Chapter 9 High pressure studies: Metals, alloys and compounds

Handbook on the Physics and Chemistry of Rare Earths, edited by K.A. Gschneidner, Jr. and L. Eyring (~ North-Holland Publishing Company, 1978

Chapter 9 HIGH PRESSURE STUDIES: METALS, ALLOYS AND COMPOUNDS A. JAYARAMAN Bell Laboratories, Murray Hill, New Jersey 07974, USA

Contents 1. Introduction 2. P r e s s u r e induced structure change in metals 2.1. The case of Ce, Eu and Yb 3. Fusion b e h a v i o r under pressure and P - T diagrams of R E metals 4. P r e s s u r e effect on the resistivity of rare earth metals 4.1. Y t t e r b i u m 5. Static and shock c o m p r e s s i o n m e a s u r e m e n t s on rare earth metals 5.1. Shock c o m p r e s s i o n 5.2. C o m p o u n d s 6, Magnetic transitions under p r e s s u r e 6.1. Some useful t h e r m o d y n a m i c equations 6.2. Molecular-field a p p r o x i m a t i o n 6.3. Indirect e x c h a n g e 6.4. Pressure studies in metals and alloys 6.5. Rare earth c o m p o u n d s 6.6. Theoretical a s p e c t s of the pressure studies on magnetic transitions 7. M ö s s b a u e r studies at high p r e s s u r e on rare earth s y s t e m s 8. Synthesis of new phases and c o m p o u n d s involving rare earths at high pressure and t e m p e r a t u r e References

ce = specific heat at c o n s t a n t pressure D = density EF = Fermi energy G = Gibbs' free energy g = L a n d é ' s g factor H = magnetic field J = total angular m o m e n t u m K = compressibility kf = w a v e v e c t o r of cond. electron L = latent heat M = atomic mass m = magnetic m o m e n t m* = effective mass of electron n = molecular field coefficient P = pressure R = gas c o n s t a n t S = entropy = spin q u a n t u m n u m b e r T = temperature U = internal e n e r g y Up = particle velocity Us = shock v e l o c i t y V = volume w~ = magnetic e n e r g y « = linear coetticient of thermal expansion B = volume coefficient of thermal e x p a n s i o n F = coupling c o n s t a n t tz~ = Bohr m a g n e t o n p = resistivity cr = specific magnetization ~r~ = saturation m a g n e t i z a t i o n 0c = ferrimagnetic Curie t e m p e r a t u r e 0vl = ferrimagnetic Curie t e m p e r a t u r e 0N = Néel t e m p e r a t u r e 0p = p a r a m a g n e t i c Curie t e m p e r a t u r e

708 708 712 713 717 720 721 721 727 728 729 731 732 733 738

740 741

742 744

Symbols A i = e x c h a n g e interaction 707

708

A. JAYARAMAN

1. Introduction

From the point of view of high pressure studies, the rare earth metals, their alloys and compounds have been one of the most exciting systems. P.W. Bridgman was the earliest to study rare earth elements under pressure (Lawson, 1956). Bridgman measured the resistivity as well as the compressibility of the entire series up to about 100 kbar and noted anomalies in some of the elements. Bridgman was the first to discover the now well-known electronic transition in Ce at 7 kbar at room temperature. Since Bridgman's earlier measurements, the melting behavior and phase stability including magnetic transitions of almost all the rare earth elements have been quite extensively investigated. The resistivity and compressibility measurements have been extended to ultra-high pressure regions (several hundred kbar static pressure) and P - V relationships to the megabar range, using shock wave techniques. The introduction of many new techniques of study at high pressure, and the extension of the pressure range to ultra-high pressure regions have unraveled several unusual and new phenomena in rare earth systems. Very interesting pressure-induced structural transformation sequence, pressure-induced electronic transitions (valence state changes) and unusual melting behavior have come to light. In earlier general reviews on phase transformations in solids at high pressure (Klement and Jayaraman 1966, Pistorius 1976) phase changes in rare earths have been covered briefly. Also, in the present volume the behavior of Ce under pressure and the valence changes in compounds a r e especially covered in chs. 4 and 20, respectively. In this chapter we will be concerned with the effect of pressure on structure, fusion behavior, resistivity, P - T diagrams of rare earth elements, compressibility and shockwave studies, magnetic transitions under pressure and synthesis of new phases involving rare earths at high pressure and temperature.

2. Pressure-indueed structure change in metals

The rare earth metals crystallize in close packed structures (Gschneidner, Jr. 1961a, Gschneidner, Jr. 1961b) with the exception of Eu which has the body centered cubic (bcc) arrangement. Normally La, Pr, Nd and Pm have the double hexagonal close packed (dhcp), Sm a rhombohedral, Ce and Yb the face centered cubic (fcc) and Gd to Lu the hexagonal close packed (hcp) structure. These structures represent different stacking arrangements of the atomic layers; hcp-ABAB... (hhh), Sm-type ABABCBCAC,ABAB... (hhc, hhc), dhcpABACABAC (hchc...) and fcc:-ABC, A B C . . . (ccc). Further, most of the rare earth metals undergo a temperature induced transformation to the bcc structure at high temperatures, before melting. The range of stability of the allotropes of rare earth metals as a function of temperature and also the structures that occur in intrarare earth alloys have been particularly well covered in the reviews of Koch (1970) and Altstetter (1973). The latter reviews have also discussed the pressure-induced phase transformations in the rare earth metals and intrarare earth alloys.

METALS, ALLOYS AND COMPOUNDS

709

Bridgman noted anomalies in resistivity as well as in compressibility in the case of Ce at about 7 kbar, in Yb - 40 kbar, in La - 25 kbar and in Gd - 25 kbar (see Lawson, 1956); the transformation is found to be rather sluggish in the latter two. Subsequent studies have shown that these anomalies are associated with crystal structure changes; in the case of Ce due to y to o~-Ce transition (see ch. 4), in Yb due to fcc-~bcc transition (Hall et al. 1963), in La due to d h c p ~ f c c transition (McWhan and Bond, 1964) and in the case of Gd due to hcp-~ Sm-type rhombohedral structure change (Jayaraman and Sherwood, 1964a). Further, Sm has been found to transform to the dhcp structure near 30 kbar (Jayaraman and Sherwood, 1964b). The high pressure phases of Gd and Sm were made by pressurizing samples to 35 kbar at about 300°C and the transformed phases were found to be metastably retained at atmospheric pressure and room temperature; the Sm-type phase of Gd was however less stable compared to the dhcp phase of Sm. Based on these results, and from the structural pattern observed in the intrarare earth alloy systems involving a lighter and a heavier rare earth, Jayaraman and Sherwood (1964b) proposed, that there exists a pressure-induced transformation sequence in the rare earth elements, from hcp~Sm-type--* dhcp-~fcc, with increasing pressure, the same being true for the alloy systems Jayaraman and Sherwood (1964b) proposed that there exists a pressure-induced have been reported; in Pr and Nd from dhcp to fcc (Piermarini and Weit, 1964, King and Harris, 1970); in Tb, Dy and Ho, from hcp to Sm-type (McWhan and Stevens 1965 and Stephens and Johnson, 1969) and similar transformation (hcp ~ Sm-type) in Tm and Lu (Liu et al. 1973, and Liu 1975). Perez-Albuerne et al. (1966) reported a transformation from hcp to dhcp in Ho, Er and Tm (quoted pressures are 75, 90, and 110 kbar respectively) and this has been construed as a violation of the proposed sequence of transformation. However the recent work of Liu et al. (1973) and Liu (1975) has definitely shown that there is no violation of the sequence. It is possible that in the work of Perez-Albuerne et al. the pressures were in excess for the Sm-type phase to be stable and therefore the Sm-phase was missed. It is also likely that the additional Debye Scherrer lines that appear with the loss of cubicity could also be easily missed because of broadening and preferred orientation problems that are usually present in the anvil type high pressure cells. The most remarkable change in the physical property associated with the transition in Gd is the disappearance of ferromagnetic ordering in the Sm-type structure; in the latter structure Gd shows antiferromagnetic ordering (Jayaraman and Sherwood, 1964a; McWhan and Stevens, 1965). This is also found to be true in the intrarare earth alloys of Gd, wherein ferromagnetic ordering exists only in the hcp phase (Jayaraman et al., 1966). Several explanations have been advanced to rationalize the observed sequence of close-packed structures, namely, hcp-~ Sm-type -~ dhcp-~ fcc: (1) correlations with an averaged effective atomic number (Lundin, 1966; Harris and Raynor, 1969); (2) Influence of 4f electrons (McWhan and Stevens 1965, Gschneidner and Valletta 1968); (3) stability of close packed structures on the basis of a theory of interactions between pairs of close packed planes (Hodges, 1967), and (4) phase transitions at certain critical values of an atomic parameter f which can be

710

A. JAYARAMAN

related to the pseudopotential (Johansson and Rosengren, 1975). The correlation proposed by Lundin is a size effect correlation while that of Harris and Raynor is a rationalization based on the c/a ratio, which falls into distinct regions as a function of atomic number or average atomic number for the intrarare earth alloys (see fig. 9.1). McWhar, and Stevens (1965) suggested that the degree of delocalization of the 4f electron with pressure and hence the degree of participation of the 4f electron in the bonding might be responsible for the transformation sequence. Gschneidner and Valletta (1968) expanded on this idea of 4f electron contribution to the bonding and have attempted a semiquantitative correlation between the observed structure and the ratio Rm/R46 Rm being the metallic radius of the rare earth metal and Raf the radius of the 4f electron. According to this, fcc is stable when Rm/R4f ~ 3.24, d h c p - 3.28 ~
1.640

f

[

l

l

l

[

1

I

1

[---I

I

1

• c/a • c/2o

L

• c/4.5a

1.620 w

.! a

1.600

1.580

I 560

I

I

I

I

t

I

I

I

I

I

1

L

I

[

I

to 57

Ce 58

Pr 59

Nd 60

Prn 6t

Sm 6.2

Eu 6'3

Gd 64

Tb 65

Dy 66

NO 67

Er 68

Tin 6.9

Yb 70

tu 7q

ATOMIC NUMBER

F= RW5 RI 1-90

1.$0

130,

J

L0

Ce

Or

Nd

Pm Sm Eu

Od

Tb

Dy

H0

Er

Tm

Yb

Lu

Fig. 9.1. c/a ratio (upper fig.) vs atomic number, the ratio of Wigner-Seitz radius (Rws) to the ionic radius (RI) (lower fig.) vs atomic number for the lanthanide metals (from Johanssori and Rosengren, 1975).

METALS, ALLOYS AND COMPOUNDS

711

ratio Rm]R4~for the pressure induced polymorphs in the elements they assumed the 4f radius to be independent of pressure, and calculated the metallic radius from the known compressibility data. The agreement between the semiquantitative calculations and experimental data appears reasonable. The approach of Hodges (1967) is through establishing a connection of the interaction energy (stacking fault energy) between pairs of close-packed planes and the deviation from the ideal c[a ratio. Again, Hodges seems to have obtained good agreement for the rare earths. Although these correlations are interesting they are not free from objections. For instance pressure effect is in the opposite direction from the size effect. The influence of 4f bonding may also be questioned, since there are systems such as LaY where the influence of 4f electron may not exist. Johansson and Rosengren's (1975) approach although empirical appears to be free from most of the objections. As mentioned earlier, one of the puzzling facts about the pressure-induced transition sequence is, the more an element is compressed the more its structure tends to be "light element like". Johansson and Rosengren (1975) have argued that this difficulty disappears when one considers the ratio Rws/Rb where Rws is the W i g n e r - S e i t z radius and R~ is the ionic radius, as the factor determining the structural stability. They argue that when the volume decreases, Rws decreases, but the ionic radius remains insensitive to pressure and this would cause the free electrons (which now have less volume available because of smaller Rws), to act in a relative sense as if Rt has increased. H e n c e the greater the pressure the smaller will be the Rws/Ri and the system will be forced to behave like the lower atomic number element (see fig. 9.1). The above arguments are similar to those of Gschneidner and Valletta, but do not involve the 4f electrons. In their paper Johansson and Rosengren (1975) have rationalized the observed crystal structures in the rare earths by using a characterizing parameter f: f = rs/re, where rs is the value which minimizes the total energy E (E = Ekin + EnF + Eco= + Eps~u«+ Ubs + Uew, where the various energy contributions are the kinetic, H a r t r e e - F o c k , correlation, pseudopotential and the Ubs and U~w are associated with the first and second order pseudopotentia ! and the i o n - i o n interaction energy respectively) for a given value of the pseudopotential core radius rc (rc is an atomic parameter, proportional to the radius of the outer orbital of the ion). The quantity f increases with the atomic number. Using the alloy data from the G d - P r system they calculate rc and obtain rc =0.381 for the Pr concentration at which the structure changes from hcp to the Sm-type, a value corresponding to a "fictitious element" between Sm and Gd. For this "fictitious element" they calculate the corresponding equilibrium density, from which the critical value of f is obtained for hcp to Sm-type structure transformation as f = 6.88. According to Johansson and Rosengren (1975) the pressure of transition for a particular rare earth element can also be calculated by finding the volume at which the energy dependence on c/a for the element under consideration can be matched with that of the "fictitious element". Apparently this matching occurs only at a certain critical volume of the element. The compression required to obtain this critical volume represents the critical pressure for the transition. Adopting this

712

A. J A Y A R A M A N

procedure the transition pressures for the hcp ~ Sm-type transition for the heavy rare earths from Gd to Lu have been calculated and the values are found to be in good agreement with the experimental values. Further, the onset of the transition occurs near the predicted f value of 6.88 (see table 9.1). For Sm-type to dhcp transition they obtain fcritical = 6.64 from the element Nd. The above approach is v e r y useful, in view of the inherent inability in carrying out precisely the cohesive energy calculations for different structures and showing which one would be favored under a given condition. The changes involved are subtle and must be co~nected with subtle changes occurring in the Fermi-surface Brillouin Zone interactions and hence must be traced to electronic instabilities in the system. To understand them fully, experimental work of a rather sophisticated nature, perhaps on single crystals needs to be done. 2.1. The case of Ce, Eu and Yb Cerium metal is discussed in ch. 4 and only a brief mention of its high pressure behavior will be made here (for references see the list in ch. 4). Cerium can exist at atmospheric pressure i n the fcc (3') or dhcp (/3) form and undergoes an isostructural transition near 100 K to another fcc-form referred to as a-Ce. The 3"-a Ce transition occurs at 7 kbar a t room temperature and this transition is accompanied by about 8% volume decrease. This is one of the most widely studied transitions as a function of pressure and temperature and is believed to involve a valence change from 3+ towards a higher valence state (3.7+). The 3' to a transition line terminates at a critical point; the very first example in which a s o l i d - solid transition was shown to exhibit a liquid-vapor-like critical point. A pressure-induced p h a s e transition near 50kbar, initially reported to be yet another isostructural transition has been shown to be from fcc (a-Ce) to an orthorhombic phase with the a - U structure. Stager and Drickamer (1964) have reported a pronounced resistance anomaly near 120kbar indicative of a phase transition, but the nature of this transition is unknown. The fusion behavior of Ce is again unique in that it exhibits a minimum. TABLE 9.1

Calculated and experimental vaiues for hcp~Sm type structure transition (Johansson and Rosengren, 1975). Critical pressure (kbar) Element

Calculated

Experimental

Gd Tb Dy Ho Er Tm Lu

23 36 54 73 92 117 167

32 38 52 72 99 119 - 200

Critical value of f 6.89 6.90 6.91 6.92 6.93 6.94 6.96

METALS, ALLOYS AND COMPOUNDS

713

Both Eu and Yb are divalent in the metallic state and exhibit a striking r e s e m b l a n c e to the alkaline earth metals Ba and Sr in their properties including the high pressure behavior. T h e y are similar in their crystal structure at atmospheric pressure; Eu and Ba are both bcc, Yb and Sr are fcc. The existence of a hcp phase in v e r e pure Yb has been established in recent low temperature studies (see Altstetter, 1973). Europium shows a sharp rise in resistivity at about 150 kbar (revised pressure scale) followed by a decrease (Stager and Drickamer, 1964). Johansson and Rosengren (1975) (also in Rosengren and Johansson 1976) have calculated the enthalpies for di- and trivalent Eu as a function of pressure and find a transition near 150 kbar. The static c o m p r e s s i o n data of Eu in the low pressure region and the c o m p r e s s i o n obtained f r o m the shock wave data for the high pressure region h a v e been presented in support of the occurrence of such a transition. Since Ba b e c o m e s hcp at the 55 kbar transition, a similar transition may be e x p e c t e d in Eu. Ytterbium has been shown to undergo a structural transition from fcc to the bcc structure near 40 kbar at room temperature, by Hall et al. (1963). The latter B a v e argued that this transition involves a change in the valence stare from 2 + to the 3 + state but this has been shown to be untenable and the f c c - bcc transition is the same as the t e m p e r a t u r e induced f c c - b c c transition occurring at atmospheric pressure (see fig. 9.4 in the next section, J a y a r a m a n , 1964). Strontium exhibits similar behavior and there can be no valence change in Sr (Jayaraman et al., 1963). Also subsequent high pressure studies on Yb ( K a t z m a n and Mydosh, 1972) have not given support to any valence transition in the 1 to 100kbar region. F r o m binding energy calculations, J o h a n s s o n and Rosengren (1975) predict a valence change f r o m 2 + to the 3 + state in Yb metal near 140 kbar and again present the static and shock compression data as a support. Both Eu and Yb, whose divalent character is an anomaly a m o n g the rare earth metals, can be expected to b e c o m e trivalent at high pressure. Even if the transition pressures are larger by a factor of two than the predicted values, it should be possible to verify its occurrence by a direct high pressure X-ray diffraction study.

3. Fusion behavior under pressure and P - T

diagrams of RE metals

For a first-order transition the criterion for equilibrium between two phases is the equality of the Gibbs free energy G G = U-

TS+PV

(9.1)

of the phases. By equating infinitesimal variations in G along the transition line one obtains the well-known Clapeyron equation dTxr

AV

T~ - äS-

A VTTr, ~

(9.2)

where Txr is the transition temperature at standard pressure, A V is the volume

714

A. JAYARAMAN

change, AS is the entropy change and L is the latent heat of transition. When dT/dP is determined for a transition AV or AS can be calculated via the Clapeyron equation, if one of the latter two quantities are known. If the transition is second-order the Ehrenfest relation can be employed dTTr Afl AK d P - VTT, AC p - ~

(9.3)

if /3 is the volume coefficient of expansion, K the compressibility and Cp the specific heat at constant pressure of the two phases are known. For a )t-type second-order transition dTTr A/3 dR - VTTr-~p-- 3

V

_ (Aa) TTrACp,

(9.4)

where Aa is the difference in the linear thermal expansion coefficients between the two phases. The fusion behavior of most of the rare earth metals has been investigated to moderate pressures, except those of the very high melting end members; in the latter only the initial slopes have been established (Jayaraman, 1964, 1965a, 1965b; Klement and Jayaraman, 1966 and Young, 1975). The P - T diagrams of the lanthanide elements are shown in fig. 9.2 and the thermodynamic data of interest obtained are presented in table 9.2. Using the published experimental data and adopting certain fitting procedures, Johansson and Rosengren (1975) have constructed a generalized phase diagram for the trivalent lanthanide (see fig. 9.3). The various solid-solid transitions and the melting curves are fused in the diagram. Not fitted into the general scheme are the anomalous cases; Ce, Eu and Yb. The phase diagram for Ce is shown in figs. 4.1 and 4.2 and a discussion is presented in ch. 4, section 2 about its anomalous features. In fig. 9.4 the P - T diagrams of Eu and Yb are presented. Europium exhibits a fusion curve maximum and possibly Yb has also a maximum. It is seen that the f c c - b c c transition encountered at 40kbar for Yb at room temperature is due to the intersection of the f c c - b c c line coming down from the high temperature region. The P - T diagrams of Eu and Yb are strikingly similar to that of Ba and Sr respectively, at least in so rar as the moderate pressure region goes. If the predicted valence change from 2 + to the 3 + state were to occur in Eu and Yb near 150 kbars, this region of the P - T diagram would be very interesting and quite anomalous. • Recently Carter et al. (1975) have extended the melting curves of the rare earth metals to the ultra high pressure region by calculation and have predicted melting curve maxima for almost all the rare earths. Some of these diagrams are presented in fig. 9.5. A rather interesting plot (see fig. 9.6a) is the initial melting slope dT[dP of the rare earth elements versus atomic number. In this plot the divalent and trivalent lines are weil established from the slopes of Eu and Yb and from La, Gd and Lu respectively. The quadrivalent line drawn parallel to these is perhaps not unreasonable. The deviations of the data points from the tfivalent line, of Sm

METALS, ALLOYS AND COMPOUNDS I

LANTHANUM

SAMARIUM

30

•

\ 2O

dhcp

40

fcc bc~,~

,.

10

dhcp

0

I

",o,.

20

(Sm)

500

1000 CERIUM

O0

40E

<: /

• OrthorhombicI %

4O A

30'-

,

,.,'~''~1

0 -

, ,

,

500

Liq bcc

, I~,

,

,

.

/ /Li q

1000

1500

:I O0

[

II

1000

I0

I

I

2000

! hcp

/ Liquid

",

1000

0

I'b

uld

ERBIUM

5

30

hcp

Liquid

h~p

PRASEODYMIUM

HOLMIUM

GADOLINIUM Rhombohedral lbcc (Sm-i-/pe)

10

0

1000

500

~"X

20

fcc I ( {z ) ~ d h c p ~ ~c~) ~ f .

20

••

Rhombohedrol

, t J i

80 60

ib~#

715

2(300

Q

L

1000

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/ I 2000

i

i

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f:c

|

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dhcp

20

~./~b¢

bee

hcp

/J Liq

,,,,11,1,,I 0 , , , ~ 1500 1000 0

".

hcp

I0

LIq Id

c 0

l

i 0

'

I000

60 40

hcp dhcp 0

i

I lO00

I

,I

I

1000

I

2000

t

2000

LUTETIUM 10

hop

j [ bcc Liq

I0 .,~l~,..il,l,[ 5OO 1000

I

2000

DYSPROSIUM

N~ODYMIUM

20

Liquid

5

01

I

1000

L~quid

i

2000

L

TEMPERATURE (*K) Fig. 9.2. P - T diagrams of the lanthanide metals, from Young's (1975) compilation of Jayaraman, 1965 and Stephens, 1965 data. Pure Ho at atmospheric pressure does not appear to have a bcc allotrope, but apparently the bcc phase field appears at high pressure. and the heavier rare earths (Tb through Tm) were attributed to a partial change in the valence to the divalent state upon melting and to a partial change to the quadrivalent state in the case of Ce and Pr. In this connection it is interesting to compare the plot of the ionization energy I of the divalent rare earth ions against atomic number (fig. 9.6b) taken from the paper of Johansson and Rosengren (1975) with fig. 9.6a. The resemblance is striking. H o w e v e r there appears to be no evidence from high temperature enthalpy data (AHfus) for any valence change upon melting.

716

A. J A Y A R A M A N

TABLE 9.2. T h e r m o d y n a m i c data for lanthanide metals S-S = t r a n s f o r m a t i o n to bcc structure; S - L = melting. From J a y a r a m a n (1965); Melting and transformation t e m p e r a t u r e from ch. 2, tables 2.15 and 2.14, respectively.

R.E. metal La Ce Pr Nd Sm Eu Gd Tb Dy Ho Er. Tm Yb Lu

" MP (°C) 918 798 931 1021 1074 822 1313 1356 1412 1474 1529 1545 819 1663

Transformation temperature to bcc (°C)

dT/dP°/kbar

AS/mol. S-S e.u. S-L

865 726 795 863 922

0.67 0.70 0.71 0.63 0.625

1235 1289 1381

0.607 0.80 ... ...

795

0.396

S-S

1.34 1.157 1.365 1.314 1.53 2.23 1.53 1.56 2.04 2.25 2.67 2.31 1.64 1.71

za V/mol. S-S cm 3 S-L

S-L

5 -1.4 --2 a -2" - 3b - -1.5 c -0.4 c ~5.0 c - 12c'd

- 16 -8.5

2.5 -4.7 -0.1 3.5 11.5 15 6.5 9 -- 12 - 15 - 15 - 12 19

0.14 -0.04 0.06 0.05 0.08 -0.04

-0.26

0.14 -0.22 0.005 0.19 0.72 1.39 0.41 0.61 0.93 1.4 1.66 1.25 1.26 0.64

adhcp ~ bcc; brhombohedral ~ bcc; Chcp ~ bcc; aThe bcc phase in H o apparently exists at high pressure.

«~

~

\

2ooo---I

/ tl

~oo

I II 'k~~

~oo

~c

\ Is~-TYPE .'..I IP, i_L~....... "--.

~':~ ..........

i;~,~,,~

1400

,

i

~ I000 '~°°~~

~°°~~~ 600

400 2~mO 2OO - 0

ùL~...,

o

zo

r

ùo ,

20, 20 40

4'o 6'o 8b

"',

-

\ \\ \

,òo ,~o ,4o ,~o ,~o zSo 2~o 2~o P(kbar)

Fig. 9.3. Generalized P - T diagram of the lanthanide metals. The points are measured transitions. The w a v y line on the P - a x i s denotes the highest p r e s s u r e for which a known phase transition of the element was utilized for the construction of the diagram (from J o h a n s s o n and Rosengren, 1975).

METALS, ALLOYS AND COMPOUNDS 10001

I

LIQUIDI

'

,,o

/

LIQUID

/

/

/

95O

717

%

.~"

\

EUROPIUM

~ 900

BCC

BCC

~cc \ \

85o

800 0

20

60

4

PRESSURE

80

o

(k BAR)

Io

2O

30

40

so

PRESSURE (k BAR)

Fig. 9.4. P-T diagram of Eu and Yb (from Jayaraman, 1964).

4. Pressure effect on the resistivity of rare earth metals

The resistivity under pressure and in some cases Hall effect m e a s u r e m e n t s under pressure on rare earth metals have been the subject of several studies. Bridgman's early resistivity m e a s u r e m e n t s are summarized in the review by L a w s o n (1956). Stromberg and Stephens (1964) carried out resistivity measurements on a n u m b e r of rare earth metals to about 150 kbar. Stagèr and Drickamer (1964) extended the resistivity m e a s u r e m e n t s to several hundred kilobar pressure at 296 K, 197 K and 77 K. (See also Drickamer 1965.) Most of the elements exhibit one or several anomalies (see fig. 9.7); rather pronounced resistivity anomalies for Pr near 300 kbar, for Eu near 170 kbar, for Nd near 150 kbar, for Tb near 200 kbar are observed. For m o s t of the rare earth metals there is some sort of anomaly below 100 kbar, which is evident even in the room temperature data. These are undoubtedly due to the structural transformations involving the stacking arrangements of the atomic layers discussed earlier. The origin of the resistance anomaly in the case of Ce near 120 kbar and the anomalies in Pr, Nd and Yb at high pressure are yet to be resolved. More recently resistivity and Hall effect m e a s u r e m e n t s under hydrostatic pressure have been reported on single crystals of Dy and polycrystalline Gd and Tb by V i n o k u r o v a et al. (1973, 1972a, 1972b) and by Fujii et al. (1972) on h e a v y rare earth metals. The resistivity variations with pressure are in general difficult to interpret because they involve several contributing factors in materials like the rare earth metals; in the paramagnetic region there is the spin disorder contribution, contributions from the change in the exchange interaction with pressure and variations related to the change in the effective mass of the conduction electrons, all superimposed on the normal terms. In some cases OplaP can yield information on these, if the

718

A. J A Y A R A M A N LANTHANUM

\

ZO

/

/

/ /

oò_ _

/

__l

500

[ 1500

1000 I /

ùoooù,oT..

/

/

/

/

/

/

I 1500

__

00

CALCULATED \ /SOLIO- LIQUID

/

//

bcc

30

/

»°

zo LIQUID

,1/ IO00

DYSPROSIUM /

/ HUGONIOT-~./ / / /

J~

\ 1

/

l ~~ ~ ~ I rhomb I 500 I(X~O

IO

I

o

1500

/

/

•

/ /

CALCULATED ~/ If~- rhomb-bcc / / e / i PHASEBOUNDARY/ / ESTIMATED -O LIQUID HUGONIOT~.// [ / ~ ~-/SOLID PHASEB UNDARY ," I bcc / i / /ù ù p /

B~O~~o'

0

i/

m%~/~

._

2000

,ooo

\

\

\f

\

CALCULATED ~-SOLID- LIQUID 20 PHASE BOUNDARY

YTTERSIUM

\

L,OUO l

__

3000

\

_ _ _

HU«ONlOT-.>. 1"

I

/

/ !

/ /

hcp I IOOO

\ CALCULATED \\ SOLID- LIQUID PHASE BOUNDARY

io

\ J 500

// ESTIMATED HUGONIOT~ / / /

\

/

0

LIQUID ISO0

GADOLINIUM

\

(rhomb) / 0

\

/~/e /,/

2C

\

B~

40

/

I 5OO

CALCULATED \~SOLID- LIQUID PHASEBOUNDARY

\

50

kk~PHASEBOUNDARY \

~

/

/

/ /

J 3500 -

/

60

HUGONIOT~/

J I __1_ L:~XX) 2500 :5000

SAMARIUM

/

70

B

uou,o

HUOON'Or~//

,o

\ /

PHASE BOUNDARY

/

/

/

CALCULATED

"~souo-uou,o

//

///

20

fO00

B"

/

/

~

/

I dhcp

EUROPIUM

/

/

/

« ( fcc ) ( ,bcc _,..._.--.-~)'(fcc) ~ I 5OO lOOO 1500

30

"=

/

/ /

/

=0

l i L

500

__/ 0

/

CALCULATED /SOLID - LIQUID I PHASEeOUNDARY

/

0

20

I_ 200(

I I

20

Q. v(.D Q-

HUGONIOT~

LIQUID

PRASEODYMIUM

/

30

CALCULATED /~ PHASEBOUNDARy bcc/

/

/ I /

/~~SOLID-LiQUID

B

/,~~

40

/

/

/

CERIUM

/

/

HUGONIOT~ ~ / /

\

»

bcc\. / _ _ I ,,~ JLIO 1500

TEMPERATURE

Fig. 9.5.

500

(*K)

/

/

/ b=

/

IOOO

1500

2000

METALS, ALLOYS AND COMPOUNDS

719

I (.v)

2° I 18

25

16

14

/ ~

//

/ ~

12

9'

/

\

,

/ 1/

,g

~,

~'.

~~ 24

I

\~~ / / /

+qVAIENCF~

23

/ 22

.

_\

/

/ 21 I

//

-t. ". Jr ~'«;m ~'~~'oJ, 4 ~'y "o 6 ~~ ~'~~u

La Ce Pr Nd Pm Sch

Eu Gd

Tb Dy Ho Er

Tm Vb Lu

Fig. 9.6. Melting slope dT/dP and ionization energy I for divalent lanthanide ions against atomic number, from Jayaraman (1965) and Johansson and Rosengren (1975)respectively. To be noted is the remarkable resemblance of the two sets of data. The smooth curve is the interpolated binding energy difference between divalent and trivalent metallic states.

ù 4 " o "~'~--~'" ~ | ' B .

# . f ~. ~

~97°CI ~ 1

. 2 ~

~,

~o.~, ,

200 400 600 PRESSURE klar

" k '

'

½~i~ ,~, , ~°.~r ~-hrf

!o.~K 0

"~J~ '

i

,

r

,

,q

0

'

'

'[

'

Sm

12[ ,

~~L~

' 7~o~,~ ~

2"°l-'r~''''

I'

'F~

~.o~

200 400 PRESSURE kbar

7'

ä~

G0

0l

~

0

I

,

']

29°°4

~ 7 7 ° K

J-

600

l

{

-~

L I

,J

2O0 4O0 600 PRESSURE kBar

'-t 296 ° K

~
"--

~

7

197° K"~'t

~:

0.71

0

~

t

,

I

7~I"1

200 400 600 PRESSURE kl~r

7°K

¢1

0

"

PRESSUR£ kl:~r

•

0

,

I 200

,

I 400

,

- I

,/

600

PRESSURE kbar

Fig. 9.7. Pressure versus resistance for some rare earth metals (from Drickamer, pressures are now believed to be lower by about 30% according to revised calibration.

1965). The

Fig. 9.5. Proposed P - T diagram for some rare earth metals. Pressure in GPa (1 GPa = 10 kbar). The solid lines are experimentally determined portions. The intersection of the Hugoniot with the calculated melting line, close to the experimental point is taken as strong evidence for melting under shock pressure. To be noted is also the increasing stability of the bcc phase in going from La to Eu (from Carter et al•, 1975)•

720

A. J A Y A R A M A N

various contributions can be sorted out. Fujii et al. (1972) made some precision measurements on Gd, Tb, Dy, Ho and Er up to 10 kbar on samples of 99.9 purity,, in the temperature range 150-400 K. From the data in the paramagnetic region the spin disorder contribution to p has been evaluated and from this d In F[d In V has been obtained; F is the s-f exchange coupling constant (see section 6). Sawaoka and Tomizuka (1971) have also measured the resistivity of Gd under hydrostatic pressure. 4.1. Ytterbium A rather special case is Yb in which the resistivity and Hall effect measurements under pressure have been made by several investigators at different temperatures (Bridgman, 1954; Souers and Jura, 1963; Stager and Drickamer, 1963; Jayaraman et al., 1963; Stromberg and Stephens, 1964; Jayaraman, 1964; McWhan et al., 1969; Holzapfel and Severin, 1971; Iida, 1972; Jullien and Jerome, 1971; Katzman and Mydosh, 1972). The resistivity of Yb rises by several orders of magnitude with pressure at low temperatures and then abruptly decreases at about 40 kbar. At room temperature the rise in resistivity is not as spectacular, but it is still quite striking. In fig. 9.8 this behavior is shown (from I

I

I

I

YTTERBIUM i 0 -I

4.2°K,fcc

10-2

10-3 2 9 8 ° K , fcc

10-4

10-5

10- 6

4.2°K bcc --~x

I0

I 20

I 30

I 40

50

PRESSURE (k bar)

Fig. 9.8. P r e s s u r e versus resistance for Yb metal at 4.2 K and at R.T. The sharp decrease at about 40 kbar is due to f c c - b c c transition (from M c W h a n et al. 1969).

METALS, ALLOYS AND COMPOUNDS

721

McWhan et al., 1969). The sharp drop in resistance near 40 kbar is due to the f c c - b c c transition (Hall et al., 1963). The rise in resistivity before this transition has been attributed to a gradual transition from the metallic to the semlconducting state in fcc Yb, due to the removal of the band overlap. Some of the other divalent fcc metats (Ca, and Sr) exhibit similar behavior and these pressure induced metal-semiconductor or metal-semimetal transitions (in Sr, see McWhan et al., 1969) have stimulated many theoretical studies, including band structure calculations on Yb (Johansen and Mackintosh, 1970; Jepsen and Anderson, 1971) and related materials (see Vasvari et al., 1967 and see McWhan et al., 1969). Although the calculations of Vasvari et al. do not involve Yb as such, it is believed that a similar picture would be valid for Yb; in the case of Yb the Fermi surface shrinks to the point that an energy gap opens up, making it a semiconductor. From the temperature dependence of resistivity of b c c - Y b in the temperature range 1.3 K to 100 K at pressures in the range 50 to about 160 kbar, Katzman et al. (1972) have concluded that bcc Yb is divalent. Among the compounds the resistivity of many divalent rare earth monochalcogenides has been investigated under pressure and this will be discussed in ch. 20.

5. Static and shock c o m p r e s s i o n m e a s u r e m e n t s on rare earth metals

The compressibility Of the rare earth metals was first investigated up to 40 kbar by Bridgman (see Lawson's review, 1956) for most of the members of the series, and in some cases to about 90kbar. Since Bridgman's earlier measurements, Stephens (1964) has published compression data on Pr, Eu, Tb, Yb and Sc to 45 kbar and Perez-Albuerne et al. (1966) have reported on the compressibility of Ho, Er and Tm to about 200 kbar (see Drickamer et al., 1966). More recently Liu et al. (1973) and Liu (1975) have measured the compressibility of Tm and Lu respectively in a diamond anvil high pressure X-ray apparatus to several hundred kbar. Syassen and Holzapfel (1975) have reported on the Compression of La to 120 kbar. Anomalies corresponding to the phase transitions discussed earlier were noted in some cases in these static compression measurements; at the 3' to a - C e transition near 7 kbar (ch. 4, section 2.1) and in La at the d h c p - f c c transition near 25 kbar (Bridgman, see Lawson's review, 1956), in Yb at the f c c - b c c transition near 40 kbar (Stephens, 1964) and in Lu from the hcp to Sm-type transition near 230 kbar (Liu, 1975). Bulk moduli evaluated from these data are plotted in fig. 9.11. For Gd, Dy, and Er single crystal elastic constant data and their pressure variation have been obtained (Fisher et al., 1973).

5:1. Shock compression Compression studies of rare earth metals into the megabar range have been carried out using shock wave techniques by several investigators (Al'tshuler et

722

A. JAYARAMAN

al., 1966a,b, 1968; Al'tshuler and Bakanova, 1969; Bakanova et al., 1970; Gust and Royce, 1973; Carter et al.. 1975). The shock wave techniques are quite well known (see Rice et al., 1958 and McQueen, 1963). When the shock velocity (Us)-versus-particle velocity (Up) relationship is linear, i.e., Us = Co + dp Up, the Hugoniot relations for pressure and volume can be expressed as P = DoUp(Co+ qbUp) . . . .

V/Vo =

[Co + ( , ~ -

1)up]/Co+ , ~ u p

....

(9.6)

(9.7)

p = DoC2ort[(1 _ ~~)2,

where = 1 - V/Vo,

V[ Vo = Do/D,

(9.8)

and the D ' s are the densities. The shock data can be presented conveniently by plotting Us against U v, since the relationship is usually linear (Us = Co + qbUp where the Hugoniot intercept Co and the slope @ are determined from the data by the method of least squares). If there are no phase changes the intercept Co should correspond to the bulk speed of sound at P = 0. Since the slope is linearly related to the pressure derivative of the adiabatic bulk modulus (aßJ,gP)s a linear U s - Up Hugoniot reflects a nearly linear dependence of Bs on the pressure. If the linear U s - Up relation holds, the Rankine-Hugoniot equations can be used to express the pressure and energy as a function of volume along the Hugoniot. Shock data for several rare earth elements are shown in figs. 9.9 and 9.10. Throughout the rare earth series kinks in the U s - Up relationship are ubiquitous. In table 9.3 the numerical values of the data for the rare earths along with other parameters of interest are presented. Reynolds and Barker (1974) find from the data of Gust and Royce (1973), the compression of rare earth elements can be expressed in the form A V [ V o = a l P + a 2 p 2 + a 3 P 3 and have determined the coefficients. They find that the anharmonic contributions are evident and these are of considerable importance. The shock data of the various investigators are in reasonable agreement; all of them show kinks in the U s - Up curves but the interpretation of the data differ. The cusps and kinks are indicative of some kind of phase transition. (See Doran and Linde, 1966). In general the rare earth metals are much more compressible compared to a typical d-band metal such as Hf, Ta or W. While Al'tshuler et al. (1966, 1968) ascribe the high pressure stiffening of the Hugoniots to electronic transitions, Gust and Royce (1973) have argued that the stiffening of the Hugoniots is related to the onset of repulsive interaction between the noble-gas cores and regard that neither melting, nor structural or electronic transitions are the cause of the kinks in the U s - Up plots. On the other hand Carter et al. (1975) have argued in favor of interpreting their data as due to melting. They calculgte the temperature T and entropy S along the Hugoniot and then combine this with the known enthalpy to obtain the free energy (G = H - T S ) along the Hugoniots of both phases. Once these are obtained the melting curve can be calculated, setting A G = 0. The results are then extended to get the free energy in the region

METALS, ALLOYS A N D COMPOUNDS

r • •

T

~

F

I

PRASEOOYMIUM (U I ) NEODYMIUM ( U = ÷ I ) ÷

~

723

/

~

t

• CERIUM ( US } • EUROPIUM (Us÷I) ÷

7

6 -

--

61-

~5-

--

~

-

~L Z~L

,

I O

e • •

i __

O§

1.0

I

]

I

I

I

1.5 2,0 Up( krn/s }

I

25

30

I

I

GADOLINIUM {U l} {:)YSPROSIUM ( U t * [ )

l

P 35

ill

G

~

I,O

I •

I

l__l

O5

1

I

_L_

J

1.5 2-0 25 Up( k r n / s )

I

30

3,5

[

1

~

TERBIUM (Us}

7

I

O

1

05

1

O

J

15 20 Up(krn/s }

25

30

31

40

_

O

05

]O

I5 20 Up ( k r n / s )

25

30

35

Fig. 9.9 Shock wave velocity Us against particle velocity Up for a number o f rare earth metals. Kinks in the U~-Uprelationship occur for most of the rare earth metals (from Carter et al., ]975).

of interest and from this the melting curve is extended to very high pressure regions. By this procedure Carter et al. (1975) have shown that the extrapolated experimental phase lines (Jayaraman, 1965a and 1965b) intersect the Hugoniots in the neighborhood of the observed transition point in all cases, which they consider as strong evidence for melting. Some of their proposed P - T diagrams are shown in fig. 9.5. Further they predict maxima in the fusion curve for all the rare earth elements and in this connection have suggested that a continuous electronic transition in the liquid phase may be occurring in all cases. The interpretation of Carter et al. (1975) is not untenable and indeed is quite interesting. The proposed fusion curve maxima, in several cases, fall well within

724

A. JAYARAMAN

1.4 1.2 1.0

0.8 0.6 0.4 0.2

I'~

1.4

1.0 0.8I 0.6 0.4 0.2

I

I

~

I

I

I

] -4 /

1.2 1.o 0.8 0.6 0.4 0.2 I 0.3

t

I

I

I

1.o

1.2

0.3

t .4 /

r

,

~

O.t4

0.5

0.6

0.7

i

i

[

I

J

0.9

0.3

0.7

I

0.5

0.8

I

0.6

1 .o

OOK

0.6

I

0.4

- ~"?'-----

0.7

0.8

0.7

0.8

0.9

.0

0.9

1.0

i

0.8 0.6 0.4 0.2 0.5

0"rK

0.2

0.8

N~

04

I

Dy

0.8 0,6 0.4

O°K

r

0.9

0.3

Yb

O° 0.4

RELATIVE VOLUME

Kink 0.5

0.6

(V/Vo)

Fig. 9.10. Pressure-volume relationship for rare earth metals deduced from shock data. The position of the kinks in the Us - Up relationship is indicated by an arrow. The 0 K isotherm is also shown (from Gust and Royce, 1973). Pressure in mega bar. the capabilities of e x i s t i n g static apparatus and h e n c e with n e w t e c h n i q u e s d e v e l o p i n g such as the split sphere s u p e r - h i g h - p r e s s u r e s (megabar), with the capability peratures ( K a w a i i and E n d o , 1970), or the laser heated

can be verified. Further, apparatus for generating of attaining high t e m d i a m o n d anvil apparatus

METALS, ALLOYS AND COMPOUNDS TABLE 9.3. Shock c o m p r e s s i o n data (from ~") G u s t and Royce, 1972 and Cb) Carter et al., 1975). Element and , atomic no. (Z)

Average initial density (g/cc)

yca) (39)

4.513

L a ~a) (57)

6.134

Ce {a} (58)

6.759

Pr {a) (59)

6.758

Nd Ca) (60)

6.983

Sm ~a) (62)

7.477

Eu ~a)

5.282

Pressure (P) (kbar)

Relative volume

( V[ Vo)

Temperature on Hugoniot (103 K)

93 172 217 234 329 423 562 891 85 225 361 653 929 1090 74 164 233 469 674 969 1170 89 232 374 621 849 1140 86 88 139 165 241 365 613 1070 101 255 414 653 89O 1190 67 65 122 185 276 363

0.847 0.758 0.721 0.704 0.638 0.607 0.555 0.497 0.798 0.667 0.602 0.556 0.520 0.505 0.696 0.666 0.649 0.583 0.565 0.522 0.506 0.795 0.618 0.549 0.525 0.497 0.472 0.082 0.798 0.737 0.706 0.643 0.579 0.533 0.469 0.818 0.655 0.577 0.525 0.488 0.488 0.691 0.711 0.5% 0.515 0.446 0.378

0.35 0.51 0.66 0.76 1.4 2.05 4.03 8.7 0.51 1.59 3.35 6.5 11.9 15.5 1.26 1.79 2.15 5.40 7.05 14.5 ... 0.4 1.39 3.3 5.56 11.5 ... 0.41 0.41 0.59 0.75 1.37 2.94 5.5 14.6 0.41 1.25 2.88 5.55 9.4 1'6.8 0.52 0.47 O.96 1.85 4.03 22.5

725

726

A. J A Y A R A M A N TABLE 9.3 (Cont.) Element and atomic no.

Average initial dcnsity

Pressure

(P)

Relative volume

(z)

(g/cc)

(kbar)

( V/ Vo)

450 669 883 99 152 262 4O3 660 1150 150 190 33O 480 620 800 1400 91 262 391 682 1200 100 220 400 500 720 1200 100 220 520 840 1100 1450 80 230 520 830 1100 1600 61 125 163 150 197 214 270 306 593 1020

0.426 0.385 0.365 0.821 0.764 0.665 0.605 0.551 0.476 0.764 0.730 0.634 0.581 0.550 0.520 0.460 0.839 0.686 0.615 0.524 0.456 0.842 0.729 0.634 0.602 0.551 0.483 0.853 0.727 0.597 0.527 0.515 0.474 0.882 0.725 0.595 0.528 0.486 0.436 0.744 0.607 0.516 0.589 0.515 0.535 0.511 0.489 0.441 0.389

Gd (a) (64)

7.912

Tb (b) (65)

8.27

D y (a) (66)

8.559

Ho(b) (67)

8.80

Er (b)

9.05

(68)

T m (b) (69)

9.33

y b (a)

6.966

TemperatHre on Hugoniot (10 3 K) 5.2 19.0 ,

°

,

0.41 0.55 1.25 2.43 4.79 13.3

0.39 1.03 1.97 4.95 12.2

0.35 0.75 2.35 0.89 2.35 1.71 2.28 3.88 11.2

METALS, ALLOYS AND COMPOUNDS

1000 ~XTi 900

727

xHf x Zr

800

< 700 u to 6 0 0 L0 o 500

x SC

HEÄVIER R.E.

_~~ 4 0 0 co 5 0 0

LIGHTER R.E.

_J a 0 2OO x

ce

m

Yb x

100

x Eu

I I I 10 20 30 40 SPECIFIC VOLUME IN CC (LOG SCALE )

Fig. 9.11. A plot of the log of bulk modulus against log of speciflc volume for rare earth metals. The heavier and lighter rare earths fall into two groups and the ambivalent Ce, and the divalent cases Yb and Eu metals are distinct.

(Ming and Bassett, 1974), these predictions can be checked in almost all cases. Until a direct experimental check up confirms the proposed P - T diagrams, the conclusions of Carter et al. (1975) have to be treated as good speculations. In fig. 9.11 we present a rather interesting plot of the log of the bulk modulus versus log of the specific volume for the rare earth elements. It is seen that in this plot the divalent and trivalent cases fall in distinct groups, while Sc which is normally trivalent is quite outside these two groups. 5.2. Compounds Among the compounds the compressibilities of divalent monochalcogenides and a few members of the monopnictides have been investigated. In several of the divalent monochalcogenides and CeP the occurrence of phase transition involving valence change has been established through their P - V relationships. These will be discussed in chapter 20. In fig. 9.12a the compressibilities of EuTe, EuSe, EuS and EuO are shown. The first three do not show any evidence for a valence change in the range of pressure investigated, although in general they are found to be quite compressible. The discontinuities in them are due to a phase change from NaC1 to the CsCI structure (Chatterjee et al., 1972 and Jayaraman et al., 1974). A useful plot of the bulk modulus data for related

728

A. JAYARAMAN

1.000

EuO P - V RELATIONSHIP FOR EUROPiUM MONOCHALCOGENIDES

0.960

1000 800 C

0.920

~ 600

YbSeX~xEuS SmSeX~ EuSe

0.880

TmTeß CaT~YbTe

~ . .

:;9 o.84o

i 400

EUO

.

»

0.800

g

0.760

SmTe - / ~ EuTe BaSe/ ~ e

2OO

0.720 0.680

I

I

100

20O 500 P (k bar)

4O0

500

0

10

20 40 60 SPECIFIC VOLUMEcm 3

80 100

Fig. 9.12. Pressure-volume relationship for Eu monochalcogenides (left fig.) and a plot of the log of bulk modulus against log of specific volume for R.E. monochalcogenides showing the straight line relationship. In the P - V relationship of Eu monochalcogenides the discontinuities are due to NaCI to CsC1 transition. In EuO the first discontinuity is due to a valence transition in Eu (from Jayaraman et al., 1974). compounds is the log of B0 vs log of specific volume shown in fig. 9.i2b for the divalent rare earth chalcogenides (Jayaraman et al., 1974). A straight line relationship holds and this can be taken advantage of to compute the bulk modulus of a substance belonging to this class, provided the cell dimension is known. In table 9.4 the data of interest for many of the compounds are presented. In the case of pnictides the compression has been measured up to 200 kbar pressure for CeP (Jayaraman et al., 1976) and to about 80 kbar in the case of GdN (McWhan, 1965). The pressure-volume relationship (see fig. 9.13) of CeP shows anomalies due to a valence change (see ch. 20).

6. Magnetic transitions under pressure High pressure studies on magnetic transitions in rare earth metals, intra-rare' earth alloys and compounds (the monochalcogenides, ferrites, spinels (RFe204) and garnets (R3FesOj2 where R is a rare earth element)) have been numerous and all the work prior 1969 has been reviewed by Bloch and Pavlovic (1969). For the discussion on pressure studies of magnetic transition in this chapter, much material has been drawn from the above review. For experimental details, high pressure apparatus and techniques, references to original articles can be found in the review by Bloch and Pavlovic (1969). Briefly, the most common methods used in following a magnetic transition are: change in the mutual inductance sensed through a set of coils placed around the specimen in a transformer-like set up, magnetic susceptibility, electrical resistivity and in some cases thermal dilation. To a limited extent more sophisticated

METALS, ALLOYS AND C O M P O U N D S

729

TABLE 9.4. Lattice parameters and bulk moduli of divalent rare earth monochalocogenides (Jayaraman et al., 1974).

Substance

Lattice parameter a(Ä)

EuTe

6.60

400 --- 50

43.3

EuSe

6.19

520 -+ 50

35.7

EuS

5.97

610 --- 50

32.0

EuO

5.14

1100 ± 50

20.45

YbTe YbSe YbS TmTe SmTe SmSe SmS

6.36 5.93 5.68 6.34 6.60 6.22 5.97

460 -+ 50 610 -+ 50 720 ± 50 460 - 50 400 ± 50 400 --- 50 151 (?)

38.75 31.42 27.55 38.33 43.2 35.86 32.0

GdS**

5.56 5.49

1200 ± 50

25.5 24.9

YS**

Bulk modulus B0(kbar)

M/p(cm 3)

Bulk modulus B0(kbar) other work 400 + 30(a) 360 --- 50*(b) 526 + 100ra) 476 ± 50 *(b) 555 -+ 55(a) 500 ---75 *(b) 900 ± 150(a~ 900 -+ 100*(b~ 610t 740t 465t 400t 520t 600t 476 ± 50(c)(d~ 1200 ± 50 998 td)

*adiabatic values; **trivalent; tfrom fig. 9.12; (a)Levy and Wachter (1970); ~b)Shapira and Reed (1972); CC)Kaldis and Wachter (1972), also Penney et al. (1972); (d)Penney (private communication). techniques such as measuring the magnetization neutron scattering have been employed. 6.1. S o m e u s e f u l t h e r m o d y n a m i c

through

NMR,

Mössbauer

equations

With a magnetic material the usual m o d y n a m i c s t a t e o f t h e m a t e r i a l is

Gibbs

function

describing

the

ther-

(9.9)

G = U - TS + PV - Hm

w h e r e H is t h e m a g n e t i c terms are well-known.

and

f i e l d a n d m is t h e t o t a l m a g n e t i c

moment;

the other

For a reversible process the change in the Gibbs' function becomes dG =-SdT

+ VdP-m

(9.10)

dH

and since this must be an exact differential one immediately

obtains

( O m / a P ) n , T = -- (0 V/c3H)p,T

(9.11)

D ( o t r l o P ) H , T = -- V - l ( O V[OH)p,T = - (äto/OH)p,T,

(9.12)

or

730

A. JAYARAMAN

t.0 ...... 6501

600~

R

P

0.9

~

Q LaP

o 550 0.8

5.00

4.60

P-V Relotionlhlpin CeP 0.7 0

LoCePrNdPmSmEuGdbDyHoErTmYb

I

I

1

I

1

i

't00 Pkbar

l

t

I

I

200

Fig. 9.13. Lattice parameter vs atomic number plot for R.E. pnictides. The deviation of a of CeN is due to the higher valence state of Ce. The right fig. is the P - V relationship for CeP and the anomaly is due to a valence change in Ce towards the 4+ state. The data point for LaP is shown for comparison (from Jayaraman et al., 1976). w h e r e D is the density of the material, ~r is the specific m a g n e t i z a t i o n and (0~o/0H)p,T the f o r c e d v o l u m e m a g n e t o s t r i c t i o n . T h e specific s p o n t a n e o u s m a g n e t i z a t i o n ~r0 of a f e r r o m a g n e t i c material at t e m p e r a t u r e T can be written as

O's = o'of(T/Oc)

(9.13)

w h e r e ~r0 is the specific s p o n t a n e o u s m a g n e t i z a t i o n at T = 0 K and it is a s s u m e d that f(T/Oc) varies with pressure only by virtue of its v o l u m e d e p e n d e n c e of 0c the Curie temperature. F r o m this relation it can be s h o w n (see B l o c h and Pavlovic) that

1

(0o','~

1 {0O'o~

T

(0o','~ ~

(,98«'~

o-~ \~gP ) = o'ö \ OP,I - o'---~~\OT ] Oc \-O-fr/

(9.14)

is a g o o d a p p r o x i m a t i o n . In dealing with a f e r r o m a g n e t i c material one w o u l d like to m e a s u r e both o-s and (Oc) as a f u n c t i o n o f pressure. T h e a b o v e e x p r e s s i o n can be used to c o m p u t e (1/O'o)(Oo'o/,gP) f r o m e x p e r i m e n t a l values of other quantities or dOc/dP w h e n the a s s u m p t i o n is m a d e that (1/O'o)(aO'o/dP) = 0. M o r e orten it is the logarithmic v o l u m e d e p e n d e n c e of these quantities (0 log 0c'~ 0 log V ] r

and

(0 log O'o]

\ ~ ] T

(9.]5)

that are w a n t e d to e x t r a c t i n f o r m a t i o n a b o u t the e x c h a n g e interactions a m o n g

METALS, ALLOYS AND COMPOUNDS

731

the magnetic ions. Therefore a knowledge of the compressibility of the material becomes a prerequisite for the analysis of the data. In ferromagnetic materials there exists a volume anomaly A Vo at absolute zero. For an isotropic substance the magnetic energy Wm is related through the equation (9.16) The volume anomaly A Vo is the difference between the true volume and the volume which would exist in the absence of magneto-elastic interactions and can be obtained by extrapolation of the empirical volume temperature relation, from the high temperature phase. 6.2. Molecular-field approximation The molecular field theory has been quite successful in describing the magnetic properties of many simple ferro-ferri- and antiferromagnetic spin arrangements in solids. According to this, the expression for the magnetic ordering temperature of various types of order and crystal structures is (9.17) where S is the total spin quantum number of the atom and k is Boltzmann's constant. The sums E (±)A~(i) and X (---)Az(j) are of the exchange interactions of the nearest and next nearest neighbor atoms respectively where (±) is associated with parallel and antiparallel configurations. For an fcc lattice with 12 ferromagnetically coupled nearest-neighbor atoms and six ferromagnetically coupled next nearest neighbor atoms (9.18) In several magnetic materials A2 is negative and much larger than AI, leading to an antiferromagnetic state with N6el temperature (9.19) One would obtain the same expression if among the 12 nearest neighbors six were ferromagnetically coupled and six were antiferromagnetically coupled with the central atom. In the above case with magnetic atoms in well defined S-states, the effect of pressure influences only the value of exchange interaction A2 and then (9.20) where (9.21)

732

A. JAYARAMAN

The term in parenthesis in the denominator arises because of temperature variation of ON due to the thermal expansion of the lattice. The magnetic energy of this lattice can be approximated (9.22) and its volume dependence is given by (9.23) From these relations one can obtain an expression for the exchange interaction in terms of experimentally accessible quantities (9.24) The same approach has been applied to ferrimagnetic materials with two magnetic sublattices (see Bloch and Pavlovic, 1969). The volume dependence of 0Fi can be related to that of the molecular field coefficients n by the relation (9.25) When applied to a ferromagnetic material the molecular field theory gives for the Curie temperature (9.26) where J is the total angular momentum, M the atomic mass of the material, tr0 specific magnetization at absolute zero, R the gas constant. The volume dependence of the molecular field coefficient is the interesting quantity, since it is related to the exchange integral. For a constant J one has (9.27) In this case one has to know the volume d e p e n d e n c e of the Curie temperature as well as the specific magnetization o'0 at absolute zero. 6.3. Indirect exchange Although the molecular field approximation, which rests on the direct exchange mechanism, seems to have wide applicability including to magnetic rare earth systems, it is well accepted now that the indirect exchange mechanisms mediated via the conduction electrons are the dominant interactions for rare earth metallic systems. For nonmetallic systems this indirect exchange is often mediated by the electrons of the anion (superexchange); oxygens in ferrites and garnets, etc. The indirect coupling mechanisms involve the so-called Ruderman-Kittel-function

METALS, ALLOYS AND COMPOUNDS

733

and the expression for the magnetic ordering temperature is

O _ 37rZ~ F 2 4k ~ (g - 1)2J(J + 1) ~'~ F(2kFRmn)

(9.28)

where Zi is the ionie charge, F the coupling constant between the spin of a 4f electron and a conduction electron, EF the Fermi energy kF the wave vector of the conduction electron, V the atomic volume, g Landé's factor of the ions, R~, the distance between the ions m and n and F(P) is the oscillatory RudermanKittel function: The magnetization AM of the polarized conduction electrons is given by

3ZiF AM = (g - l)J "~F/XB

(9.29)

and the magnetic resistivity

Pm --

3Ir m* 8

~ e 2 (g

D2 F 2 - " ~ J(J + 1),

(9.30)

where m* is the effect mass of the electron. The sum appearing in the expression for 0 has been shown to be independent of volume. Therefore the pressure derivatives of 0, A M and Pm can easily be written in terms of the volume variation of the coupling constant F and m*

1 (1 00~ K \õõ-ff]n,T

=_~+2(ologr~ \~,]H,T

, [ologm*~

"1-\õ "-~Oi'~-]H,T

l ( lOp~ù~ =_l+2{ologF~ + 2 / 0 log m*~ K \Õ~ OP/H,T \0 log V/H,T \Õ ~og V ]H,T

1

K ( A 1 õÕ-ffM)n,r = ~+

[ Olog F~ kO log V]n.r

+

[O log m*~ \ö~og V-]n,r

(9.31) (9.32) (9.33,

It is the coupling constant which is quite sensitive to volume. Another useful expression for metallic systems is 0 In 0c = _ 2 + 2 0Fs_____ In ~0 In E_______F 0 In V 0 In V 0 In V

(9.34)

where F« is the sf exchange interaction and EF is the Fermi energy. 6.4. Pressure studies on metals and alloys The rare earth metals exhibit a variety of ordered states from ferromagnetic to complicated antiferromagnetic structures; collinear, spiral, helical, conical and fan structures, which can be altered by temperature, magnetic fields or by the application of pressure (Nikitin et al,, 1972). These complicated arrangements of spins result from the balance in energy between magnetocrystalline anisotropy and exchange forces (Elliott, 1965). Much pressure work has been done on pure rare earth metals and alloys in the last decade especially, and measurements

734 cover

A. JAYARAMAN the effect of pressure

on the

netization and magnetocrystalline

transition

anisotropy.

temperature,

saturation

mag-

B l o c h a n d P a v l o v i c (1969) h a v e

e x t e n s i v e l y c o v e r e d in t h e i r article w o r k o n r a r e e a r t h m e t a l s a n d alloys p r i o r to 1968. I n t a b l e s 9.5 a n d 9.6 t h e p r e s s u r e d a t a o f i n t e r e s t a r e p r e s e n t e d .

6.4.1.

Gadolinium

Gd metal exhibits a transition directly from the paramagnetic

to t h e f e r r o -

m a g n e t i c s t a t e a t 291.8 K . I t is f o u n d t h a t p r e s s u r e d e p r e s s e s t h e C u r i e t e m p e r a t u r e 0c in G d a n d t h e b e s t v a l u e f o r dOc/dP b a s e d o n h y d r o s t a t i c m e a s u r e m e n t ( B a r t h o l i n a n d B l o c h , 1967, 1968) y i e l d s a s l o p e o f - 1 . 4 8 - + 0.02 K / k b a r .

TABLE 9.5. Pressure data for the magnetic transitions in rare earth metals. Rare earth element

0N or 0c (K)

dO/dP

Eu

(ON) 91

Gd Tb

(0c) 290.1 (0N) 227 --+1

Dy

(ON) 179 _+2

Ho

(0~ F) 8 4 . 7 (ON) 118

- 0

Er

(0s) 85 (0~ F) ~ 20

0 In 0 0 In V

(K/kbar)

o~lOo'JOP (x 103 kbar)

- 0 el) -1.1 -+0.3~«)

2.2 1.8

-3.8 _+0.4(77 K) ~b) 1.4 - 0.15 -+0.2(77 K) th) -8.4 -+0.5~d~ 1.4 - 11.73 -+0.78 ~d~

~")McWhan and Stevens (1965); ~b)Bloch and Pauthenet (1965); tC)Bartholin and Bloch (1%7); td)Vinokurova and Kondorskii (1964); t°~Milton and Scott (1%7); ~f)McWhan et al. (1966); ~g)Menyuk et al. (1971).

TABLE 9.6. Pressure and volume variations of some physical quantities for Gd, Tb, Dy, Ho {01ogF] Element \ ä log V]n,r

Gd Tb Dy Ho

2.6 1.6 a 1.2 1.9 2.0a 2.3

(älogm*] \ olÕ]ößg V ]H,r - 1.7 -0.2 a 0.3 - 1.1 - 1.4a -1.2

"From Austin and Mishra (1967).

öAM~

( 1 \~~p-p

- 4.1 -4.1 - 3.9 -4.6

}H,r

METALS, ALLOYS AND COMPOUNDS

735

Measurements of various investigators fall between - 1.2 K/kbar and - 1.8 K/kbar. Among the values for (1/O0(dOs/dP) (Kondorskii and Vinokurova, 1965; Bloch and Pauthenet, 1965) the value of -1.1-+0.3 × 10-3/kbar obtained by Bloch and Pauthenet appears to be consistent. The rate of change of Curie temperature with pressure for Gd was calculated from the experimentally determined acrJaT and (l[o'o)(Ocro/OP) using equation 9.14 as dOc/dP=-l.63K/kbar, in good agreement with experiment. Also (a log Fro log V)H,T, (c9 log m*/a log V)Vt.T and (I/AM)(aAM/aP)H,T were calculated (see table 9.6). The results show that the coupling constant F is a rapidly varying function of volume. The investigations of Robinson et al. (1964) and McWhan and Stevens (1965) have shown that above 25 kbar two new peaks appear in the secondary voltage versus temperature data. This has been attributed to the h c p - S m type transition reported by Jayaraman and Sherwood (1964a). The high pressure phase was found to be antiferromagnetic by McWhan and Stevens (1965) in accordance with the earlier observation of Jayaraman and Sherwood (1964a) on quenched material. 6.4.2. Tb, Dy, H o and Er The magnetic behavior of the above rare earth metals is much more complicated, since they undergo the complex type of antiferromagnetic spin arrangements, before ordering ferromagnetically. These metals have been studied and in fig. 9.14 are shown the data of McWhan and Stevens (1965) for Gd, 300 I ~ o G d

I

I

I

I

I

1

I

I

I

71

I

I\ Tb

50

I lo

I

I

20

[

30

40 50 p (ksA~)

60

0

I

80

90

Fig. 9.14. Change in magnetic ordering temperature with pressure of Gd, Tb, Dy and Ho (from McWhan and Stevens, 1965).The break in the curve in each case is due to hcp to Sm-type transition.

736

A. JAYARAMAN

T b , D y a n d H o to 80 k b a r p r e s s u r e , the h i g h e s t p r e s s u r e at w h i c h t h e m a g n e t i c t r a n s i t i o n s in r a r e e a r t h m e t a l s h a v e b e e n i n v e s t i g a t e d . T h e p l o t s h o w s the v a r i a t i o n o f ON w i t h p r e s s u r e . T h e a b r u p t c h a n g e s are d u e to the hcp---> S m t y p e p h a s e t r a n s i t i o n in t h e s e m a t e r i a l s . T h e y h a v e also b e e n s t u d i e d u n d e r s t r i c t l y h y d r o s t a t i c p r e s s u r e to a m a x i m u m of 6 o r 7 k b a r ; m a g n e t i z a t i o n s t u d i e s as w e i l as dOs/dP d e t e r m i n a t i o n s ( B l o c h a n d P a u t h e n e t , 1965; V i n o k u r o v a a n d K o n d o r s k i i , 1965a,b; B a r t h o l i n a n d B l o c h , 1968). I n s o m e s t u d i e s , r e s u l t s h a v e b e e n o b t a i n e d w i t h single c r y s t a l s ; W a z z a n et al. (1967) u s e d an e l e c t r i c a l r e s i s t i v i t y t e c h n i q u e , a n d T a t s u m o t o e t al. (1968) u s e d s u s c e p t i b i l i t y m e a s u r e m e n t s . D y s p r o s i u m u n d e r g o e s a t r a n s i t i o n to a n A F p h a s e w i t h h e l i c o i d a l s t r u c t u r e at 178 K a n d an A F to F t r a n s i t i o n at 85 K , at a t m o s p h e r i c p r e s s u r e . S o u e r s a n d J u r a (1964) a n d R o b i n s o n et al. (1966) m e a s u r e d dON/dP of D y using the e l e c t r i c a l r e s i s t i v i t y a n o m a l y , to r a t h e r high p r e s s u r e s . T h e A F t r a n s i t i o n in H o w a s also s t u d i e d b y K a w a i i e t al. (1967) w h o u s e d e l e c t r i c a l r e s i s t i v i t y a n d b y U m e b a y a s h i et al. (1968) b y n e u t r o n diffracfion. I n the l a t t e r s t u d y the p r e s s u r e d e p e n d e n c e of t h e h e l i c a l t u r n angle o~ w a s also m e a s u r e d . E r b i u m is m u c h m o r e c o m p l i c a t e d in its m a g n e t i c b e h a v i o r , e x h i b i t i n g t h r e e m a g n e t i c t r a n s i t i o n s . O n l y t w o p r e s s u r e s t u d i e s a r e o n r e c o r d on E r ( M i l t o n a n d S c o t t , 1967, o n ON a n d V i n o k u r o v a a n d K o n d o r s k i i , 1964 on the m a g n e t i z a t i o n ) . T h e m a g n e t i c s u s c e p tibility of H o a n d E r u n d e r p r e s s u r e w a s s t u d i e d b y O k a m o t o e t a l . (1968). T h e m a g n e t i c p r o p e r t i e s of lighter r a r e e a r t h s u n d e r p r e s s u r e h a v e n o t b e e n s t u d i e d . F i s k a n d M a t t h i a s (1969) r e p o r t t h a t t h e m a g n e t i c s u s c e p t i b i l i t y of P r u n d e r p r e s s u r e r e s e m b l e s t h a t of C e at n o r m a l p r e s s u r e . 6.4.3. Rare earth alloys M a n y p r e s s u r e s t u d i e s h a v e b e e n m a d e on i n t r a r a r e e a r t h a l l o y s , as w e l l as on r a r e e a r t h i n t e r m e t a l l i c c o m p o u n d s . In t a b l e 9.7 s o m e s e l e c t e d d a t a a r e presen-" ted. A m o n g the i n t r a r a r e e a r t h a l l o y s , s y s t e m s i n v o l v i n g G d h a v e e v o k e d r a u c h TABLE 9.7. Pressure data for some rare earth alloys 0c or ON (1 bar)

dO[dP

System

K/kbar

Phase transition kbar

Tbo.gsYo.os(a) Tbo.9oYoao(~) Tbo.8oYo.2o(a) Tb0.60Y0.40(a) Tb0.30Y070(a) Gdo.ssYoa5(b) Gdo.7oYo.3o(b) Gdo.91Luo.o9(b) Gdo.soLuo.zo(b) Gdo.7oLuo3o(b)

219 211 196 169 111 268(0c) 220(0c) 267(0c) 259(0c) 221(0c)

-0.80 -0.77 - 0.63 - 0.41 -0.28 - 1.3 - 1.23 - 1.46 -0.130 - 1.25

30 40 60 > 70 > 85 ------

ta)McWhan and Stevens (1967); tb)Austin and Mishra (1967).

METALS, ALLOYS AND COMPOUNDS

737

interest; Gd-Dy alloys (Milstein and Robinson, 1967); Gd-Lu and GdY (Austin and Mishra, 1967); Gd-Y alloys (Jayaraman et al., 1966; McWhan and Stevens, 1967; Ito et al., 1972; Ito, 1973). The hcp alloys in the Gd system, involving Gd and a lighter rare earth viz, La, Nd, Pr, show ferromagnetic ordering and undergo the hcp-Sm type transition at high pressure. The Tb-Y system was TABLE 9.8. Curie temperatures, the initial pressure dependences and din Tc/dln V for rare earth intermetallic compounds. The last column may be called the magnetic Gruneisen parameter

dTc/dP Tc/d In

Compound

TcK

K/kbar

d In

Y2Fe17(f) Er2Fel7 (g) YCo3 (c) Y2Co7(a) YCo5 (c) YzCo17~b) PrCo2 (b) PrCo3 (c) NdCo2 ~b) Nd2COl7~c) GdCo2 ~b) GdCo3 (a) Gd2Co7 ~a) GdCo» ~c) Gd2Co17(c) TbCoz (b) TbCo3 (a) DyCo2 ~b) HoCo2 ob) ErCo2 (~~ Er2Co~ff ) L u C o J a~ YzNi17(a) GdNi2 ~b) Dy2Nij7 la) Ho2Nilff ) ErzNil7 (~~ GdCu (h) GdAg ~hl GdAI2°) TbAI2°)

310 309 301 639 977 1167 54 349 98 1150 395 612 775 1008 1209 228 506 135 74 33 1186 362 151 77 154 152 140 144 ~ 140

-9.8 -4.1 -3.8 -5.9 - 1.0 -0.3 -0.75 - 1.8 -0.8 +0.7 -2.45 -9.5 -3.5 -0.8 +0.6 - 1.1 -5.7 -0.8 -0.65 -0.4 +1.1 -2.3 -0.44 0 -0.44 -0.44 -0.44 0.03 0.43 0.71 0.60

33 18 12.8 13.5 1.5 0.4 15 5.9 9 -1.0 6 19.6 6.4 1.1 -0.8 5 14.5 6 9 13 -1.6 8.5 4.5 0 4.3 4.4 4.7 -0.09 - 1.6

V

(")Bloch and Chaisse (1972); (b)Bloch et al. (1971); («~Brouha and Buschow (1973); te)Jaakkola et al. (1975); c~~Jaakkola and Parviainen (1974); a~ Givord et al. (1971); (*)Brouha and Buschow (1973); (h)Sekizawa et al. (1970); °)Jaakkola (1974).

738

A. JAYARAMAN

studied by McWhan et al. (1966b) in detail and other heavy rare earth alloys by Yagasaki et al. (1973). A m o n g the rare earth intermetallics the magnetic transitions, in RA12 compounds (Jaakkola, 1974), in R - C o and R - F e intermetallics (Brouha et al., 1974); Brouha and Buschow 1973a, 1973b, Voiron and Bloch, 1971; Voiron et al., 1973 and Bloch and Chaisse, 1972), in RzNi17 (Jaakkola and Parviainen, 1974 and Jaakkola et al., 1975) have been studied. Some rare earth intermetallic compounds with CsCI structure have been investigated; GdZnl_xlnx by Hiraoka (1974) and Hiraoka and Fuchikami (1974), GdCu and GdAg by Sekizawa et al., (1970). In table 9.8 the pressure data of interest are presented. 6.5. Rare earth compounds A m o n g the chalcogenides by far the most extensively investigated compounds are the Eu monochalcogenides. Most recent pressure studies, not included by Bloch and Pavlovic (1969) are of Lara and Xavier (1974) on EuO and EuS, Hidaka (1970-71) and Schwob (1969). The pressure data of interest are summarized in table 9.9 which also shows the exchange interaction coetticients and the logarithmic volume derivatives. The effect of pressure on the Curie temperature of some ferrimagnetic (0Fi) iron rare earth garnets are shown in fig. 9.15. The iron rare earth garnets have the general formula R3FesOi2 (R = rare earth element). The 0El increases linearly with pressure at a rate of about 1-2 K/kbar in the pressure range of 10 kbar. However, in a more recent study Bocquillon et al. (1973a) have extended the measurement to 60 kbar pressure (see fig. 9.15). According to this study, the Curie temperature increases with pressure, following a parabolic law (õFi = 0Fi.0"1" bP + cp2). The data are presented in table 9.10 in which the pressure and volume TABLE 9.9. Pressure data on the magnetic transition in Eu chalcogenides and GdN.

Substance

Ordering 0 K

EuO EuS

(0c) 69.3 (#c) 16.0

EuSe

(ON) 4.6

dO dP K/kbar 0.4-+ 0.1(a)

OIn A a ö In V x l02

OIn A 2 ö In V × 102

- - 0 . 0 7 (d)

0 . 2 8 (b)

0.20(¢) 0.24(«) -- 1(b) 0(d)

-0.09(d) 0.37

0.55

3.42

-0.10

O. 16 (c)

EuTe GdN

(ON) 9.64

0.10(a) 0.08 ± 0 . 0 4 (~)

ca)Sokolovaet al. (1966); (b)Schwoband Vogt (1967); (c)Srivastavaand Stevenson (1968); (a)Hidaka 097!); (°)McWhan (1966).

METALS, ALLOYS AND COMPOUNDS

~4°1ca>

,so

YIG

330

I

,//

/

A¢

739

[

(b)

S,~G

340 330

j

.o

J

~¢

/~

~HoIG

/ / -- / / //

290 I

i

~ol~ 270 0

290 / 10

20

30

40

50

60

280 0

70

10

20

30 40 P (kbar)

50

60

~0

350,

(c)

GdlG /

33o

1~,IG

,,f

320 316

29O

0

10

20

30

40

50

60

Fig. 9.15. C h a n g e in the ferrimagnetic ordering temperature 0 with pressure for some rare earth iron garnets (from Bocquillon et al., 1973a).

70

P (kbaO

TABLE

9.10.

Relative variations with volume of Curie 0Fi and c o m p e n sation temperatures 01 of rare earth ion garnets. (RaFesO~2) (Bloch and Pavlovic).

Garnet

d0Fi/dP °K/kbar

d In 0 d In V

°K/kbar

dOt/dP

d In Ot d In V

Y3FesOt2 Gd3FesO~2 Tb3F%O12 Dy3FesOi2 Ho3Fe~Ol2 Er3FesOt2 Yb3FesOi2

1.25 _+0.05 1.28 ± 0.05 1.23 ± 0.05 1.15-+0.05 1.28 ± 0.05 1.22 ± 0.05 1.08 -+ 0.05

-3.40 -3.48 - 3.45 -3.22 - 3.55 - 3.44 -3.08

0.95 +--0.07 0.77 --- 0.05 0.40 +--0.1 0.38±0.2 ----

-4.8 -4.5 - 2.7 -4.2 ----

740

A. JAYARAMAN

derivatives are summarized. Application of pressure produces a variation of the exchange interactions within each of the two sublattices, as well as between the two sublattices (see ch. 29, sections 3.2 and 3.5 for a detailed description of the sublattices involved in garnets). Apparently in these systems not only the variation in the interatomic distance affects the exchange interaction but also the angle change between the oxygen ion and the magnetic ions. Another aspect that has been studied under pressure in garnets is the shift in the compensation point (see Bloch and Pavlovic, 1969). The logarithmic volume derivative for the compensation temperature is given by (0 log Õcomp'~ = /Ologn] O log V /«comp \O log VJocomp

(9.35)

These data are also included in table 9.11. The effect of pressure on the anisotropy constants has also been investigated for some of the compounds (Timofeev et al., 1973a, 1973b). 6.6. Theoretical aspects of the pressure studies on magnetic transition The pressure studies on magnetic properties of rare earth metals and alloys have led to several experimental interaction curves for the rare earth systems. The inadequacy of the Bethe-Slater interaction curve or the Néel interaction curve to account for the results on R.E. metals was first recognized by Robinson et al. (1964), and they proposed an interaction curve to fit Gd and Tb. In this curve Oc and Op were plotted against the ratio of interatomic distance D to 2R, R being the diameter of the unfilled 4f shell. McWhan and Stevens (1965) found that their results on Dy were not in agreement with the interaction curve proposed by Robinson et al. (1964) in that it predicted a positive dOc/dP for Dy while experimentally a negative dOc/dP is observed. Consequently McWhan and Stevens proposed a new interaction curve for the rare earth and intrarare earth alloys in which they plotted the ordering temperature T divided by the DeGenne's function ( g - l ) Z J ( J + 1) versus R/r, the ratio of the interatomic distance R to the unfilled 4f shell radius r (see fig. 9.16). The data thus plotted fall into two curves representing the low and high pressure phases of the heavy rare earth metals and show that the exchange interaction increases smoothly in going from Gd to Ho with increasing R/r. Other experimental interaction curves have been proposed (see fig. 9.16), based on intrarare earth alloy data, in which the effective exchange interaction J(Q) was plotted against (r2Ol/z/V 113(McWhan and Stevens, 1967); 0p divided by DeGenne's function plotted against c/a ratio (Milstein and Robinson, 1967), and ON/(g-1)2j(j + 1) vs c/a (Wazzan et al., 1967). While these experimental interaction curves are of some value in interpreting the behavior, they do not lead to a deeper understanding of the interaction mechanism. More recently the role played by the electronic band structure on the magnetic ordering in rare earth metals and alloys has been stressed. Since exchange interaction in rare earth metals is mediated via the conduction electron, the detailed features of the Fermi surface geometry has a

H~

METALS, ALLOYS AND COMPOUNDS

i

30

26

f

44

+

GyT/~//

i

/

14

/

i

l

,tO

36

/

FC

Tbo'3Y07~

HO

22

"4

741

o~~~~

Tbo'6è~Y0325 T

32

28

/

10

24 6

36

~

J

3.8 °»

4.0 R/r

i

4.2

4.4

0.140

0144

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tl2

0t48

0152

~13

Fig. 9.16. Two of the proposed experimental interaction curves for rare earth metals and alloys. The two sets of curves in left fig. are for hcp (top set of 4) and for the high pressure phases (bottom set of 5) (from McWhan and Stevens, 1965 and 1967). strong influence on the magnetic ordering (Keeton and Loucks, 1968; Evenson and Liu, 1968, 1969; Fleming and Liu, 1970). Kasuya (1966) has discussed s-d and s - f interactions in rare earth metals. The complex magnetic structures that occur in heavy rare earth metals lead to superzone boundaries and open up gaps in the Fermi surface and this situation appears to be not dissimilar to that of chromium. The lowering of electronic energy brought about by the existence of the spin ware structures would then be responsible for their stability, and a nesting of the hole and electron part of the Fermi surface apparently is involved (Keeton and Loucks, 1968). Since conduction electrons are involved in the indirect exchange model the Fermi surface variation with pressure is of rauch importance to a detailed understanding of the pressure effects. More experiments combined with calculations on the electronic band structure as a function of volume may be expected to lead to further progress in the field.

7. Mössbauer studies at high pressure on rare earth systems Mössbauer studies under pressure in metals with )61Dy, ]7°yb and 151Euhave been reported (Holzapfel, 1975). The isomer shift measurements on Yb metal (Boehm, 1970) with pressure have not clearly indicated any changes in the valence

742

A. JAYARAMAN

state or transfer of 4f electrons. The observed changes can be explained on the basis of the conduction electron contribution, as in the case of n5Eu in E u metal (see Holzapfel, 1975). Quite a few Eu compounds have been investigated (Wortmann et al., 1972; Klein et al., 1973, 1976). Eu z+ compounds in general show a stronger variation of the isomer shift, compared to Eu 3+. High pressure Mössbauer studies on EuO and EuS suggest that all seven 4f electrons remain weil localized up to 100 kbar, in agreement with other pressure studies on Eu chalcogenides (see Jayaraman et al., 1974). In Eu2TizO7 the change of the electric-field gradient has also been evaluated (Klein et al., 1973, and Klein et al., 1976). It was observed that the effect of pressure is stronger by about a factor of 4 than what one would expect from a simple point charge model. The conclusion is that the valence electron contribution dominates even in this 4f6(7F0) configuration and that this contribution varies significantly more strongly than V -1. Some Mössbauer studies have been carried out on rare earth oxides (Boekema et al., 1975, and Halasa et al., 1974). The isomer shifts and hyperfine field changes have been measured. More recently, Mössbauer studies on Sm monochalcogenides have been made on SmS and in doped systems and these will be discussed i n chapter 20, A complete coverage of Mössbauer studies under pressure can be found elsewhere (Drickamer and Frank, 1973).

8. Synthesis of new phases and compounds involving rare earths at high pressure and temperature

Ever since the successful synthesis of diamond under high pressure the high pressure-high temperature method has been tried for synthesizing new materials and in polymorphic forms in which they do not normally exist. Many new compounds and phases involving rare earths have been prepared in this manner. Some of these developments have been covered by Klement and Jayaraman (1966) and more recently by Pistorius (1976). One of the earliest systems in which pressure-induced transformations were found is the rare earth sesquioxide R203 (R = rare earth and Y). The rare earth sesquioxides involving Ho to Lu and Y were known only in the cubic forms, but application of 15 to 60 kbar and temperatures in the range 500 to 1500°C were found to convert them into the monoclinic-form (Hoekstra and Gingerich, 1964; Hoekstra, 1966). Marezio et al. (1966a) studied rare earth garnets under pressure and temperature and found that Y3FesO12 broke down to 3YFeO3+ Fe203; the former with the perovskite-like structure and the latter with the corundum structure. This route was used to prepare many of the rare earth ortho ferrites, gallates and aluminates in the perovskite-like structure (Marezio et al., 1966b, 1968; Dernier and Maines, 1971; see also Goodenough et al., 1972). Shimada (1972) has claimed to have made denser modifications of R.E. garnets Y3FesOl2 and Gd3FesOl2 with a distorted perovskite-like structure, by treating them at pressures in the range 25-65 kbar at 1500°C. Other perovskite-like compounds that have been made under high

METALS, ALLOYS AND COMPOUNDS

743

pressure and temperature conditions are RInO3 (R = Eu, Gd and Dy) (Sawamoto, 1973); RMnTO1 compounds with R - - L a , Nd (Bochu et al., 1974; Chenavas et al., 1974). Some of the other oxide compounds involving rare earths, which have been prepared under high pressure and temperature treatment are: NaRGeO4 and NaRSiO4, where R is a rare earth element or Y, in the tetragonal form (originally in the olivine' structure, Chenavas et al., 1969); Tm2Si207 in a new form as weil as in the monoclinic gamma form (BocquiUon et al., 1973b; Sm2Ti207 in the monoclinic form (Bocquillon et al., 1971; see also Queyroux et ai., 1971); LiRO2 compounds in the monoclinic form (Waintal and Gondrand, 1967). Cannon et al. in a number of publications have recently reported pressureinduced transitions in several intermetallic compounds involving rare earth elements: transformation to the cubic structure in RA13 (Cannon and Hall, 1975); cubic MgCu2 type to the hexagonal MgZn2 type in RRu2 and ROs2 where R is a lanthanide (Cannon et al., 1972, 1973); synthesis of cubic Laves phases of PrFe2, NdFe2, YbFe2 (Cannon et al., 1972); LaCo2 (Robertson et al., 1972); R Te22-x compounds with tetragonal structure and LuTe3 with the orthorhombic structure at 100 kbar and 1200°C(Cannon and Hall, 1970). The following compounds have also been studied under pressure and some synthesized: ROF compounds with R = La, Sm, Gd and Er by Pistorius (1973), phase transitions in ROF with R = L a , Pr, Nd, Sm, Eu, Gd to the PbC12 structureg Gondrand et al., 1970); R2C3 compounds (with R = Y, La-Er) with Pu2C3 type structure (Krupka and Bowman, 1970 at 35 kbar and 1400°C; and GdSb2 and TbSb2 in LaSb2 structure (Eatough and Hall, 1969), denser forms of GdSb2 and TbSb2 with orthorhombic structure (Johnson, 1971) and only in the denser form of RSb2 with R = Y, Dy to Lu (Eatough and Hall, 1969). Rare earth polysulfides with tetragonal LaS2 structure have been prepared for Tm, Yb and Lu and new polymorphs with the cubic LaS2 structure for Gd to Lu and Y at high pressure (Webb and Hall, 1970a); sesquiselenides in Th3P4 cubic structure (Eatough and Hall, 1970); and polyselenides in the tetragonal ErSe2 structure (Webb and Hall, 1970b); RSn3 compounds with the fcc (AuCu3) structure at 85 kbar for R = Tb to Er and Y (MiUer and Hall, 1972, 1973) have also been made. A new pressure-induced form of DyF» which is metastable at atmospheric pressure was made by Vezzoli (1970). Most of the pressure-induced phases were metastably retained at room temperature on release o f pressure and in some cases their physical properties have been studied. Some of the studies were undertaken to check whether 4f bonding has any influence in determining the crystal structure in a particular series, or the size effects of the rare earth ions is the determining factor. A typical system in which such a study was done is the RAI3 system (Cannon and Hall, 1975). However, the results obtained do not give a clear cut answer. The one definite result of the study on RA13 seems to be that application of high pressure tends to make the lower-atomic weight lanthanide behave more like those of higher atomic weight. Thus the pressure-induced phase changes in the RA13 system were in the direction of structures with increased cubic character.

744

A. JAYARAMAN

Acknowledgments I w i s h to t h a n k R . G . M a i n e s f o r h e l p i n g in m a n y w a y s d u r i n g t h e p r e p a r a t i o n o f t h e a r t i c l e a n d M r s . K a r e n M i l l e r f o r t h e p a i n s t a k i n g e f f o r t in g e t t i n g t h e m a n u s c r i p t t y p e d . I w o u l d a l s o l i k e to t h a n k D r . B. J o h a n s s o n , Dr. W . H . G u s t , Dr. W.J. Carter and Dr. D.A. Young for supplying originals of figures, from w h i c h s o m e o f t h e f i g u r e s f o r t h i s a r t i c l e w e r e c o m p o s e d a n d to M r . H . H . T e i t e l b a u m f o r his h e l p in t h e l i t e r a t u r e s u r v e y .

References ltShuler, L.V. and A.A. Bakanova, 1969, Sov. hys. Usp., 11, 678. ltshuler, L.V., A.A. Bakanova and I.P. Dudoladov, 1966a, Zh. Eksp. Teor. Fiz. Pisma Red., 3, 483. ltshuler, L.V., A.A. Bakanova and I.P. Dudoladov, 1966b, JETP Lett. 3, 315. ltshuler, L.V., A.A. Bakanova and I.P. Dudoladov, 1968, Sov. Phys. JETP, 26, 1115. Altstetter, C.J., 1973, Met. Trans., 4, 2723. Austin, I.G. and P.K. Mishra, 1967, Phil. Mag., 15, 529. Bakanova, A.A., I.P. Dudoladov and Yu. N. Sutulov, 1970, Sov. Phys. Solid State, 11, 1515. Bartholin, H. and D. Bloch, 1967, C.R. Acad. Sci., Paris, 264, 1135. Bartholin, H. and D. Bloch, 1968, J. Phys. Chem. Solids, 29, 1063. Bloch, D. and F. Chaisse, 1972, C.R. Acad. Sci. Paris, Ser. B, 274,221. Bloch, D., F. Chaisse, F. Givord and J. Voiron, 1971, J. Phys. (Paris), 32, C1-659. Bloch, D. and R. Pauthenet, 1965, Study of the Magnetic Properties of the Rare Earth Elements Under Hydrostatic Pressure, in: Proceedings of the International Conference on Magnetism, Nottingham, 1964 (Institute of Physics, London) pp. 255-259. ~~ Bloch, D. and A.S. Pavlovic, 1969, Magnetic/ ally Ordered Materials at High Pressure, in: Bradley, R.S., ed., Advances in High Pressure Research, 1969, Vol. 3 (Academic Press, New York and London) pp. 41-147. Bochu, B., J. Chenavas, J.C. Joubert and M. Marezio, 1974, J. Solid State Chem., 11, 88. Bocquillon, G., C. Loriers-Susse, M. Dellalian and J. Loriers, 1973b, C.R. Acad. Sci., Paris, Ser. C, 276, 543. Bocquillon, G., C. Loriers-Susse and J. Loriers, 1973a, High Temp.-High Press., S, 161. Bocquillon, G., F. Queyroux, C. Susse and R. Collongues, 1971, C.R. Acad. Sci., Paris, Ser. C, 272, 572. Boehm, H.G., 1970, Dissertation, Technische Universität, München. Boekema, C., F. Van der Woude and G.A. Sawatzky, 1975, Phys. Rev. B, 11, 2705.

Bridgman, P.W., 1954, Proc. Am. Acad. Arts Sci., 83, 1. Brouha, M. and K.H.J. Buschow, 1973a, J. Phys. F. (GB), 3, 2218. Brouha, M. and K.H.J. Buschow, 1973b, J. Appl. Phys. 44, 1813. Brouha M., K.H.J. Buschow and A.R. Miedaßfa, 1974, I.E.E.E. Trans. Magn. (USA), 10, 182. Cannon, J.F. and H.T. Hall, 1970, Inorg. Chem., 9, 1639. Cannon, J.F. and H.T. Hall, 1975, J. LessCommon Met., 40, 313. Cannon, J.F., D.L. Robertson and H.T. Hall, 1972, J. Less-Common Met., 29, 141. Cannon, J.F., D.L. Robertson, H.T. Hall and A.C. Lawson, 1973, J. Less-Common Met., 31, 174. Carter, W.J., J.N. Fritz, S.P. Marsh and R.G. McQueen, 1975, J. Phys. Chem. Solids, 36, 741. Chatterjee, A., A.K. Singh and A. Jayaraman, 1972, Phys. Rev. B, 6, 2285. Chenavas, J., J.C. Joubert and M. Marezio, 1974, High Pressure Synthesis and Crystal Structure of a New Series of Perovskite Compounds . . . . International Crystallography Conference on Diffraction of Real Atoms and Real Crystals, Melbourne, Australia, 1974, II J-3/221-2. Chenavas, J., A. Waintal, J.J. Capponi and M. Gondrand, 1969, Mater. Res. Bull., 4, 425. Dernier, P.D. and R.G. Maines, 1971, Mater. Res. Bull., 6, 433. Doran, D.G. and R.K. Linde, 1966, Shock Effects in Solids, in: Seitz, F. and D. Turnbull, eds., Solid State Physics, 1966, Vol. 19 (Academic Press, New York and London) pp. 230-288. Drickamer, H.G., 1965, Effect of High Pressure on the Electronic Structure of Solids, in: Seitz, F. and D. TurnbuU, eds., Solid State Physics, 1965, Vol. 17 (Academic Press, New York and London) pp. 1-127. Drickamer, H.G. and C.W. Frank, 1973, Electronic Transitions and The High Pressure Chemistry and Physics of Solids, (Chapman and Hall, London). Drickamer, H.G., R.W. Lynch, R.L. Clendenen

METALS, ALLOYS AND COMPOUNDS and E.A. Perez-Albuerne, 1966, X-ray Diffraction Studies of the Lattice Parameters of Solids Under Very High Pressure, in: Seitz, F. and D. Turnbull, eds., Solid State Physics, 1966, Vol. 19 (Academic Press, New York and London) pp. 135-228. Eatough. N.L. and H.T. Hall, 1969, Inorg. Chem., 8, 1439. "' Eatough, N.L. and H.T. Hall, 1970, Inorg. Chem., 9, 417. Elliott, R.J., 1965, Theory of Magnetism in the Rare Earth Metals, in: Rado, G.T. and H. Suhl, eds., Magnetism, Vol. II A (Academic Press, New York and London) pp. 385-424. Evenson, W.E. and S.H. Liu, 1968, Phys. Rev. Lett., 21, 432. Evenson, W.E. and S.H. Liu, 1969, Phys. Rev., 178, 783. Flsher, E.S., M.H. M a n g ~ m and R. Kikuta, 1973, J. Phys. Chem. Soff/ts, 34, 687. Fisk, Z. and B.T. Matthias, 1969, Science, 165, 279. Fleming, G.S. and S.H. Liu, 1970, PhYs. Rev. B, 2, 164. Fujii, H., H. Tani, T. Okamoto and E. Tatsumoto, 1972, J, Phys. Soc. Jap. 33, 855. Givord, D., F. Givord and R. Lemaire, 1971, J. Phys (Paris), 32, C1-668. Gondrand, M., 1970, Bull. Soc. Fr. MineralCristallogr., 93, 421. Gondrand, M. and A. N. Christensen, 1971, Mater. Res. Bull., 6, 239. Gondrand, M., J.C. Joubert, J. Chenavas, J.J. Capponi and M. Perroud, 1970, Mater. Res. Bull., 5, 769. Goodenough, J.B., J.A. Kafalas and J.M. Longo, 1972, High Pressure Synthesis, in : Hagenmuller, P., ed., Preparative Methods in Solid State Chemistry (Academic Press, New York and London) pp. 1--69. Gschneidner, Jr., K.A., 1961a, Crystallography of the Rare-Earth Metals, in: Spedding, F.H. and A.H. Daane, eds., The Rare Earths (John Wiley and Sons, Inc., New York and London) pp. 190-215. Gschneidner, Jr., K.A., 1961b, Rare Earth Alloys, (Van Nostrand, New York) pp. 1-65. Gschneidner, Jr., K.A. and R.M. Valletta, 1968, Acta Met., 16, 477. Gust, W.H. and E.B. Royce, 1973, Phys. Rev. B, 8, 3595. Halasa, N.A., G. De Pasquali and H.G. Drickamer, 1974, Phys. Rev. B, 10, 154. Hall, H.T., J.D. Barnett and L. Merrill, 1963, Science, 139, 111. Harris, I.R. and G.V. Raynor, 1969, J. LessCommon Met., 17, 336. Hidaka, Y., 1970, J. Phys. Soc. Jap., 29, 515. Hidaka, Y., 1971, J. Sci. Hiroshima Univ. (Jap.), 35, 93. Hiraoka, T., 1974, J. Phys. Soc. Jap., 37, 1238. Hiraoka, T. and T. Fuchikami, 1974, J. Phys Soc. Jap., 36, 1488. Hodges, C.H., 1967, Acta Met., 15, 1787. Hoekstra, H.R., 1966, Inorg. Chem., 5, 754. Hoekstra, H.R. and K.A. Gingerich, 1964, Science, 146, 1163.

745

Holzapfel, W.B., 1975, C.R.C. Critical Reviews in Solid State Sciences, 5, 89-123. Holzapfel, W.B. and D. Severin, 1971, Phys. Lett., 34A, 371. Iida, K. and G. Fujii, 1972, Res. Rep. Fac. Eng. Meiji Univ. (Jap.), 26, 43. Ito, T., 1973, J. Sci. Hiroshima Univ. (Jap.), 37, 107. Ito, T., H. Fujii, T. Okamoto and E. Tatsumoto, 1972, J. Phys. Soc. Jap., 33, 854. Jaakkola, S., 1974, Phys. Lett., 50A, 35. Jaakkola, S. and S. Parviainen, 1974, Phys. Status Solidi A, 21, K53. Jaakkola, S., S. Parviainen and H. Stenholm, 1975, Z. Phys. B, 20, 109. Jayaraman, A., 1964, Phys. Rer., 135, A1056. Jayaraman, A., 1965a, Phys. Rev., 139, A690. Jayaraman, A., 1965b, Phys. Rev., 137, A179. Jayaraman, A., W. Klement, Jr. and G.C. Kennedy, 1963, Phys. Rev., 132, A1620. Jayaraman, A., W. Lowe, L.D. Longinotti and E. Bucher, 1976, Phys. Rev. Lett., 36, 366. Jayaraman, A. and R.C. Sherwood, 1964a, Phys. Rev. Lett., 12,22. Jayaraman, A. and R.C. Sherwood, 1964b, Phys. Rev., 134, A691. Jayaraman, A., R.C. Sherwood, H.J. Will~tLms and E. Corenzwit, 1966, Phys. Rev., 148, 502. Jayaraman, A., A.K. Singh, A. Chatterjee and S. Usha Devi, 1974, Phys. Rev. B, 9, 2513. Jepsen, O. and O.K. Andersen, 1971, Solid State Comm., 9, 1763. Johansen, G. and A.R. Mackintosh, 1970, Solid State Comm. 8, 121. Johansson, B. and A. Rosengren, 1975, Phys. Rev. B, 11, 2836. Johnson, Q., 1971, Inorg. Chem., 10, 2089. Jullien, R. and D. Jerome, 1971, J. Phys. Chem. Solids, 32, 257. Kaldis, E. and P. Wachter, 1972, Solid State Commun., 11, 907. Kasuya, T., 1966, s-d and s-f Interactions and Rare Earth Metals, in: Rado, G.T. and H. Suhl, eds., Magnetism, Vol. II B (Academic Press, New York and London) pp. 215-291. Katzman, H. and J.A. Mydosh, 1972, Z. Phys., 256, 380. Kawaii, N. and S. Endo, 1970, Rev. Sci. Instr., 41, 1178. Kawaii, N., M. Sakakihara, A. Marizumi and A. Sawaoka, 1967, J. Phys. Soc. Jap., 23, 475. Keeton, S.C. and T.L. Loucks, 1968, Phys. Rev., 168, 672. King, E., and I.R. Harris, 1970, J. Less-Common Met., 21, 275. Klein, U.F., G. Wortmann, G.M. Kalvius and W.B. Holzapfel, 1973, Verh. Dtsch. Phys. Ges. VI, 8, 350. Klein, U.F., G. Wortmann and G.M. Kalvius, 1976, J. Magn. and Magn. Mater. 3, 50. KIement Jr., W. and A. Jayaraman, 1966, Progress in Solid State Chemistry, Vol. 3 (Pergamon Press, Oxford and New York) pp. 289-376. Koch, C.C., 1970, J. Less-Common Met., 22, 149. Kondorskii, E.I. and L.V. Vinokurova, 1965,

746

A. JAYARAMAN

Effect of Hydrostatic Pressure on Magnetization of Some Rare Earth Metals, in: Proceedings of the International Conference on Magnetism, Nottingham, 1964, (Institute of Physics, London) pp. 260-265. Krupka, M.C. and M.G. Bowman, 1970, Coll. Internatl. C.N.R.S., 188, 409. Lara, S. and R.M. Xavier, 1974, Notas Fis. (Brazil), 22, 91. Lawson, A.W., 1956, Prog. Met. Phys., 6, 1. Levy, F. and P. Wachter, 1970, Solid State Commun., 8, 183. Liu, L., 1975, J. Phys. Chem. Solids, 36, 31. Liu, L., W.A. Bassett and M.S. Liu, 1973, Science, 180, 298. Lundin, C.E., 1966, Denver Res. Inst. Rept. 2326, (Denver University, Denver, Colorado). Marezio, M., J.P. Remeika and P. Dernier, 1966b, Mater. Res. Bull., 1,247. Marezio, M., J.P. Remeika and P. Dernier, 1968, Inorg Chem., 7, 1337. Marezio, M., J.P. Remeika and A. Jayaraman, 1966a, J. Chem. Phys., 45, 1821. McQueen, R.G., 1963, Laboratory Techniques for Very High Pressures and The Behavior of Metals Under Dynamic Loading, in: Gschneidner, Jr., K.A., M.T. Hepworth and N.A.D. Parlee, eds., Metallurgy at High Pressures and Temperatures (Gordon and Breach, New York) pp. 44-132. McWhan, D.B., 1966, J. Chem. Phys., 44, 3528. McWhan, D.B. and W.L. Bond, 1964, Rev. Sci. Instr., 35, 626. McWhan, D.B., E. Corenzwit and A.L. Stevens, 1966b, J. Appl. Phys., 37, 1355. McWhan, D.B., T.M. Rice and P.H. Schmidt, 1969, Phys. Rev., 177, 1063. McWhan, D.B., P.C. Souers and G. Jura, 1966a, Phys. Rev., 143, 385. McWhan, D.B. and A.L. Stevens, 1965, Phys. Rev., 139, A682. McWhan, D.B. and A.L. Stevens, 1967, Phys. Rev., 159, 438. Menyuk, N., K. Dwight and J.A. Kafalas, 1971, J. Appl. Phys., 42, 1301. Miller, K. and H.T. Hall, 1972, Inorg. Chem., 11, 1188. Miller, K. and H.T. Hall, 1973, J. Less-Common Met., 32, 275. Milstein, F. and L.B. Robinson, 1967, Phys. Rev., 159, 466. Milton, J.E. and T.A. Scott, 1967, Phys. Rev., 160, 387. Ming, L.C. and W.A. Bassett, 1974, Rev. Sci. Instr., 45, 1115. Nikitin, S.A., L.I. Solntseva and V.A. Suchkova, 1972, Izv. Akad. Nauk, SSSR. Ser. Fiz., 36, 1449. Okamoto, T., H. Fujii, T. Ito and E. Tatsumoto, 1968, J. Phys. Soc. Jap., 25, 1729. Penney, T. (private communication). Perez-Albuerne, E.A., R.L. Clendenen, R.W. Lynch and H.G. Drickamer, 1966, Phys. Rev., 142, 392. Piermarini, G.J. and C.E. Weir, 1964, Science, 144, 69.

Pistorius, C.W.F.T., 1973, J. Less-Common Met., 31, 119. Pistorius, C.W.F.T., 1976, Progress in Solid State Chemistry, Vol. II (Pergamon Press, Oxford and New York) pp. 1-120. Queyroux, F., G. Bocquillon, C. Susse and R. Collon~lues, 1971, Some Ln2TizO 7 Compounds änd Their Pressure Induced TransIormation, in: Field, P.E., ed., Proceedings of the Ninth Rare Earth Research Conference, Blacksburg, Virginia, 1971, Vol. 1 (U.S. Department of Commerce, Springfield, Virginia) pp. 103-112. Reynolds Jr., C.L. and R.E. Barker, Jr., 1974, J. Chem Phys., 61, 2548. Rice, M.H., R.G. McQueen and J.M. Walsh, 1958, Compression of Solids by Strong Shock W~ves, in: Seitz, F. and D. Turnbull, eds., Solid State Physics, 1958, Vol. 6 (Academic Press, New York and London) pp. 1-63. Robertson, D.L., J.F. Cannon and H.T. Hall, 1972, Mater. Res. Bull., 7, 977. Robinson, L.B., F. Milstein and A. Jayaraman, 1964, Phys. Rev., 134, A187. Robinson, L.B., S. Tan and K.F. Sterrett, 1966, Phys. Rev., 141, 548. Rosengren, A., and B. Johansson, 1976, Phys. Rev. B. 13, 1468. Sawamoto, H., 1973, J. Appl. Phys. Jap., 12, 1432. Sawaoka, A. and C.T. Tomizüka, 1971, Phys. Lett. 37A, 211. Schwob, P., 1969, Phys. Kondens. Materie, 10, 186. Schwob, P. and O. Vogt, 1967, Phys. Letters, " 24A, 242. Sekizawa, K., H. Sekizawa and C.T. Tomizuka, 1970, J. Phys Chem. Solids, 31, 215. Shapira, Y. and T.B. Reed, 1972, Compressibilities and Debye Temperatures of the Europium Chalcogenides, in: AIP Conference Proceedings, No. 5, Part 2, pp. 837839 (Seventeenth Annual Conference on Magnetism and Magnetic Materials, Chicago, 1971). Shimada, M., 1972, Jap. J. Appl. Phys., 11,964. Sokolova, G.K., K.M. Demchuk, K.P. Rodio"nov and A.A. Samokhvalov, 1%6, Sov. Phys. JETP, 22, 317. Souers, P.C. and G. Jura, 1963, Science, 1411, 481. Souers, P.C. and G. Jura, 1964, Science, 145, 575. Srivastava, V.C. and R. Stevenson, 1968, Can. J. Phys., 46, 2703. Stager, R.A. and H.G. Drickamer, 1963, Science, 139, 1284. Stager, R.A. and H.G. Drickamer, 1964, Phys. Rev., 133, 830. Stephens, D.R., 1964, J. Phys. Chem. Solids, 25, 423. Stephens, D.R., 1%5, J. Phys. Chem. Solids, 26, 943. Stephens, D.R. and Q. Johnson, 1%9, J. LessCommon Met., 17, 243.

METALS, ALLOYS AND COMPOUNDS Stromberg, H.D. and D.R. Stephens, 1964, J. Phys. Chem. Solids, 25, 1015. Syassen, K. and W.B. Holzapfel, 1975, Solid State Commun., 16, 533. Tatsumoto, E., H. Fujiwara, H. Fujii, N. Iwaka and T. Okamoto, 1968, J. Appl. Phys., 39, 894. Timofeev, Yu. A., E.N. Yakovlev, A.N. Ageev and A.G. Gurevich, 1973a, Effect of High Pressure on Anisotropy and Relaxation in Rare Earth Doped Ferromagnetic Garnets, in: AIP Conference Proceedings, No. 10, Part 1, pp. 155-163 (Eighteenth Annual Conference on Magnetism and Magnetic Materials, Denver, 1972). Timofeev, Yu.A., E.N. Yakovlev, A.G. Gurevich and A.N. Ageev, 1973b Sov. Phys. Solid State, 14, 2835. Umebayashi, H., G. Shirane, B.C. Frazer and W.B. Daniels, 1968, Phys. Rev., 165, 688. Vasvari, B., A.O.E. Animalu and V. Heine, 1967, Phys. Rev., 154, 535. Vezzoli, G.C., 1970, Mater. Res. Bull., 5, 213. Vinokurova, L.I. and E.I. Kondorskii, 1964, Sov. Phys. JETP., 19, 777. Vinokurova, L.I. and E.I. Kondorskii, 1965a, Sov. Phys. JETP, 21, 283. Vinokurova, L.I. and E.I. Kondorskii, 1965b, Sov. Phys. JETP, 20, 259. Vinokurova, L.I., E.I. Kondorskii, V. Yu. Ivanov, V. M. Eva and K.H. Rakhimova, 1973, Sov. Phys. Solid State, 14, 2981.

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Vinokurova, L.I., E.I. Kondorskii, V.Yu. Ivanov, and K.H. Rakhimova, 1972a, Izv. Akad. Nauk. SSSR Ser. Fiz., 36, 1419. Vinokurova, L.I., E.I. Kondorskii, K.H. Rakhimova and V. Yu. Ivanov, 1972b, Sov. Phys. Solid State, 14, 613. Voiron, J., J. Beille, D. Bloch and C. Vettier, 1973, Solid State Commun., 13, 201. Voiron, J. and D. Bloch, 1971, J. Physique (Paris) 32, 949. Waintal, A. and M. Gondrand, 1967, Mater. Res. Bull., 2, 889. Wazzan, A.R., R.S. Vitt and L.B. Robinson, 1967, Phys. Rer. 159, 400. Webb, A.W. and H~T. Hall, 1970~, Inorg. Chem., 9, 1084. Webb, A.W. and H.T. Hall, 1970b, Inorg, Chem., 9, 843. Wortmann, G., U.F. Klein, G.M. Klavius and W.B. Holzapfel, 1972, Pressure Dependence of the Isomer Shifts and Quadrupole Splittings of Di- and Trivalent Europium Compounds, Presented at the International Conference on Applications of the Mössbauer Effect, Ayeleth Hashabar, Israel, 1973. Yagasaki, K., H. Fujii and T. Okamoto, 1973, J. Phys. Soc. Jap., 34, 832. Young, D.A., 1975, Phase Diagrams of the Elements, U.C.R.L. Report No. 51902, Lawrence Livermore Laboratory, University of California (USA), September 1975.