f 30

. Rhombohedral (Sm-type)

L^bcc

] :

Pres

sure

—

to

o

o

— hep \ r 1 i

• i

n 1 1 -

40


Fig. 60. The phase diagram of gadolinium.

3 0 -

2

20-

10 -

1 1 1 1 1 TERBIUM

Rhombohedral (Sm-type) ~

^ x X •

X 1 X

X — X ^-bec —

X X % _ Liquid

hep ~

' . , . 1, -0 1000 2000 3000 Temperature - K

Fig. 61 . The phase diagram of terbium.

-39-

evidence of further phase t r a n s i -138 t ions . The approximate hcp-Sm-

type boundary i s based on a genera l ly 1

ized ra re -ea r th phase diagram. Shock-wave experiments show a

kink in the u -u curve at 400 61 s p 61

kbar. This i s ascribed t o melt ing. The bcc-hcp phase boundary and the melting curve have been determined

131 t o about 25 kbar. x

Two s e t s of shock-wave exper i ments show kinks in the u -u curve

s p for dysprosium at 480 kbar 6 2 and 305 kbar 61 The f i r s t report ascr ibes

62 the kink to xenon-core repuls ions , while the second I d e n t i f i e s i t with melting. The bcc-hcp boundary and the melting curve have been de te r mined to 25 and 8 kbar, r espec t ive ly .

DYSPROSIUM HOLMIUM

The phase diagram of dysprosium is shown in Fig. 62. Under room conditions dysprosium is hep. A transition to the Sm-type phase occurs at 45-50 kbar and room tempera-

60,149 D . ^ t u r e . Resistance measurements on dysprosium show anomalies near 200 kbar , which may ind ica te a phase t r a n s i t i o n .

The phase diagram of holmium i s shown in Fig. 63. Under room condit ions holmium i s hep. A t r a n s i t i o n to the Sm-type phase occurs a t 65

149 kbar and room temperature. Resistance measurements on holmium to 600 kbar show no c lear evidence of any fur ther phase changes.

0 1000 2000 3000 Temperature - K

Fig. 62. The phase diagram of dysprosium.

15

2 10

* 5

-1 1 1 1 '

HOLMIUM ;

- (L—-bcc .

_i_

i_L

i

hep 1 Liquid _

- 1 I 0 1000 2000 3000

Temperature - K

Fig. 63. The phase diagram of holmium.

-40-

Shock-wave experiments show a kink in the u -u curve of holtnium s p a t 440 kbar, which i s ascribed to melting 61 The hcp-bcc phase

boundary and the melting curve have 131 been determined to 10 kbar.

The phase diagram of erbium i s shown in Fig. 64. Under room condit ions erbium i s hep. A t r ans i t i on to

149 the Sm-type phase occurs a t 90 kbar. Resistance measurements made to 600 kbar show no indicat ion of a phase t r a n s i t i o n .

Shock wave experiments show a kink in the u -u curve at 440 kbar,

s p 61 which i s ascribed t o melting. No bec phase has been detected before melt determined to 10 kbar

131 The melting curve has been 131

"" 1 1 ERBIUM

i •• •

- -K w — 3 •

' 1 5

n

•

hep

I 1 .

Liquid | I

I I

i |

Fig,

0 1000 2000 3000 Temperature - K

64. The phase diagram of erbium.

THULIUM

The phase diagram of thulium i s shown in Fig. 65. Under room condit ions thulium I s hep. A t r a n s i t i o n to the Sm-type phase occurs a t room

149 temperature near 110 kbar. Resistance measurements t o 500 kbar show no clear evidence of any further

138 phase changes. Shock-wave experiments show a

kink in the u -u curve, which i s s p 61 ascribed to melt ing. No bec phase

131 has been detected before melt . The melting curve has been determined

131 t o 10 kbar. x

15

_g 10 -

5 -

-., ! 1 1 '

THULIUM

1 1

1 1

1 1

hep

"'"" 1-•

1 1 , , 0 1000 2000 3000

Temperature - K

Fig. 65. The phase diagram of thulium.

The phase diagram of ytterbium is shown in Fig. 66. Eelow 300 K

-41-

0 500 1000 1500

Temperature - K

Fig. 66. The phase diagram of ytterbium.

and 2 kbar, ytterbium exists in a 151 diamagnetic hep phase. A

martensitic phase transformation at 300 K and atmospheric pressure produces a paramagnetic fee phase. The hep-fee phase boundary has been determined, and it is clear that the

152 hep phase disappears above 2 kbar. At room temperature, increasing

pressure causes a serieB of changes

in r e s i s t i v i t y . Below 20 kbar

ytterbium behaves l i ke a metal ,

between 20 and 40 kbar it behaves like a semiconductor, and at 40 kbar a phase change takes place to a bcc

153 metallic phase. These changes have been explained in term?3 of the opening and closing of band gaps with

154 Increasing pressure . The fcc-bcc 147 phase boundary has been determined,

and it intersects the p « 0 axis above 1000 K.

Stephens reports that a new hep phase appears between the fee and bcc phases below 15 kbar, but this may be the result of impurities. A pressure-independent resistance anomaly variously observed at 743 K 1 4 7 and 898 K , 1 5 5 has been ascribed to another phase transition. Static compression of ytterbium at room temperature to 280 kbar shows no further resistance anomalies above 40 kbar 153

Three s e t s of shock-wave exper i

ments show kinks in the u -u curve ft? s P

a t 130 kbar, 160 k b a r , 6 1 and 490 146 kbar. The kinks are ascribed to

xenon-core repuls ion, melt ing, and

electronic phase transitions, respectively. Johansson and Rosengren consider the 130 kbar anomaly to indicate an electronic phase transition Involving a shift from the divalent to the trivalent ionic state in the solid 141 The melting curve has been determined to

147 35 kbar. The ytterbium phase diagram closely resembles that of strontium.

-42-

LUTETIUM

The phase diagram of lutet ium i s shown in Fig. 67. Solid lu te t ium at low pressures i s hep. Compression to 230 bbar at room temperature causes a t r a n s i t i o n to the Sin-type l a t t i c e . The hcp-Sm-type phase boundary has not been determined. The melting curve has been determined to 10 kbar 131

33 1 , 1 , . LUTETIUM -

~ J 10

1 1

1 1 -;

Pres

sure

-

_ hep 1 Liquid ..

J 0 1 i , ll , "

HAFNIUM F i g . 6 7 .

1000 2 0 0 0 3000

Temperature - K

The phase diagram of lu te t ium.

Under roost conditions hafnium is hep. At atmospheric pressure a t r ans i t i on occurs near 2270 K to a bcc phase. The bcc phase i s s l i g h t l y more dense than the hep, implying a negative value of dp/dT for the phase boundary. A s ta t i c -h igh-pressure search for the hexagonal ID phase found in ti tanium and zirconium fai led to show any change of phase.

Three s e t s of shock-wave exper i ments showed anomalies in the u -u c u r v e . 6 2 ' 6 6 ' 1 4 6 Gust and Royce" P

ascribed a kink at 600 kbar t o xenon-core repuls ion. McQueen, £ t al -ascribed a discont inui ty a t 400 kbar

to a so l i d - so l i d phase t r a n s i t i o n . 146 Bakanova, e_t a l . ascribed a kink

at 450 kbar to an e lec t ron ic t r a n s i t ion . Hafnium melts at 2495 K . 5 3

The melting curve has not been reported.

TAHTALUM

The phase diagram of tantalum is shown in Fig. 68. Solid tantalum is bcc. An approximate melting curve

158 has been determined to 60 kbar. T

1000 2000 3000 ' 4000 Temperature - K

Fig. 68. The phase diagram of tantalum.

- 4 3 -

TUNGSTEN IRIDIUM

The phase diagram of tungsten is shown in Fig. 69. Solid tungsten is bcc. An approximate melting curve

159 has been determined to 50 kbar.

1000 2000 3000 4000 Temperature - K

Fig. 69. The phase diagram of tungsten.

Solid rhenium is hep. Static compression of rhenium at room temperature to 350 kbar showed no phase transitions. Rhenium melts at 3433 K. The melting curve has not been reported.

Solid iridium is fee. Room temperature compression to 175 kbar showed no phase transition. Iridium

63 melts at 2716 K. The melting curve has not been reported.

PLATINUM

The phase diagram of platinum is shown in Fig. 70. Solid platinum is fee. The melting curve has been approximately determined to 50

159,162 kbar. *

1000 2000 Temperature - K.

3000

Fig. 70. The phase diagram of platinum.

OSMIUM

Solid osmium is hep. Osmium melts at 3300 K. The melting curve has not been determined.

The phase diagram of gold is shown in Fig. 71. Solid gold is

-44-

Temperature - K

Fig. 71- The phase diagram of gold.

fee. The melting curve has been 75 determined to 65 kbar.

MERCURY

The phase diagram of mercury is shown in Fig. 72. Solid mercury at low temperatures has a body centered tetragonal structure. In this phase each rlom has two nearest neighbors and eight second nearest neighbors. With increasing temperature, a transformation to a rhombohedral structure occurs. This structure may be regarded as a distorted fee lattice. The tetragonal-rhombohedral phase boundary has been determined to 65 kbar.

80

1 ' 1 ' 1 ' - MERCURY

J 60 Rhombohedral v j I

- (a) X / -

Pres

sure

- Tetragonal / / " ( ( J ) / / • M~ / / Liquid

20 / / ' ^/\A . 0 200 400 600

Temperature - K

Fig. 72. The phase diagram of mercury.

A third phase, named y, has been found at very low temperatures by straining the solid. Its structure and equilibrium phase boundaries have not yet been determined 164 The melting curve of mercury has been determined to 65 kbar.

THALLIUM

The phase diagram of thallium is shown in Fig. 73. Below 500 K at atmospheric pressure, thallium is hep. Above 500 K, it is bcc. A high pressure fee phase occurs above 35 kbar and 388 K. The solid-solid phase boundaries have been determined to 60 kbar. The melting curve has


-45-

80 -

i 6 0

40 -

20

- 1 1 1 1 1 l~ THALLIUM

' 1

- fee j -- / 1 -

_ _ / / _ — ~ \ bcc

- hep \

1 1 \ /

'Liquid

• 1 0 200 400 600 800

Temperature - K

Fig. 73. The phase diagram of thallium.

80 - n -•i i | i i i i | i i i i | LEAD

i i

60 /

-

40 fee / Liquid •

i

20

, , , / -

0 500 1000 1500 Temperature - K

Fig. 74. The phase diagram of lead.

LEAD

The phase diagram of lead i s shown in Fig. 74. Solid lead at low pressure i s fee. At 137 kbar and room temperature a t r a n s i t i o n to a

165,166 _. . hep phase occurs. The phase boundary has not been determined. The melting curve has been determined to 60 k b a r . 7 7

BISMUTH

The phase diagram of bismuth i s shown in Fig. 75. This diagram i s of spec ia l importance to high pressure physics because i t s many phase t r a n s i t ions have been used as ca l ib ra t ion s tandards . There i s s t i l l controversy over the exis tence of some t r a n s i t i o n s , and r a the r l i t t l e x-ray s t r uc tu r e work has been done on the high pressure

phases. The low pressure so l id phase i s rhombohedral, i s o s t r u c t u r a l with arsenic and antimony. Conflicting claims have been made for the s t r u c ture of phase I I , with no c lear

1 83 agreement. Duggin suggests that phase I I I i s t e t r agona l , s imi la r to the high pressure phase of a r sen ic . A study of phase VI at 90 kbar a t room temperature has shown i t to be bcc. The phase boundaries shown are a synthesis of severa l

„ ,. 84,168,169 ' . s t ud ie s . The phases XX, VII I , and VI meet i n a t r i p l e point a t 135 k b a r , 1 6 9 and the VI-IX phase boundary then proceeds to higher pressures . This boundary was p r e sumably detected in a study at room temperature and 300 kbar 170 The melting curve has been determined to 55 k b a r . 8 4

-46-

140 -

120 -

100 -

80 -

60

40 -

2 0 -

' — r i 1 i ' 1 • 1

- , BISMUTH -

- IX -

- -

-> •

- -

-VIII

bcc •

- (VI) ~

- \ \ \ V \

-

1 / ' \ K.ms \

IV [ \

— Tetragonal 1 /

(III) /

-Liquid

-

' 1

Rhombohedral \ to \

i i ., . i i \ i i i 200 400 600

Temperature - K

Fig. 75. The phase diagram of bismuth.

800

- 4 7 -

POLONIUM RADIUM

At atmospheric pressure and below room temperature, polonium has a rimple cubic structure, the only known example of this structure in the elements at zero pressure. A sluggish phase transition occurs somewhere near room temperature (291-327 K) to a simple rhombohedral form which is a slight distortion of the simple cubic. The rhombohedral form is slightly more dense, leading to a negative dp/dT. The phase boiuidary has not been determined. Polonium melts at 519 K. The melting curve has not been reported.

ASTATINE

Astatine is a very unstable element and its physical properties have not been determined.

RADON

The crystal structure of solid radon has not been reported. Radon

172 melts at 202 K. ' The melting curve has not been determined.

FRANCIDM

Francium is a very unstable element and its physical properties have not been determined.

Solid radium is bcc at room temperature. Radium melts at 973 63 K. Wo high pressure work has been

reported.

ACTINIUM

Solid actinium is fee at room temperature. Actinium melts at 1323 63

K. No high pressure work has been reported.

THORIUM

Solid thorium under room condi

t ions i s fee. Superconductivity

measurements to 160 fcbar show an

anomaly tha t could be due t o a phase 173 change near 70 kbar. At atmos

pher ic pressure near 1670 K, thoritim

transforms to a bcc phase. The

volume change of the t r a n s i t i o n i s

zero to within experimental e r r o r .

The t r a j ec to ry of th^ phase boundary

has not been reported. Thorium melts

at 2024 K. The melting curve has

not been determined.

PROTACTINIUM

Solid protactinium under room

conditions i s body centered t e t r agona l .

Metal s o l i d i f i e d from the melt i s fee ,

suggesting tha t t h i s i s the high

•48.

temperature form of the solid. No direct measurements of phase transitions have heen made, however. Protactinium melts at about 1810

174 K. No high pressure work has been reported.

URANIUM

The phase diagram of uranium is shown in Fig. 76. Under room conditions solid uranium has an orthorhombic structure with four atoms per unit

60 - i — i — i — i r T 1 1 r

URANIUM

40

2

20 - Orthorhombic ( a )

Tetragonal

1 1 , 1

bcc <T>

Liquid


1500

Fig. 76. The phase diagram of uranium.

-49-

cell. At 940 K and atmospheric pressure, a transition to a complex tetragonal form with 30 atoms per unit cell occurs. The precise space group remains to be determined. At 1050 K another phase transition leads to a bcc phase. The solid-solid phase boundaries have been determined, and indicate a triple point for the three phases near 30 kbar. The melting curve has been determined to 40 kbar. 1 7 6

NEPTUNIUM

The phase diagram of neptunium i s shown in Fig. 77. Under room conditions neptunium i s orthorhombic, with e ight atoms per uni t c e l l and two d i s t i n c t types of atomic pos i t i ons . At 550 K and atmospheric pressure a phase t r a n s i t i o n to a te t ragonal phase with four atoms per uni t c e l l and two types of atomic posi t ions occurs. A bcc phase appears above 840 K. The s o l i d - s o l i d phase boundaries and the melting

curve have been determined to 35 , , 177 kbar.

PLUTONIUM

The phase diagram of plutonium i s shown in Figs. 76 and 79. The plutonium diagram I s very complex.

All but one of the seven known so l id phases ex i s t a t atmospheric pressure . The low pressure port ion of the phase diagram and i t s high pressure continuation are shown in separate f igures . The low temperature a phase i s monoclinic, with 16 atoms per uni t c e l l and S c rys ta l lographica l ly d i s t i n c t types of atomic p o s i t i o n s . The 3 phase i s also monoclinic, with 34 atoms per uni t c e l l and 7 types of pos i t i ons . Both of these s t ruc tu res are qu i te i r r egu l a r and are d i f f i c u l t to co r r e l a t e with close-packed forms.

At high pressure only a and $ e x i s t , and the a-0 phase boundary shows a temperature maximum. The $ phase transforms t o orthorhombic *Y below 3.5 kbar and to 5, with undetermined s t r u c t u r e , above t h i s pressure . There i s a |S-£-liquId t r i p l e point near 27 kbar.

The next two phases are fee (<5) and body centered te t ragona l (6 ' )» which ex i s t only a t low pressures . The 6 ' phase i s followed by bcc ( e ) , which melts to a more dense l i q u i d . The te t ragonal 6 ' phase i s intermedia te in s t ruc tu re between fee and bcc . The E phase disappears at a t r i p l e point below 20 kbar. The s o l i d - s o l i d phase boundaries and the melting curve have been determined to 140 k b a r . 1 7 4 ' 1 7 8 ' 1 8 0

-50-

< 1 1 1 r- — I 1 1 1 1 1 1 f -

NEPTUNIUM

40-

30

1

20-Or'horhombic I Tetragonal

10-

Liquid'

01 i J L. •• ' • i I L — l I I 500 1000 1500

Temperature - K

Fig. 77. The phaBe diagram of neptunium.

- 5 1 -

8 -

6 -

2 -

• 1 , 1 , PLUTONIUM I ' / 1 '

-Monoclinic. 1 (0) ^ k •» / -

- Monoclinic 1 ( a ) |

-

- / f / ""ec 1 [ ( e ) 1 Liquid

-

1 1

1

Orrhorhombi<v / J

, , , / r f c c \

Tetragona ' ( 5 ' )

\ 1 1 .

1 '

"

200 400 600 800 1000 1200 Temperature - K

Fig. 78. The phase diagram of plutonium.

AMERICIuM

The phase diagram of americium is shown in Fig. 80. Americium under room conditions is dhcp. There is evidence for a transition to an fee phase at 920 ± 50 K , 1 8 1 but with very little change in volume. The dhep-fec phase boundary is therefore approximately represented by a vertical

-52'

182

dashed line in Fig. 80. Static compression of americium at room temperature shows a resistance change at 90 kbar, which may represent a continuation of the dhep-fee phase boundary Keating at atmospheric pressure above 1300 K leads to a new phase, which Stephens <£ al. suggest is bcc. The fcc-bcc phase boundary and melting curves have been determined to 35 ,. 182 kbar.

1501 r -i 1 1 1 r PLUTONIUM

-| . (-

Liquid

_L 200 400 600 800

Temperature - K 1000 1200

Fig. 79. The phase diagram of plutonium.

-53-

40

i 3 0 i

2 20

10

i i i i | I I i I | i i I I | AMERICIUM

bcCs

L_ dhcp

• ' • ' • ' •

. Liquid \ l I

I F c C II I I I ! l/i/l I

S00 1000 1500 Temperature - K

Fig. 80. The phase diagram of americium.

CURIUM

Depending on the method of preparation, curium metal is found to have either an fee or a dhcp structure under room conditions. The fee phase has the higher density. No phase boundary has been reported. The estimated melting point is 1620

174 K. No high pressure work has been reported.

BERKELIUM

Berkelium metal prepared by high temperature reduction contains a mixture of dhcp and fee structures. Here the dhcp phase is the more dense. The estimated melting point

174 i s 1260 K. No high pressure work has been reported.

-54-

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RBC/gw

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Appendix A: The Space Lattices

Lattice Axes Angles

primitive (simple) cubic body-centered cubic face-centered cubic

primitive tetragonal body-centered tetragonal

primitive orthorhombic base-centered orthorhombic body-centered orthorhombic face-centered orthorhombic i

primitive monoclinic base-centered monoclinic

t r i c l i n i c a # b # c o ^ M l

rhombohedral a » b - c a « 0 = Y

hexagonal a - b ]< c ot = g - 90°, Y = 12°°

a - b - c o - 3 " Y " 90°

a « b ji c a « B - Y - 9 0 °

a ^ b ^ c a « B = Y = 90°

a ^ b j « c o - Y » 90" ^

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phase diagrams of the elements i\\m lawrence kai

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