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 Kai LABORATORY

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UCRL-51902 PHASE DIAGRAMS OF THE ELEMENTS

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 Silicon 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!

-ill- 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- PHASE DIAGRAMS OF THE ELEMENTS

Abstract

A summary of the pressure- for each diagram. The crystal temperatur« phase diagrams of the structure of each solid phase is elements is presented, with graphs identified and discussed. This work of the experimentally determined is aimed at encouraging further solid-solid phase boundaries and experimental and theorerir»l research melting curves. Comments, including on phase transitions in the theoretical discussion, are provided elements.

Introduction

Phase diagrams are useful as they may be quite common at ultrahigh compact summaries of large amounts of pressures where the atomic shell experimental data. As such thay structure exhibits stepwise break­ provide an important challenge for down. theory, since accurate computation of Another aspect of phase diagrams phase transitions typically requires that has attracted much attention is a very high degree of accuracy in the recurrence of patterns in the solid- and liquid-state theoretical diagrams of closely related elements. models. To date there have been very This has been used successfully in few first-principles calculations of predicting the structure*? and proper­ one-component pressure-temperature ties of high pressure phases. Thus, phase diagrams. certain phase transitions observed at The experimental study of phase relatively low pressure provide boundaries has led Co the discovery important clues about the behavior of of such unexpected phenomena as materials at much higher pressure. isostructural phase transitions and Deeper theoretical understanding of melting curve extreraa. A qualitative observed phase behavior will thereby theoretical understanding of these allow quantitative prediction of phenomena has been achieved, and work properties of materials at much higher 1B continuing in this area. The sig­ pressures where experiments are diffi­ nificance of these phenomena if that cult to perform. It may also be hoped chat an adequate theory of and one or more paragraphs of com­ phase diagrams for elements will pro­ ments are provided. When appropriate, mote the more complex task of describ­ the comment? Include information on ing phase behavior in compounds and the latest theoretical understanding multi~component systems. of Che phase diagram. Cursory descriptions of complex crystal This report is aimed at encour­ structures found among the elements aging theoretical and experimental are included in the comments. For research on phase transitions. It is a summary of the experimental data details of structures, however, che obtained to date on the phase diagrams reader should consult Donohue's The of the elements. Only solid and Structures of the Elements. liquid phases are shown; the liquid- The bibliography is not vapor boundary is not considered exhaustive, since only the most here. The temperature abscissa is recent papers are cited. However, the always referred :o zero Kelvin in reader can easily work back froo the order to illustrate, the true sizes of reference? in the recent papers to the various fields of phase stability. the earlier ones. The gveat bulk of Commonly occurring solid phases are the work cited here was done since labelled with abbreviations: bcc » 1960. Two other useful surveys of body-centered cubic (two atoms per phase diagrams for the elements 2 3 unit cell), fee • face-centered exist, ' but they are already cubic, hep - hexagonal close packed, beginning to be dated by continuing and dhep - double hexagonal. Other research. Very recently, J. F. solid phases are identified according Cannon has published a critical to the 14 lattice types listed in review of the behavior cf the 4 Appendix A. Dashed lines in the elements at high pressures. figures indicate extrapolations or Cannon's review and the present one poorly determined phase boundaries. cover much the same ground, and it is hoped that these surveys will fill the For each element where data are gap left by ten years of active available, a phase diagram is 3hoi.n research.

-2- Phase Ditgrams

HYDROGEN n—•—i—•—\— I HYDROGEN The phase diagram of hydrogen L^fCubic) is shown in Fig. I. Solid and liquid 1 hydrogen are composed of diatomic I molecules interacting according to 2 van der Waals and electric-quadrupole forces. Solid hydrogen and deuterium Hexogono! in thermodynamic equilibrium (i.e.., para-H, and ortho-D,) crystallize J with the molecules centered on hep lattice sites. The molecules are essentially freely rotating. For ortho-rich H. or pars-rich D». the 0 20 40 60 stable state at zero Kelvin is cubic, Temperature - K with the molecules centered on an fee lattice and presumably ordered, Fig. 1. The phase diagram of hydrogen. with axes pointing along body diagonals.

As the cubic lattice is warmed kbar. Theoretical calculations to about 2 K, a first-order transition suggest that pure o-D» and P~H_ should (probably marfcensitic, involving the have transitions to rotationally motion of planes of molecules) to the ordered cubic lattices at zero Kelvin hexagonal phase occurs* Further and compressions corresponding to warming then apparently leads to an pressures of a few tens of kilobars. S order-disorder transition. This Recently there has been great interest occurs as the librating molecules in theoretical arid experimental begin to rotate freely. The temper­ investigations of the insulator-to- ature of the crystallographic metal phase transition in hydrogen, transition is a function of pressure which is exepcted to occur in the 9 and concentration of spin states. megabar range. The three molecular The phase boundary indicated by solid isotopes melt in a regular the das.i.«d line in Fig. 1 is for 70% sequence, and the melting curves o-H-, which has been measured to 5.3 have been determined to 3.5 kbar. 10 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."*11,1 2 Both isotopes 3 and 4 are liquid at T " 0 and p = 0 as the result of aero point motion. Under pressure, both 10 20 30 liquids solidify. At zero Kelvin and Temperature ~ K pressures above 0.1 kbar, both solids Fig. 2. The phase diagram ot helium - 3. are hep and show a transition to fee around 15 K and above 1 kbar. (Figs. 0.25 2 and 5) In Tie, a bec phase appears below 0,1 kbar and the melting pres­ sure has minimum at 0.32 K (Fig. 3). 0.20 In He, the bec field is very small, and is replaced by hep at the lowest temperatures (Fig. 6). The melting -S 0.15 - curve of He has a very flat minimum at 0.78 K. This curve has been extended to 14 kbar, at which pres­ sure the melting temperature is 7? K. £ 0.10= 3 In He the normal Fermi liquid persists down to a temperature of 0.05 - 1 mK, where a transition to recently discovered superfluid phases occurs 13 (Fig. 4). The boundary separating 2 4 the normal Fermi liquid from the A Temperature - K and B su?erfluid phases represents a Fig. 3. The phase diagram of second-orn>;c phase transition, like helium - 3. 0.05 i | i | i | r 0.05 1 —r HELIUM-3 i • i|n—r - . HELIUM-4 1 hep 1 0.04 -- bcc (Solid) — 0.04 _- — . . - bcc / - 0.03 - -3 0.03 - A liquid Y"/ 1 1 '

^ 0.02 - 8 0.02 1 , i B liquid / Liquid 11 1 /Fermi liquid 0.01 _- 0.01 - - -

, j/, 1,1, . i , i\ . i 1 0.001 0.002 0.003 1 2 3 Temperature - K Temperature - K The phase diagram of Fig. 6. The phase diagram of helium - 3. helium - 4.

that in He. The A-B phase boundary is a first-order phase transition, and it joins the Fermi liquid at a tri- critical point. The A and B fluids are thought to be superfluids that result from weak coupling of fermions similar to that found in supercon­ ductors. In He the normal fluid (I) undergoes a second-order transition (A-transition) to a superfluid phase (II), which arises from the Bose- Einstein condensation as it is modi­ fied by the He-He pair interactions (Fig. 6).

0 10 20 30 LITHIUM Temperature - K The phase diagram of lithium is Fig. 5. The phase diagram of helium - 4. shown in Fig. 7. Upon cooling to

-5- 1 ' 1 ' 80 - LITHIUM - which suggests that a melting point maximum will occur at a somewhat - O - greater pressure. 60 - BERYLLIUM

The phase diagram of beryllium 40 is shown in Fig. 8. Beryllium has a - Liquid 1 transition from hep to bcc just before melt. The bcc phase is about V- 20 - P% more dense, giving rise to the bcc j/ f - negative slope of the phase boundary. ep : The hep-bec phase boundary has been n ._u_ 1 . 1 /, determined to 60 kbar. The same 0 200 400 600 study yielded two other resistance Temperature - K anomalies belcw 1000 K that appear to Fig. 7. The phase diagram of lithium. correspond to fluctuations in the hexagonal c/a lattice ratio, rather about 80 K, lithium changes from bcc than to genuine phase transitions. to a close-packed (cp) structure. The identity of this structure (or structures) is not yet agreed upon. This is a martensitic transition with a considerable temperature hysteresis. The change in transition temperature with pressure is very small, as 14 me'isurements to 3 kbar have shown. Stager and Drickamer have found a sharp drop in resistance at 70 kbar and 296 K, which is shown by the circle in Fig. 7. The structure of the high pressure phase is not 500 1000 1500 2000 known. The melting curve of lithium Temperofure - K has been determined to 60 kbar. Fig. 8. The phase diagram of The melting temperature becomes beryllium. nearly constant at this pressure, -6- Static high pressure resistance at pressures above 100 kbar and tem­ 18 measurements by Marder showed a peratures near 2000 K, but the discontinuity at 93 kbar and 293 K, probability of sample contamination but other investigators have been in this work was large. Boron 19 22 unable to repeat this result. expands very slightly upon melting 23 The melting curve has been determined near 2350 K, which implies a melt­ to 60 kbar. ing curve with positive slope. The melting curve has not been directly measured.

Solid boron is covalently bonded. CARBON The phase diagram is essentially unknown. Many different crystal The phase diagram of carbon is structures of boron have been shown in Fig. 9. This phase diagram described in the literature* but has been the subject of much experi­ their relationship to one another is mental work owing to the problem of unclear. Furthermore, contamination producing artificial diamonds. of boron with metals and the formation of boron-rich borides has a strong effect on the crystal structure. It is suspected that many of the struc­ tures reported for pure boron are in fact those c- borides.

Solidification of liquid boron Liquid yields the "S-rhombohedral" structure with 105 atoms per unit cell and 16 distinct atomic positions. This very complex structure can be resolved into groups of linked lcosahedra of boron atoms. It is likely to be the stable phase at low pressures. Static high pressure resistance measurements up to 250 kbar show no 20 2000 4000 6000 evidence of phase transitions. 21 Temperature - K Wentorf reported a new boron polymorph of unknown structure obtained Fig. 9. The phase diagram of carbon.

-7- However, the very high temperatures Shock wave experiments up to a and pressures involved have made the fdw hundred kbar clearly show the measurement of the phase boundaries graphite-diamond transition, but this extremely difficult, and the phase is dominated by nonequilibrium effects diagram cannot be said to be firmly and the initial state of the graphite. 26 established. The significance of shock data Graphite, the stable phase at indicating a new phase at yet higher low pressures, has hexagonal lattice pressure is still uncertain. Very symmetry. Graphite consists of plane recently, Vereshchagin's group has sheets of covalently bonded atoms. observed a transition from the diamond The sheets are bonded to each other to a metallic phase at pressures of 27 by weaker van der Waals forces. The approximately 1 Mbar. They also high pressure diamond phase is cubic, observed that the transition pressure with eight atoms per unit cell. Each drops with increasing temperature, atom is covalently bonded to four which is similar to the behavior of neighbors located at the corners of the semiconductor-to-metal transitions a tetrahedron. in silicon and germanium. Because diamond is metastable at The melting temperature of room temperature and pressure, the graphite shows a maximum near 5000 K free energy difference between graphite and 50 kbar according to recent 28 and diamond can be computed from work. Uncertainties in the tempera­ measured thermodynamic data, and the ture measurements are large. Melting graphite-diamond phase boundary can of diamond has not been reported, but 24 be established. This has been done the melt ng curve is assumed to have with reasonable accuracy up to 1200 K. a negative slope by analogy with and 40 kbar. Beyond this, the actual silicon. transformation of graphite to diamond in transition-metal matrices has been 24 NITROGEN carried out. These measurements extend the phase boundary to 80 kbar. The phase diagram of nitrogen is The dashed line is a linear extrap­ shown in Figs. 10 and 11. Nitrogen olation of the lower-temperature in the solid and liquid phases is results. Together with the melting composed of diatomic molecules curve, this yields a graphite- weakly bonded to each other by van der diamond-liquid triple point near 100 Waals and electrlc-quadrupole forces. 29 kbar and 3500 K. Three solid phases are known. In •' • 1 ' 1 1 '- / NITROGEN 8 -- - 1

Tetragonal -

1 ^S \ 4 - Hexagonal - (0)

2 -- Cubic / - (a) / - Liquid -

i . / i 1 ^T 1 1 i 20 40 60 80 100 120 Temperature - K Fig. 10. 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 pre­ sumably 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 mole­ The phase diagram of nitrogen. cular axes all aligned and lying In -9- the plane of the sheet. The direction is antiferroiragnetic, due to the of the molecular axis shifts by 90° ordering of the spins in the triplet from one sheet to the next. The ground state. A transition to the solid-solid phase boundaries have rhomb oh edral 0 phase, which is para­ been determined to about 10 kbar magnetic, takes place at 24 K. This (Fig. 10) 30 The melting curve has transition is definitely first order, been determinedete d to about 25 kbar although martensitlc. Another 2i (Fig. 11) transition to the cubic Y phase, also paramagnetic, takes place with large OXYGEN volume change at 44 K. This phast. shows some rotational disorder. All The phast diagram of oxygen is of these phases may be regarded as shown in Fig. 12. Oxygen in the close packed with distortions intro­ solid and liquid phases is composed duced by the non-spherical molecules. of diatomic molecules weakly bonded The solid-solid phase boundaries have by van der Waals and electric- 32 been determined to a few kbar The quadrupole forces. Three solid phasa melting curve has also been determined are known. The monoclinic a phase 33 to 3.5 kbar.

n FLUORINE 10 —i—'—i—'—i—'—r OXYGEN The phase diagram of fluorine is shown in Fig. 13. Fluorine in Che solid and liquid is composed of diatomic molecules weakly bonded by

1.5 - ' 1 1 1 ' 1 ' - S; FLUORINE Monoclinic/ Rhombohedral J J 1.0 1 IT | (a) / (, Cubic 0.5 - Monoclinic(a ) /// Pressur e - i * 1 J-Z-J L 0 , 1 , 1 1,1 20 40 60 20 40 60 80 Temnertiture - K Temperature - K

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 fluorine is tnonoclinic with a structure very

similar to a-02- At 46 K a transition with a large volume change takes place to cubic g-£luorine. This phase is isostructural with Y-0-, and the lattice is rotationally dis­ ordered. The similarity between

B-F2 and y-Oo is seen in the close agreement in the transition temperatures and the melt temperatures in the two elements. The a-$ phase boundary in

Fig. 13 Was determined from the AH 5,34 and AV of transition The melt­ 50 100 ing curve has been determined to Temperature - K only a few bars. Fig. 14. The phase diagram of neon. NEON

The phase diagram of neon is shown in Fig. 14. Neon in the solid and liquid states is composed of atoms weakly bound by van der Waals forces. Solid neon is fee. The malting curve has been determined to 10 kbar.36

SODIUM

The phase diagram "f sodium is shown in Fig. 15. Below 36 K, sodium is hep. At 36 K a martensitic phase 200 400 change leads to a bec structure which Temperature - K persists up to melt. The phase boundary separating the two phases Fig. 15. The phase diagram of sodium.

-11- i | i i I i | i i i i | i i has not been reported, but the densi­ MAGNESIUM ties are so nearly equal that the 40 initial value of dl/dp should be close to zero, as indicated in Fig. IS. 30 Static high pressure measurements in 2 the solid up to 600 kbar reveal no phase changes. The melting curve has been determined to 80 kbar. I- hep Liquid

10

MAGNESIUM

Ql I II [ I I i I I I I The phase diagram of magnesium is 500 1000 1500 shown in Fig. 16. Solid magnesium is Temperature - K hep. Resistivity and x-ray measure­ ments on magnesium under static high Fig. 16. The phase diagram of pressure show indications of a slug­ magnesium. gish phase transition near 100 kbar. 37 The structure of the high pressure phase is undetermined. The melting 38 curve has been determined to 40 kbar' 80 i i i | i i i i | i i i i and the results have been corrected ALUMINUM to the atmospheric-pressure melting point In Fig. 16. 60

S 40h n ALUMINUM fee f Liquid 20- The phase diagram of aluminum is shown In Fig, 17. Solid aluminum is fee. Static high preaaure measure­ L • • i •*! • 500 1000 1500 ments tentatively indicate a partial 0UJ 39 Temperature - K transformation to hep at 205 kbar. The melting curve haa been determined Fig. 17. The phase diagram of 40 to 60 kbar. aluminum. -12- 250 i i i i | i i i i | i i I i | i i SILICON SILICON The phase diagram of silicon is 200- Tetragonal shown in Fig. 18. Normal solid silicon (white tin) is covalently bonded semiconductor with the cubic diamond structure. Static high pressure measurements .3150 show a sharp drop in resistivity near 41 200 kbar. Subsequent x-ray work 100 showed this phase to have the tetra- 42 gonal white tin structure. Here each atom has four nearest neighbors 50 and two next nearest neighbors lying slightly farther away. The accurate determination of the phase boundary • ' • is complicated by its sensitivity to 500 1000 1500 shear stresses. In addition, recovery Temperature • of silicon compressed above 100 kbar has yielded a complex cubic form with Fig. 18. The phase diagram of silicon. 43 16 atoms per unit cell. This uncertainty in the phase diagram is indicated by a dashed line in Fig. 18. At low pressures, solid silicon melts to a more-dense metallic liquid. 30 T ' I ' ' ' The melting curve Has been measured PHOSPHORUS to 200 kbar, and a clear-cut triple 44 point occurs at ISO kbar. Shock­ £ 20- wave experiments also show phase transitions in the 100-200 kbar Ortho rhombic Liquid 45 region, but their precise nature Jiof- is unknown.

PHOSPHORUS 500 1000 1500 Temperature - K The phase diagram of phoaphorua Is shown in Fig. 19. Of Che various FiE. 19. The phaae diagram of allotropic form of phosphorus that phosphorus. -13- have been prepared, black phosphorus molecules) per unit cell in a very appears to be the most stable phase complex arrangement. Above 360 K, at atmospheric pressure. Black phos­ the solid is monoclinic, with 48 phorus has an orthorhombic structure atoms (6 molecules) per unit cell. consisting of puckered layers of The orientations of two of the six covalently bonded atoms. molecules in each unit cell are dis­ At room temperature and about ordered. 50 kbar, black phosphorus undergoes There is much disagreement about a phase change to a rhombohedral the structures of the high pressure lattice, isostructural with arsenic. 46 phases and the phase boundaries A further transition near 110 kbar separating them. The phase diagram to a simple cubic structure was also shown in Fig. 20 is due to Vezzoli, 46 observed. The rhombohedral lattice et al. ~ The phase boundaries in is a simple distortion of the simple the solid were detected by means of cubic, and thus the phase transition volumetric, optical, and electrical- is easily reversible. Conductivity resistance techniques. studies indicate that the cubic phase The phase transitions are often 47 is metallic. Solid-solid phase difficult to detect, as indicated by boundaries have not been determined. the dashed boundaries in Fig. 19. The melting curve of othorhombic The large number of phases can be black phosphorus has been determined understood as a series of stepwise 48,49 to about 20 kbar conformational changes in the Sg rings with changes in temperature and pressure. The structures of the SULFUR phases other than the well-known I

The phase diagram of sulfur is and 11 have not been worked out, shown in Fig. 20. The literature on although there is evidence that phase the allotropy of sulfur presents the XII is monociinic, with closely most complex and confused situation packed helical chains of atoms of all the elements. Solid sulfur similar to the selenium and tellurium 53 under room conditions is composed of rfructures. Resistance measurements covalently bonded S„ rings that inter­ on sulfur compressed to 400 kbar act with each other through van der showed no transition to a metallic Waals forces. Below 360 K at atmos­ scate.. .5 4 pheric pressure sulfur has an ortho- The melting curve shows a number rhombic lattice with 128 atoms (16 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 diatomic molecules bonded to neighbors boundaries. In addition, Vezzoli by van der Waals forces. Solid 52 et al. have discovered a number of chlorine has an orthorhombic struc­ "phases" (indicated by letters) in ture, composed of approximately the liquid using DTA techniques. close-packed layers of molecules. The These regions in the liquid appear to meltinp curve has been determined to be different polymeric states result­ 7 kbar. ing from the breakup of the Sg rings. The nature of the transitions joining ARGON the liquid phases is not clearly understood. The lower portion of the The phase diagram of argon is melting curve given by Vezzoli £t_ al. shown in Fig. 22. Argon in the solid has been independently confirmed. and liquid is composed of atoms weakly bonded by van der Waals forces. Solid CHLORINE argon is fee. The melting curve has 31 been determined to 26 kbar. The phase diagram of chlorine is shown in Fig. 21. Chrlorine in the POTASSIUM solid and liquid states exists as The phase diagram of potassium is i—i—r- T shown in Fig. 23. Solid potassium is CHLORINE bcc. No martensitic transition of the

.s 30 — | ! i '••'i • - ARGON /- 4 - -§20-

- • Orthorhombic Liquid fee 10—- f Liquid " 100 200 300 1,1.1 Temperature - K 100 200 300 400 Temperature - K Fig. 21. The phase diagram of chlorine. Fig. 22. The phase diagram of argon.

-16- 1 ' 1 - • I'" 40 80 - POTASSIUM - i 1 1 60 _ 30

1 40 tfc bcc 1 o 20 20 j:

10 n i , ,y ,• 0 200 400 600 Temperature - K 500 1000 1500 Fig. 23. The phase diagram of potassium. Temperature -

Fig. 24. The phase diagram of calcium. kind occurlng in Li and Na is found in potassium upon cooling to 5 K. However, Stager and Drickamer found measurements at 77 K showed a sharp two resistance anomalies at 280 kbar rise in resistance near 140 kbar and and 360 kbar at 77 K. These transi­ a subsequent sharp drop near 400 58 tions were not observed at 296 K. kbar. These data were ascribed to The authors suggest that the more two rather sluggish phase transitions, dramatic second transition is analo­ first cu . semimetallic, then to a gous to the low temperature transition metallic phase. These data are in in Li and Na. The melting curve of rough accord with later Soviet 59 potassium has been determined to work. The melting curve of calcium 80 kbar.16 has been determined to 40 kbar.

CALCIUM SCANDIUM

The phase diagram of calcium is Scandium is hep at atmospheric shown in Fig. 24. Under room condi­ pressure. Static high pressure re­ tions calcium i* fee. Near 700 K at sistance measurements at room temper­ one atmosphere it undergoes a transi­ ature showed no evidence of a phase tion to a bcc structure. The phase change to 140 kbar. Shock wave boundary has been measured to 30 measurements by Carter, e_t_ al_. showed kbar. High pressure resistance a kink in the u -u curve at s p -17- approximately 350 kbar. This was Shock wave experiments show a ascribed to a sluggish low pressure strong break in the u -u curve for s p solid-solid phase change. No kink titanium, indicating a phase change was found in the shock v?ave work of occurring at 175 kbar. The nature Gust and Royce. Scandium melts at of this phase transition has not been 1812 K. The melting curve has not determined. Titanium melts at been reported. 1941 K. The melting curve has not been reported. TITANIUM VANADIUM The phase diagram of titanium is shown in Fig. 25. At room temperature Vanadium is bcc. No solid-solid and pressure titanium is hep. A phase transitions have been reported. transformation to a bec phase occurs Vanadium melts at 2178 K. The near 1150 K. The phase boundary has melting curve has not been reported. been determined to about 110 kbar, where a triple point occurs. CHROMIUM The low temperature, high pressure ui The phase diagram of chromium i phase may be regarded as a distorted shown in Fig. 26. Pure chromium is bec lattice with hexagonal symmetry. antiferromagnetic below 311 K and This structure has three atoms per paramagnetic above this temperature. unit cell and two distinct types of Although there has been some contro­ atomic positions. versy about various allotropes of

TT 1 | I I I 1 J 111111111 1111II11 1 1 II 1111 8 7"l""l""- CHROMIUM - Hexagonal o 3 6 : (w) i ^-'Tetragonal Liquid - s § / TITANIUM J V ^ Orrhoihombic sur e - kba r mp J mp ~ hep I 2 bcc bcc U-iquid;: • 1 \, , ,' *. i i i 1 • • i ' 111 1 11 1 11i V i i i i* 0 . J_ 11 1 • i i i 1 i • i i 1 • i i 500 1000 1500 2000 2500 500 1000 1500 2000 2500 Temperature - K Temperature - K

Fig. 25. The phase diagram of Fig. 26. The phase diagram of titanium. chromium.

-18- chromium, it Is probable that the 50 I I I I I I 1 I I I I l— I I I I paramagnetic phase is simple bcc up MANGANESE to the melting point. Below 311 K, the paramagnetic phase transforms to 40 an antiferromagnetic phase by a first- order phase transition. This phase _8 30 is in a spin-density wave state In which the polarization is perpendicular Liquid to the wave vector. This magnetic 8 20 state is inconsistent with the reten­ Cubic tion of full cubic symmetry, and the (a) lattice instead takes on a very slight 10 orthorhombic distortion of the bcc lattice.

At 123 K, another first-order 0|_i—i—i—i—L_ tr sition occurs to a new antiferro­ 0 500 1000 1500 Temperature - K magnetic spin-density wave state in which the polarization and wave vectors Fig. 27. The phase diagram of manganese. 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 deter­ mined to 8 kbar. ' Static pressure centered cubic lattice with 58 atoms per unit cell and 4 different types measurements at room temperature to of atomic positions. At atmospheric 55 kbar show no other phase changes. 70 pressure near 1000 K, a transition Chromium melts at 2148 K. The occurs to the fi form, thought to have melting curve has not been reported. 20 atoms per unit cell and 2 types of atomic positions. Near 1370 K a MANGANESE transition to the fee Y phase occurs, The phase diagram of manganese and near 1520 K a further transition is shown in Fig. 27. There are four to the bcc 6 phase occurs. The 'phase allotropes, all of cubic symmetry. boundaries and the melting curve have 71 The a form has a complex body been determined to 40 kbar.

-19- IRON ct-y, ct-e, and y~e phase boundaries 72 have been determined to 200 kbar. The phase diagram of iron is The y-& transition and the melting shown in Fig. 28. The phase diagram curve have been determined to 52 and especially the melting curve of kbar, where they meet in a triple iron is of great interest because of 73 point. The melting curve of the the problem of the state of the Y phase has been extended about 5 earth's core and the origin of the 73 geomagnetic field. Under room condi­ kbar beyond the triple point. tions iron is ferromagnetic and has COBALT a bcc structure. At 1044 K it passes

through the Curie point and near 1200 The phase diagram of cobalt is K it transforms to the fee phase. shown in Fig. 29. At room tempera­ The bcc phase once again becomes ture cobalt is hep. At a temperature stable before melting. Above 100 depending on the sample grain size, a kbar, the bcc phase transforms to a sluggish phase change to fee occurs. nonferromagnetic hep phase. The For large crystal grains the trans­ formation 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.

60 111 I I I 111 ] 11 1 I 11 I I I (I 11 I COBALT _ 50 I 40

£ 30 hep J fee L'quid " 1 20 mp * 10- 0 11 i i I i II i 11 i i) Ii it i I i i i i 500 1000 1500 2000 0 500 1000 1500 2000 2500 Temperature - K Temperature - K

Fig. 28. The phase diagram of iron. Fig. 29. The phase diagram of cobalt.

-20- 80 I—1—I I 1 COPPER The phase diagram of nickel is shown in Fig. 30. Solid nickel is 60 fee. The melting curve has been determined to 80 kbar. '

£ 40 ""I" "I"1'I1 80 NICKEL fee

0 60 -Q 20 40 fee i /Liquid | Liquid 1 20 at I • • •/• I ! 0. i I .... I i i • , I i ill i I . , , , 500 1000 1500 2000 2500 "0 500 1000 1500 Temperature - K Temperature - K

Fig. 30. The phase diagram of nickel. Fig. 31. The phase diagram of copper.

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.

7 ' 1 ' 1 ' | i | i • ZINC 80 ZINC J 60 - The phase diagram of zinc is / ~ shown in Fig. 32. Solid zinc has a / : | 40 hep distorted hep lattice, with the c/a f Liquid ratio considerably greater than ideal. £ 20 / Under pressure, this ratio shows I .1.1/ , 1 . * unusual fluctuations, but no clear-cut °( 2C1 0 400 600 8(1 0 1000 12C solid-solid phase changes are found Temperature - K up to 200 kbar. The melting curve has been determined to 60 kbar. Fig. 32. The phase diagram of zinc.

-21- 80 L ' ! ' I • I ' TZ\ GALLIUM GALLIUM

The phase diagram of gallium is Orthorhombic (III) shown in Fig. 33. Solid gallium at 60 atmospheric pressure has an ortiio- rhombic structure with eight atoms 2 per unit cell. Each atom in this structure has one nearest neighbor I 40 and six other near neighbors somewhat farther away. At atmospheric pressure gallium melts just above room temper­ ature, and the melting temperature 20- initially decreases with increasing Orthorhcmbic (M pressure. Gallium II is probably body centered tetragonal. The high- I I I temperature gallium-III phase is a 0 100 200 300 400 complex orthorhombic lattice with Temperature - K 40 atoms per unit cell. The phase Fig. 33. The phase diagram of gallium. boundaries, including the melting 250 | I • I i | I i I curve, have been determined to GERMANIUM ,. ,. 78,79 75 kbar. 200 GERMANIUM * Tetragonal . (white tin) The phase diagram of germanium -§ 150 is shown in Fig. 34. Solid germanium under room conditions is a semicon­ Liquid ductor with the cubic diamond struc- | 100 60 ture. Above 100 kbar shock wave and electrical resistance measure- •_ Cubic 41 50 - ments indicate the appearance of a 1 (diamond) new phase. This phase is metallic, with the tetragonal white tin struc­ ••• ilitiii.Xi.il ture. There remains some uncertainty 500 1000 1500 concerning new phases obtained from Temperature - K 81 quenching experiments. The cubic- Fig. 34. The phase diagram of tetragonal phase boundary and the germanium.

-22- netting curve have been determined up 1 ' ' I ' ' ' 44 to 200 kbat. ARSENIC 60

ARSKNIC

The phase diagram of arsenic la 40 shown in Fig. 35. Ac atmospheric £ pressure arsenic crystallizes in Che 3 prtnltlvc rhoabohedral laccice Rhombohedral Liquid characteristic of the group VB i 20 elements- High pressure resistance measurements shoved no anomaly up Co 82 200 kbar. However, arsenic that -iJ_ had been compressed to ISO kbar 0 500 1000 1500 showed a tetragonal structure, which Temperature - K may represent a high pressure phase. S3 The melting curve has been determined Fig. 35. The phase diagram of arsenic. up to 60 kbar.

SELENIUM I ' I ' I ' ! The phase diagram of selenium is SELENIUM shown in Fig. 36. Solid selenium at 60 lou pressure has a hexagonal crystal structure composed of covalently bonded helical chains of atoms. In 40 this state selenium is a semicon­ Hexagonal ductor. Near 130 kbar, a resistance discontinuity is observed, and selenium 20 - becomes a metallic conductor. * An attempt to determine the structure of this high pressure form was 87 I I I /I unsuccessful. The melting curve 0 200 400 600 800 1000 1200 has been determined Co 60 kbar. Temperature - K It shows a clear maximum in tempera­ ture. Fig. 36. The phase diagram of selenium.

-23- BROMINE 140 kbar rather than 200 kbar.59 The lower transition is Indicated in The phase diagram of bromine Is Fig. 39 by a dashed line. These shown In Fig. 37. Solid bromine Is transitions are thought to correspond composed of diatonic molecules held to those observed in cesium at low together by weak van der Haals pressure. The upper transition Is forces. The solid has an orthorhombic likely to be due to a shift In the structure, analogous to chlorine. electronic configuration of the Indirect evidence for a phase transi­ rubidium atoms. The melting curve tion in solid bromine at 35 kbar has has been determined to 80 kbar. 91 been reported, but no details of The melting temperature appears to be the phase boundary or the structure approaching a maximum near 80 kbar. of the new phase are available. The melting curve has been determined to ,„„ 56,89 STRONTIUM 10 kbar.

The phase diagram of strontium KRYPTON is shown in Fig. 40. Under room conditions strontium is metallic with The phase diagram of krypton is an fee structure. With increasing shown In Fig. 38. Solid and liquid pressure at room temperature or krypton consist of atoms bonded by below, strontium becomes semi- weak van der Waals forces. The solid 94 metallic. Hear 35 kbar, a phase Is fee. The melting curve has been 36 92 transition to the metallic bcc struc­ determined to 12 kbar. ' ture occurs. The unusual change from a more efficient to a less effi­ RUBIDIUM cient packing with increasing pres­

The phase diagram of rubidium Is sure appears to be due largely to the shown in Fig. 39. At low pressures electronic transitions mentioned. solid rubidium is bcc. Bundy and Beyond the 3S kbar transition, Strong found a sharp resistance jump strontium shows metallic conductivity 93 near 75 kbar and room temperature. with no indication of further trans­ Stager and Drickamer found a sharp itions up to 500 kbar. The fcc-bcc rise In resistance near 200 kbar at phase boundary intersects the p = 0 two temperatures. Soviet work con­ axis at 830 K. This boundary and the firmed the 75 kbar transition, but meltiig curve have been determined found the next transition near 135- to 40 kbar.

-24- 80 BROMINE "HP ' ~T 10 RUBIDIUM

60 2 ji _ OrthorhombTc I £ 40 3 i

20 2

1 I . I Oj-- 0 100 200 300 400 200 tfia 600 Temperature - K Temperature - K

Fig. 37. The phase diagram of bromine. Fi8- 39- *>« Phase diagram of rubidium.

50 11 i i | i i I i | i i i i | I 12 1 ' 1 ' 1 -r STRONTIUM KRYPTON 10 - 40

2 30 I | r i •

£20- r - fee / Liquid bec / Liquid

4 10

2 ,. l/, 1 . 1 1 I J U 0 100 200 300 0 500 1000 1500 Temperature - K Temperature - K

Fig. 40. The phase diagram of Fig. 38. The phase diagram of krypton. strontium. -25- YTTRIUM hep phase transforms to bcc. The triple point joining the three phases Solid yttrium at low pressure is occurs near 60 kbar and 1000 K. The hep. Above 110 kbar, yttriur. 95 phase bounds.-ies have been uorked out becomes a superconductor, A itudy to 70 kbar. Vereshchagln observed of the pressure dependence of the a sharp change of slope in the resist­ transition temperature indicates the ance as a function of pressure near presence of several superconducting 96 100 kbar, but what this means is modifications. However, these 97 unclear. A shock-wave study of modifications are not thought to have zirconium showed a sharp break in the different crystal structures, but u -u curve at 260 kbar, which pre- rather arise from slight changes in s P 66 band structure. sumably indicates a phase change. Static resistance measurements Zirconium melts at 2123 K.63 The to 250 kbar shew no phase transition melting curve has not been reported. 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 i i i i | i i i > | i i i i | i rn | ni_ 80 ZIRCONIUM indicated the stiffening of the solid as inner electron cores overlapped. " Hexagonal ! - Carter, e_t _ai. saw a kink in tk& u -u curve at 370 kbar and suggested 60 s p a sluggish low pressure transition as - an explanation. Yttrium melts at : y 63 1775 K. The melting curve has not £ 40 - been reported. 3 - *? hep bcc ZIRCONIUM 1 20 - Liquid The phase diagram of zirconium mp\ is shown in Fig. 41. Zirconium under room conditions Is hep. under com­ n 1il l I 1 1 1 uMl I iLI- pression it transforms to the hexagonal "0 500 1000 1500 2000 w phase isostructural with u-titanium. Temperature - K This is a distorted bec phase. Near Fig. 41. The phase diagram of 1140 K at atmospheric pressure the zirconium.

-26- KI0BIW1 RUTHENIUM

Solid niobium is bcc. No Solid ruthenium in hep. Com­ resistance anomalies have been found pression to 400 kbar at room tespera- 97 99 below 250 kber. Niobium melts at tur* showed no change of phase. 2741 K. The melting curve has not Ruthsnium melts at 2SS3 K.63 The been reported. melting curve has not been reported.

MOLYBDENUM RHODIUM

The phase diagram of molybdenum The phase diagram of rhodium is is shown in Fig, 42. Solid molybdenum shown in Fig. 43. Solid rhodium is is bcc. An approximate melting curve fee. The melting curve has been 98 has been determined to 90 kbar. approximately determined to 80 kbar.38'74 TECHNETIUM

Solid technetium is hep. 63 Technetium melts at 2443 K. The Solid palladium is fee. Palladi­ melting curve has not been reported. um melts at 1825 K. The melting curve has not been reported.

100 i—•—i—'—r 100 MOLYBDENUM

80 -

I 60t- bcc

40

20 Liquid

0. J J i 1000 2000 3000 1000 2000 3000 Temperature - K Temperature - K Fig. 42. The phase diagram of molybdenum. Fig. 43. The phase diagram of rhodium.

-27- SILVER to 250 kbar showed no strong 97 anomalies. The melting curve has 38 The phase diagram of silver Is been determined to 50 kbar. shown In Fig. 44. Solid silver Is fee. Compression to 300 kbar at room INDIUM temperature shows no evidence of a phase change. The melting curve The phase diagram of indium is has been determined to 65 kbar. shown In Fig. 46. Solid indium is body centered tetragonal. Compression

CADMIUM at room temperature to 300 k ar shows no indication of any phase changes. The phase diagram of cadmium Is The melting curve has been deter­ shown In Fig. 45. Solid cadmium Is mined to 80 kbar.78 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 The phase diagram of tin is 37 been suggested as an explanation. shown in Fig. 47. Below 290 K at Independent resistance measurements

0 200 400 600 800 Temperature - K Temperature - K

Fig. 44. The phase diagram of silver. Fig. 45. The phase diagram of cadmium.

-26- 1 1 1 1 1 1 1 atmospheric pressure, tin is cubic iNDIUM diamond like silicon and germanium. 80 - : / Above this temperature tin has the tetragonal white tin structure with | 60- - four atoms per unit cell. In this : / structure each tin atom has four i "o — Tetragonal / - nearest neighbors at the vertices of i / Liquid - a flattened tetrahedron. Two more neighbors lie slightly farther 3way. 20 - The diamond-to-white-tin I 1 J l/i 1 I 1 boundary has been determined to about 102 200 400 600 800 50 K and 10 kbar. At room Temperature - K temperatute near 90 kbar, the white tin transforms to a body-centered Fig. 46. The phase diagram of indium. tetragonal structure with two atoms per unit cell. The boundary joining the two phases has been approximately determined to 95 kbar.103'104 Tht melting curve has also been determined . ,, ,. 103,104 100 to 75 kbar. *

ANTIMONY 80

I The phase diagram of antimony is i 60 shown in Fig. 48. Solid antimony Tetragonal under room conditions is rhombohedral, (white tin) 40 - isostructural with arsenic. At room temperature, antimony has two phisa transitions, one near 70 kbar and one 20- Cubic •^(diamond) near 85 kbar (circles).105 The 70- kbar transition is sluggish and appar­ 0 200 400 600 800 ently has a very small volume change. Temperature - K The phase II structure is simple cubic, which corresponds to the Fig. 47. The phase diagram of tin. elimination of the low pressure

-29- I i | I i I i | i i i i | I TELLURIUM 100 ANTIMONY The phase diagram of tellurium °\ Tetragonal 80 is shown in Fig. 49. Solid tellurium

- v\(«o under room conditions is a semicon­ • 60 ductor, with a hexagonal structure a> - \sn composed of covalently bonded helices packed together. This structure can Liquid be regarded as a distortion of the simple cubic lattice. Near 40 kbar 20 Rh'ombohedral \ at room temperature (circle), a transition to a metallic phase occurs. 0 I I I 1 • ' ' ' ' ' 500 1000 1500 The structure of this phase has not 108 yet been determined. Near 70 koar Temperature - K at room temperature (circle), a Fig. 48. The phase diagram of further transition to a rhombohedral 108 antimony. lattice occurs. This phase is isostructural with 3-polonium. Studies of superconductivity at high rhombohedral distortion. Hie transi­ pressures indicate possible new tion, at 85 khar is wore strongly marked, with noticeable volume and T TELLURIUM resistance changes. The structure 80 of phase III is uncertain, but recent "^ Rhombohedral (III) worfe suggests a tetragonal structure S 60 S analogous to that found in arsenic at s high pressures. Phase III shows ll V 82 good metallic conductivity. The ; 40 melcing curve has been determined to 70 kbar. ' Two cusps, indicating 20 Hexagonal triple points, have been found, one at 3.9 kbar, and the other at 57 kbar. -i L J_ J L Stishov and Hkhomlrova assumed "0 200 400 600 E800 that the two triple points corresponded Temperature - K to the two room temperature transi­ Jig. 49. The phase diagram of tions, as indicated in Fig. 48. tellurium. -30- 109 phases at still higher pressures. the diatomic moleculea within the The solid-solid phase boundaries and orthorhombic unit cell. the melting curve have been deter­ At higher pressures, above 100 mined to about 70 kbar. A definite kbar, the resistance of iodine drops 113 maximum in the melting temperature rapidly to a metallic value. Here is found near 10 kbar. It is thought that the I„ molecules dissociate into an atomic metallic

IODINE structure. It is not clear whether this is a continuous or an abrupt The phase diagram of iodine is transition. Shock wave experiments shown in Fig. 50. Solid iodine at on iodine show a strong break in the low pressures is composed of diatomic plot of u vs uD at approximately molecules in an orthorhombic lattice, 700 kbar.H4 Given a transition to isostructural with solid bromine and the metallic phase at a much lower chlorine. No clearly defined phase pressure, this break is likely to transition has been found at moder­ represent a phase transition from ate pressures, but an x-ray study one metallic phase of iodine to of the solid to 60 kbar showed a con­ another. The melting curve has been tinuous shifting of x-ray determined to 50 kbar. ' 112 reflections. This was interpreted as a shifting of the orientations of XENON

n ' i • r The phase diagram of xenon is 50 - IODINE shown in Fig. 51. Solid and liquid xenon are composed of atoms bonded u 40- o by weak van der Waals forces. Solid M xenon is fee. The melting curve has g 30- Orrhorhombic 92 been determined to 7 kbar. a i 20-

CESIUM 10- The phase diagram of cesium is 0L- 0 200 400 600 800 1000 shown in Fig. 52. Cesium has been Temperature - K intensively studied because of its unusual properties. Solid cesium at

Fig. 50. The phase diagram of iodine. atmospheric pressure is bcc. At

-31- room temperature the bcc phase trans­ forms to fee at 23 kbar. Further compression yields two more phase transitions only about 1 kbar apart near 42 kbar. The first new phase is also fee, but the structure of the second (IV) has not yet been deter­ mined. The solid-solid phase boundaries have been determined, ' and they show very weak temperature depenlence, except that the upper fee phase apparently disappears at 200 400 600 low temperatures. Temperature - K The isostructural fcc-fcc transi­ Fig. 51. The phase diagram of xenon. tion occurs with a 9% volume change, and has excited much curiosity. The first theoretical attempt at an explanation proposed that the trans­ formation represents a shift from 6s 60 •"T '' ' 1 . CESIUM to 5d character of the conduction 120 band. Although details of this 50 - / IV theory have been criticized, it is

• - widely agreed to be qualitatively >.. 40 — L ~" 1 fcc^ correct. .a: A further sluggish transition in r - fee £ 30 \ solid cesium occurs near 125 kbar, accompanied by a large increase in 5° resistance. This phase (V) exhibits K - J superconductivity and it has been bcc suggested that the phase is 10 Liquid - transition-metal-like, with increased • 95 1 l/l d-electron character, 0 200 400 600 The melting curve of cesium has Temperature - K been worked out to 55 kbar.117,118 Two melting temperature maxima occur Fig. 52. The phase diagram of cesium. near the bcc-fcc transition. The

-32- decreasing melting temperature of i i i i I i r i i I 11 i i i n the close-packed fee phase is due to BARIUM the density of the liquid increasing beyond that of the solid. This phe­ nomenon has been ascribed to the smearing out in the liquid of the sharp electronic transition observed Liquid in the solid. Thus the volume con­ traction in the liquid can be thought of as a smoothly varying change in. relative concentration of two electronic species, whereas in 1 '•' '*'''' * • ' the solid this change takes place all 0 500 1000 1500 at once. The melting curve of Temperature - K phase IV once again takes on a normal appearance. 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 Drickamer found a further transi­ temperature, a well-marked phase tion at 144 kbar and room tempera­ 122 transition occurs at 55 kbar. ture, and inferred from a detailed The high pressure phase has been study that this was a melting transi­ 123 determined to be hep. There is tion. Later work indicated a solid- 129 disagreement over the trajectory of solid transition instead. A the bec-hep phase boundary, since further transition at 240 kbar was DTA measurements show dp/dT > 0 125 found at 77K, presumably to yet while resistance measurements another solid phase. The melting show dp/dT < 0. Additional curve has been determined to about evidence supports the first possi­ nn it. 124,125,128 , „. bility, which is shown in Fig. 53. 90 kbar, * * and three A second phase transition to a phase melting-curve maxima appear. It (III) of unknown structure has also seems likely that electronic phase been reported. * Stager and changes similar to those observed in 130 cesium are occurring in barium. -33- LANTHANUM while the second ascribes it to the intersection of the Hugoniot and the The phase diagram of lanthanum melting curve. The fcc-bcc boundary is shown in Fig. 54. Lanthanum and the melting curve have been exhibits three solid phases at atmos­ determined to nearly 40 kbar. pheric pressure. From 0 to 580 K, the stable phase is dhcp. At 580 K, CERIOM a pftase transition to an fee phase occurs with a decrease in volume. The phase diagram of cerium is The dhep-fee phase boundary has been shown in Fig. 55. This unusual 131 worked out to 24 kbar. At 1130 K, diagram has been intensively studied. a transition to a bec phase occurs, At zero Kelvin and atmospheric and melting occurs near 1200 K. pressure, cerium is fee. Between Electrical resistance measurements approximately 100 K and 45'J K, a made to 250 kbar sfiow a smalt resist­ dkep phase is stable. Between 450 (c ance anomaly near 100 kbar, which and 1000 K, the fee phase is again may indicate a phase transition. stable, with the difference that the Ttyo sets of shock wave ©.xperi- Y phase is ferromagnetic while the ments show kinks in the u -u_, curve a phase is paramagnetic. A bec phase es p for lanthanum at 250 kbar*2 ^a then intervenes just before melting. 61 225 kbar The first report ascribes The dhcp phase disappears at low 62 133 the fcinfc to xenon core repulsions, pressures.

40 I I | I I I I | I I r-|-r-r I • | I I I I | I I I I | T LANTHANUM I 80 CERIUM

Orthorhombic 1 1 60

Ll'qui'd' 40,

20 U (a) Liquid _| dhcp facc I I I I, 7) L' 500 1000 1500 1_L '•'"•••• I I I Temperchjre - K 0 500 1000 1500 Temperature - K Fig. 54. The phase diagram of lanthanum. Fig. 55. The phase diagram of cetium. -34- The unique feature of the cerium rx-y phase boundary and ct-a* phase diagram is the isostructural a -*• y boundary leads to points very near phase transition, which ends in a one another on the melting curve. critical point estimated from Stager and Drickamer reported a 134 resistance measurements to lie at further possible phase change near 138 17.5 kbar and 550 K. A considerable 160 kbar at room temperature. Two theoretical effort has been made to sets of shock wave data give discor- 61,62 _ explain the a •* y phase transition dant results1fc . In one case, a and critical point. The earliest kink in the u -u curve was found at s p 61 theories assumed that the transition 480 kbar and ascribed to melting. represented a promotion of the In the other case, no kink was 62 localized 4f electron to the delocal- found« *. 135 i2ed 5d band. Later theories The melting curve of cerium has 134 modified this by assuming only a been determined to 70 kbar. The 135 partial 4f derealization . Such remarkable feature is a minimum In models imply a definite increase in the melting temperature around 33 the number of conduction elections as kbar. Jayaraman explains the minimum the pressure is Increased. But in terms of isotherms similar in this is contradicted by positron- shape to the supercritical isotherms annihilation experiments that observed in the vicinity of the 134 indicate no change in the number of liquid-vapor critical point. 135 These isotherms reflect the rapid conduction electrons. In general decrease in the size of the cerium it could be said that the y -*• a atoms in the solid phase as the transition results from the Inter­ pressure is increased. action of the 4f and conduction electrons, but the precise model of this interaction is disputed. Further compression of cerium PRASEODYMIUM leads to another phase transition in The phase diagram of praseodymium the 50-60 kbar range. The new is shown in Fig. 56. Normal solid phase (a1) has been determined to be praseodymium Is dhep. A room- orthorhoiribic, isostructural with temperature transition to an fee 137 139 a-uranium. The phase boundary has phase occurs at 40 kbar (circle). been determined over a relatively The trajectory of the dhep-fee phase short temperature range, but it is boundary is difficult to follow interesting that extrapolation of the-35 - ~r i i i | i i i i | mi |"i i boundary and the melting curve have 131 80 PRASEODYMIUM — been determined to 70 kbar.

60 1 - NEODYEtCH 1 The phase diagram of neodymium 40 - \ fee 1 _ is shown in Fig. 57. Under room \ 1 Liquid " conditions neodymium is dhep. High 20 dhcp\ 1 ~ pressure tf-ray studies at room bce temperature show a transition to the \ y • 139 _L V . I #. . . 1 , . fee phase near 50 kbar (circle), 500 1000 1500 This transition is very difficult to Temperature - K detect, and the intersection of the phase boundary with the p » 0 ajds, Fig. 56. The phase diagram of although suspected, could not be praseodymium. 140 directly measured. Instead, a because it is extremely sluggish and temperature of 960 K is inferred from a generalize1UX d rare earth phase apparently quite sensitive to diagram, Resistance measurements Impurities. An approximate value for the zero-pressure transition temperature is 833 K. ** Resistance 1 -\ IT] TTTT'| 1 \ » l-JTTT- measurements to 500 kbar show 80 •-" NEODYMIUM several anomalies above that at 40 kbar, and suggest two more high- 60 -- - pressure phases of unknown structure £ / 138 ~ ' above Che fee phase. \ f" / Two sets of shock-wave experiments / show kinks in the u -u curve for Liquid 8 / r ™ P 62 ~ dh praseodymium at 300 kbar and 270 =p \ Lc kbar. The first report ascribes 20 62 the kink to xenon-core repulsions, _L, 1 1 . 1 1 1 1 \l J 1 I • !..!__) 0 500 1000 1500 while the second tentatively ascribes 0 it to an electronic rearrangement In Temperature - K the liquid. A bec phase appears Fig. 57. The phase diagram of before melt. The bcc-fcc phase neodyroium.

-36- on neodymium up to 600 kbar showed 1 1 1 1 | 1 I 1 1 | 1 1I I | I l 80 anomalies in the 100-200 kbar region SAMARIUM at different temperatures, which - could correspond to another high- 1 60 dhcp 138 pressure phase transition. 1 V - Two sets of shock-wave experiments 4 0 I bee show kinks in the u -u„ curve for 15 X s p c£ X X , . s neodymium at 280 kbar and 250 kbar. 20 _ Rhombohedral xl (Siti) 1 The first report ascribes the kink to / " 62 /Liquid" xenon-core repulsions, while the n • •••!•• i • 1 • 1 ill A 1 l_ second identifies it with melting. 61 0 500 1000 1500 A bcc phase appears before melt. The Temperature - K bcc-fcc phase boundary and the melting Fig. 58. The phase diagram of curve have been determined to 60 samarium. kbar. henceforth called "Sm-type." Resist­ ance measurements to 600 kbar at PROMETHIUM room temperature show anomalies near 50 kbar and 160 kbar that might cor­ Promethium Is dhcp at room 138 respond to phase transitions The temperature and pressure. 142 Prom­ dhcp phase appears in samarium near ethium has not been extensively worked 40 kbar and 623 K (circle). with because the element is unstab7i, Two sets of shock wave experi­ and the most-easily available isotcpe ments show kinks in the u -Up curve has a half-life of 2.6 years. The s for samarium at 310 kbar*>2 and 270 melting temperature is 1315 K. No kbar. The first report ascribes high-pressure work has been reported. the kink to xenon-core repulsions 62 while the second identifies it with melting. A phase assumed to be SAMARIUM bcc appears before melt- An inflection The phase diagram of samarium is in the bcc-to-close-packed-solid phase shown in Fig. 58. Under room condi­ boundary is assumed to represent the 131 tions samarium has a close-packed Sra-type-dhcp-bcc triple point. structure of rhombohedral symmetry. The bcc-solid phase boundary and the The arrangement of close-packed melting curve have been determined to 131 layers in this structure is ababcbcac, 60 kbar.

•37- EUROPIUM phase transformation. Bakanova 146 et al. found a kink in the u -u The phase diagram of europium is s p curve at 386 kbar and ascribed this shown in Fig. 59, Solid europium at to an electronic rearrangement. atmospheric pressure is bcc. Below It Is possible that the anomalies 88.6 K, europium is antiferromagnetic, in the shock data correspond with the with a helical arrangement of spins, 138 and it becomes paramagnetic above this resistance anomaly which has been temperature. The transition has been ascribed to a divalent-trivalent 144 determined to be first order, electronic phase transition. which means that the bcc lattice is According to this theory, the very slightly distorted in the mag­ anomalously divalent europium becomes netic phase, as in the case of more rare-earth-like aa the pressure chromium. The pressure dependence of increases. The europium melting the transition has been determined to curve has been detei-mined to 70 145 90 kbar. It has been suggested ., 147,148 . fc that as the lattice becomes less com­ kbar. A temperature maximum pressible with increasing pressure, appears near 30 kbar. The close the first-order transition simply analogy between the behavior of stops at about 20 kbar and gives way europium and barium has been pointed 144 out. to a pure second-order transition. Static high-pressure resistance measurements show a sharp change near 150 kbar and room temperature, which probably corresponds to an electronic 138 phase transition The transition pressure appears to decrease with 138 temperature. Three sets of shock wave experiments show anomalies in 61,62,146 the u -u, curve. Carter s ej; jal.61 * found a discontinuity in the u -u curve at 106 kbar, and sug- s p gested that this corresponds to the 0 500 1000 1500 intersection of Hugoniot and melting Temperature - K curve. Gust and Royce found anomalous behavior in the 180-360 Fig. 59. The phase diagram of kbar range and suggested a sluggish europium. -38- GADOLINIUM electronic transition in the solid. A bcc phase appears before melt, and The phase diagram of gadolinium a kink in the bec-hep phase boundary is shown in Fig. 60. Under room was taken to be hcp-Sm-type-bcc triple conditions gadolinium is hep. A 131 point. The melting curve has been transition to the samarium-type phase determine„ ~_4 d^ t. o 4/n0 ,kbarL . 131,148 occurs at about 25 kbar (circle) at 149 room temperature. The hcp-Sm-type TERBIUM phase boundary has not been directly determined. Resistance measurements The phase diagram of terbium is 60 138 shown in Fig. 61. Under room condi­ to 500 kbar show no anomalies. * tions terbium is hep. A resistant Two sets of shock wave experi­ anomaly indicating a transition has ments show kinks in the u -u curve s62p been reported at 27 kbar (circle), for gadolinium at 260 kbar and 345 kbar. The first report ascribes and the high pressure phase has been the kink to xenon-core repulsions, determined to be the Sm-type. while the second identifies it with an Resistance measurements to 500 kbar show smooth behavior and no clear

• | i • | 1- 40 GADOLINIUM _ 1 1 1 1 1 TERBIUM 40 1 - . Rhombohedral L^bcc Rhombohedral 30- (Sm-type) ~ 1 (Sm-type) : •f 30 2 ^x

1 X • X 1 ] i • X X — X ^-bec — 20- X Pressur e X % _ Liquid hep

o — hep \ — t o 10 - ~ r - n 1 1 1000 2000 3000 ' . , . Temperature - K 0 1000 1200,0 -3000 Temperature - K

Fig. 60. The phase diagram of gadolinium. Fig. 61. The phase diagram of terbium.

-39- evidence of further phase transi- Two sets of shock-wave experi­ 138 tions. The approximate hcp-Sm- ments show kinks in the u -u curve s p type boundary is based on a general­ for dysprosium at 480 kbar62 and 305 ly 1 61 ized rare-earth phase diagram. kbar The first report ascribes Shock-wave experiments show a the kink to xenon-core repulsions, 62 kink in the u -u curve at 400 while the second Identifies it with 61 s p 61 melting. The bcc-hcp boundary and kbar. This is ascribed to melting. the melting curve have been deter­ The bcc-hcp phase boundary and the mined to 25 and 8 kbar, melting curve have been determined 131 respectively. to about 25 kbar. x

DYSPROSIUM HOLMIUM

The phase diagram of dysprosium The phase diagram of holmium is is shown in Fig. 62. Under room shown in Fig. 63. Under room condi­ conditions dysprosium is hep. A tions holmium is hep. A transition transition to the Sm-type phase occurs to the Sm-type phase occurs at 65 149 at 45-50 kbar and room tempera- kbar and room temperature. 60,149 . ^ ture. DResistance measurements Resistance measurements on holmium to on dysprosium show anomalies near 600 kbar show no clear evidence of 200 kbar, which may indicate a phase any further phase changes. transition.

15 1 1 1 1 ' - HOLMIUM ;

2 10 - (L—-bcc . _i_i_L i

hep * 5 1 Liquid _

- 0 1000 2000 3000 1 I 0 1000 2000 3000 Temperature - K Temperature - K Fig. 62. The phase diagram of dysprosium. Fig. 63. The phase diagram of holmium.

-40- Shock-wave experiments show a THULIUM kink in the u -u curve of holtnium s p The phase diagram of thulium is at 440 kbar, which is ascribed to shown in Fig. 65. Under room condi­ melting 61 The hcp-bcc phase tions thulium Is hep. A transition boundary and the melting curve have 131 to the Sm-type phase occurs at room been determined to 10 kbar. 149 temperature near 110 kbar. Resistance measurements to 500 kbar show no clear evidence of any further 138 phase changes. The phase diagram of erbium is Shock-wave experiments show a shown in Fig. 64. Under room condi­ kink in the u -u curve, which is tions erbium is hep. A transition to s p 61 149 ascribed to melting. No bec phase 131 the Sm-type phase occurs at 90 kbar. has been detected before melt. Resistance measurements made to 600 The melting curve has been determined 131 kbar show no indication of a phase x to 10 kbar. transition. 1 15 ., ! 1 ' Shock wave experiments show a THULIUM kink in the u -u curve at 440 kbar, - s p 61 which is ascribed to melting. No _g 10 - 131 The melting curve has been bec phase has been detecte131 d before melt hep determined to 10 kbar 5 - 1 1 i •• 1 "'"" - "" 1 ERBIUM • • - - 1 1 , , K w — 0 1000 2000 3000 3 • Temperature - K '

1 5 hep Liquid | I i Fig. 65. The phase diagram of thulium. •

n I 1 . 0 1000 2000 3000 Temperature - K The phase diagram of ytterbium Fig, 64. The phase diagram of erbium. is shown in Fig. 66. Eelow 300 K -41- 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

K147 and 898 K,155 has been ascribed to another phase transition. Static 0 500 1000 1500 compression of ytterbium at room Temperature - K temperature to 280 kbar shows no fur­ Fig. 66. The phase diagram of ther resistance anomalies above 40 ytterbium. 153 kbar Three sets of shock-wave experi­ and 2 kbar, ytterbium exists in a ments show kinks in the u -u curve 151 diamagnetic hep phase. A ft? s P at 130 kbar, 160 kbar,61 and 490 146 martensitic phase transformation at kbar. The kinks are ascribed to 300 K and atmospheric pressure pro­ xenon-core repulsion, melting, and duces a paramagnetic fee phase. The electronic phase transitions, hep-fee phase boundary has been respectively. Johansson and determined, and it is clear that the Rosengren consider the 130 kbar 152 hep phase disappears above 2 kbar. anomaly to indicate an electronic At room temperature, increasing phase transition Involving a shift pressure causes a serieB of changes from the divalent to the trivalent 141 in resistivity. Below 20 kbar ionic state in the solid The ytterbium behaves like a metal, melting curve has been determined to 147 between 20 and 40 kbar it behaves like 35 kbar. The ytterbium phase a semiconductor, and at 40 kbar a diagram closely resembles that of phase change takes place to a bcc strontium.

-42- 33 1,1,. LUTETIUM LUTETIUM -

The phase diagram of lutetium is 1 ~ shown in Fig. 67. Solid lutetium at J 10 low pressures is hep. Compression to 1 -; 230 bbar at room temperature causes a hep 1 Liquid .. _

transition to the Sin-type lattice. Pressur e - The hcp-Sm-type phase boundary has not been determined. The melting J curve has been determined to 10 0 1 i , ll , " 1000 2000 3000 kbar 131 Temperature - K Fig. 67. The phase diagram of lutetium. HAFNIUM

Under roost conditions hafnium is TAHTALUM hep. At atmospheric pressure a transition occurs near 2270 K to a The phase diagram of tantalum bcc phase. The bcc phase is slightly is shown in Fig. 68. Solid tantalum more dense than the hep, implying a is bcc. An approximate melting curve 158 negative value of dp/dT for the phase has been determined to 60 kbar. boundary. A static-high-pressure T search for the hexagonal ID phase found in titanium and zirconium failed to show any change of phase. Three sets of shock-wave experi­ ments showed anomalies in the u -u curve.62'66'146 Gust and Royce" P ascribed a kink at 600 kbar to xenon- core repulsion. McQueen, £t al - ascribed a discontinuity at 400 kbar to a solid-solid phase transition. 146 Bakanova, e_t al. ascribed a kink at 450 kbar to an electronic transi­ tion. Hafnium melts at 2495 K.53 1000 2000 3000 ' 4000 The melting curve has not been Temperature - K reported. Fig. 68. The phase diagram of tantalum.

-43- TUNGSTEN IRIDIUM

The phase diagram of tungsten is Solid iridium is fee. Room shown in Fig. 69. Solid tungsten is temperature compression to 175 kbar bcc. An approximate melting curve showed no phase transition. Iridium 159 63 melts at 2716 K. The melting curve has been determined to 50 kbar. 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 3000 4000 Temperature - K

Fig. 69. The phase diagram of tungsten.

Solid rhenium is hep. Static compression of rhenium at room temper­ ature to 350 kbar showed no phase 1000 2000 3000 transitions. Rhenium melts at Temperature - K. 3433 K. The melting curve has not been reported. Fig. 70. The phase diagram of platinum.

OSMIUM

Solid osmium is hep. Osmium melts at 3300 K. The melting curve The phase diagram of gold is has not been determined. shown in Fig. 71. Solid gold is

-44- 1 ' 1 ' 1 ' 80 - MERCURY

Rhombohedral v j I J 60 - (a) X / -

Tetragonal / / " ((J) / / •Liqui dM ~ Pressur e - 20 ' ^/\A/ / . 0 200 400 600 Temperature - K

Fig. 72. The phase diagram of mercury.

Temperature - K

Fig. 71- The phase diagram of gold. A third phase, named y, has fee. The melting curve has been been found at very low temperatures 75 determined to 65 kbar. by straining the solid. Its struc­ ture and equilibrium phase boundaries 164 MERCURY have not yet been determined The melting curve of mercury has been The phase diagram of mercury is determined to 65 kbar. shown in Fig. 72. Solid mercury at low temperatures has a body centered THALLIUM tetragonal structure. In this phase each rlom has two nearest neighbors The phase diagram of thallium is and eight second nearest neighbors. shown in Fig. 73. Below 500 K at With increasing temperature, a atmospheric pressure, thallium is hep. transformation to a rhombohedral Above 500 K, it is bcc. A high structure occurs. This structure may pressure fee phase occurs above 35 be regarded as a distorted fee kbar and 388 K. The solid-solid lattice. The tetragonal-rhombohedral phase boundaries have been determined phase boundary has been determined to 60 kbar. The melting curve has 78 to 65 kbar. been determined to 50 kbar.

-45- -n -•i i | i i i i | i i i i | i i 1 1 1 1 1 l~ ' 1 80 80 -- THALLIUM LEAD

60 - fee j - 60 - i / - / 1 - 40 _- _/ / _ 40 —~\ bcc

fee / Liquid • i

20 - hep \ 20 'Liquid - 1 1 \ / • 1 ,,,/ 0 200 400 600 800 0 500 1000 1500 Temperature - K Temperature - K

Fig. 73. The phase diagram of thallium. Fig. 74. The phase diagram of lead.

LEAD phases. The low pressure solid phase The phase diagram of lead is is rhombohedral, isostructural with shown in Fig. 74. Solid lead at low arsenic and antimony. Conflicting pressure is fee. At 137 kbar and claims have been made for the struc­ room temperature a transition to a ture of phase II, with no clear 165,166 _. . hep phase occurs. The phase 1 83 boundary has not been determined. agreement. Duggin suggests that The melting curve has been determined phase III is tetragonal, similar to

77 the high pressure phase of arsenic. to 60 kbar. A study of phase VI at 90 kbar at room temperature has shown it to be BISMUTH bcc. The phase boundaries shown The phase diagram of bismuth is are a synthesis of several „ ,. 84,168,169 ' . shown in Fig. 75. This diagram is of studies. The phases XX, special importance to high pressure VIII, and VI meet in a triple point physics because its many phase transi­ at 135 kbar,169 and the VI-IX phase tions have been used as calibration boundary then proceeds to higher standards. There is still controversy pressures. This boundary was pre­ over the existence of some transitions, 170 sumabltemperatury detectee andd 30in0 akba studr y at Throoe m and rather little x-ray structure work melting curve has been determined to has been done on the high pressure 55 kbar.84

-46- ' —r i1 i ' 1 • 1 140 -- , BISMUTH -

- IX -

120 -- -

-> •

100 -- -

- • bcc VIII 80 - - (VI) ~

- - \ \ \ V \ 60 1 /'\ K. s \ mIV [ \

40 —- Tetragonal 1 / (III) /

Liquid

20-- -

Rhombohedral \ to \ ' 1 i i ., . i i \ i i i 200 400 600 800 Temperature - K Fig. 75. The phase diagram of bismuth.

-47- POLONIUM RADIUM

At atmospheric pressure and below Solid radium is bcc at room room temperature, polonium has a temperature. Radium melts at 973 63 rimple cubic structure, the only K. Wo high pressure work has been known example of this structure in reported. the elements at zero pressure. A sluggish phase transition occurs ACTINIUM somewhere near room temperature (291- 327 K) to a simple rhombohedral Solid actinium is fee at room form which is a slight distortion of temperature. Actinium melts at 1323 63 the simple cubic. The rhombohedral K. No high pressure work has been form is slightly more dense, reported. leading to a negative dp/dT. The phase boiuidary has not been deter­ THORIUM mined. Polonium melts at 519 K. Solid thorium under room condi­ The melting curve has not been tions is fee. Superconductivity reported. measurements to 160 fcbar show an anomaly that could be due to a phase ASTATINE 173 change near 70 kbar. At atmos­ pheric pressure near 1670 K, thoritim Astatine is a very unstable transforms to a bcc phase. The element and its physical properties volume change of the transition is have not been determined. zero to within experimental error. The trajectory of th^ phase boundary RADON has not been reported. Thorium melts The crystal structure of solid at 2024 K. The melting curve has radon has not been reported. Radon not been determined. 172 melts at 202 K. ' The melting curve has not been determined. PROTACTINIUM FRANCIDM Solid protactinium under room Francium is a very unstable conditions is body centered tetragonal. element and its physical properties Metal solidified from the melt is fee, have not been determined. suggesting that this is the high

•48. temperature form of the solid. No URANIUM direct measurements of phase transi­ The phase diagram of uranium is tions have heen made, however. shown in Fig. 76. Under room condi­ Protactinium melts at about 1810 174 tions solid uranium has an orthorhombic K. No high pressure work has been structure with four atoms per unit reported.

60 -i—i—i—i r T 1 1 r

URANIUM

40

2

20 - Orthorhombic bcc (a)

Liquid Tetragonal

11,1 500 1000 1500 Temperature - K

Fig. 76. The phase diagram of uranium.

-49- cell. At 940 K and atmospheric All but one of the seven known solid pressure, a transition to a complex phases exist at atmospheric pressure. tetragonal form with 30 atoms per The low pressure portion of the unit cell occurs. The precise space phase diagram and its high pressure group remains to be determined. At continuation are shown in separate 1050 K another phase transition leads figures. The low temperature a phase to a bcc phase. The solid-solid is monoclinic, with 16 atoms per unit phase boundaries have been deter­ cell and S crystallographically dis­ mined, and indicate a triple point for tinct types of atomic positions. The the three phases near 30 kbar. 3 phase is also monoclinic, with 34 The melting curve has been determined atoms per unit cell and 7 types of to 40 kbar.176 positions. Both of these structures are quite irregular and are difficult to correlate with close-packed forms. NEPTUNIUM At high pressure only a and $ The phase diagram of neptunium exist, and the a-0 phase boundary is shown in Fig. 77. Under room shows a temperature maximum. The $ conditions neptunium is orthorhombic, phase transforms to orthorhombic with eight atoms per unit cell and *Y below 3.5 kbar and to 5, with two distinct types of atomic posi­ undetermined structure, above this tions. At 550 K and atmospheric pressure. There is a |S-£-liquId pressure a phase transition to a triple point near 27 kbar. tetragonal phase with four atoms per unit cell and two types of atomic The next two phases are fee (<5) positions occurs. A bcc phase and body centered tetragonal (6')» appears above 840 K. The solid-solid which exist only at low pressures. phase boundaries and the melting The 6' phase is followed by bcc (e), curve have been determined to 35 which melts to a more dense liquid. ,, 177 kbar. The tetragonal 6' phase is intermedi­ ate in structure between fee and bcc. The E phase disappears at a triple PLUTONIUM point below 20 kbar. The solid-solid The phase diagram of plutonium phase boundaries and the melting is shown in Figs. 76 and 79. The curve have been determined to 140 plutonium diagram Is very complex. kbar.174'178'180

-50- < 1 1 1 r- —I 1 1 1 1 1 1 f-

NEPTUNIUM

40-

30 1

20- Or'horhombic I Tetragonal

Liquid'

10-

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

Fig. 77. The phaBe diagram of neptunium.

-51- • 1 , 1 , PLUTONIUM I '/ 8 - 1 ' Monoclinic. 1 - (0) ^k• » / -

6 -- Monoclinic 1 - (a) | / ""ec 1 / f [ ( e ) 1 Liquid - - 1

2 - 1 ' " Orrhorhombi

Fig. 78. The phase diagram of plutonium.

AMERICIuM dashed line in Fig. 80. Static com­ pression of americium at room tempera­ ture shows a resistance change at 90 The phase diagram of americium kbar, which may represent a continua­ 182 is shown in Fig. 80. Americium under tion of the dhep-fee phase boundary room conditions is dhcp. There is Keating at atmospheric pressure above evidence for a transition to an fee 1300 K leads to a new phase, which phase at 920 ± 50 K,181 but with very Stephens <£ al. suggest is bcc. little change in volume. The dhep- The fcc-bcc phase boundary and melting fec phase boundary is therefore curves have been determined to 35 ,. 182 approximately represented by a vertical kbar.

-52' 1501 r -i 1 1 1 r -| . (- PLUTONIUM

Liquid

_L 200 400 600 800 1000 1200 Temperature - K

Fig. 79. The phase diagram of plutonium.

-53- CURIUM i i i i | I I i I | i i I I | AMERICIUM 40 Depending on the method of preparation, curium metal is found to have either an fee or a dhcp struc­ i30i ture under room conditions. The fee bcCs phase has the higher density. No 2 20 phase boundary has been reported. . Liquid \l I The estimated melting point is 1620 174 10 L_ dhcp K. No high pressure work has been FcC I II reported.

•'•'•'• III! l/i/l I S00 1000 1500 BERKELIUM Temperature - K Berkelium metal prepared by high temperature reduction contains a mixture of dhcp and fee structures. Fig. 80. The phase diagram of Here the dhcp phase is the more americium. dense. The estimated melting point is 1260 K. 174 No high pressure work has been reported.

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RBC/gw

-63- Appendix A: The Space Lattices

Lattice Axes Angles

primitive (simple) cubic body-centered cubic a-b-c o-3"Y" 90° face-centered cubic primitive tetragonal a« b ji c a«B-Y-90° body-centered tetragonal primitive orthorhombic base-centered orthorhombic a^b^c a « B = Y = 90° body-centered orthorhombic

face-centered orthorhombici primitive monoclinic a^bj«c o - Y » 90" ^ base-centered monoclinic triclinic a # b # c o^Ml rhombohedral a » b - c a « 0 = Y hexagonal a - b ]< c ot = g - 90°, Y = 12°°

-64-