Cerium

H. Drulis, M. Drulis

2.1.3.2 Cerium

Ce

0 0.5

CP

1 1.5 2.0 GPO 2.5

P-

Fig. 10. Ce. Low pressure - low temperature region of pseudo-equilibrium phase diagram. The dashed lint in the p-Ce phase region is the extension of the u-y phase boundary to lower temperatures and pressures. CP denotes the critical point [78 K 11.

H. Drulis, M. Drulis

Landolt-BBmsfein New Scricr 111119dl

48 2.1.3.2 Ce: figures [Ref. p. 183

12 eV 10

r

8

t

d 6 ‘I

1

2

t

. b theoretical values

01 ” ” ” ” ” ’ ” J

Lo Ce Pr Nd Pm Sm EU Gd Tb Dy Ho Er Tm yb Lu Fig. 9. Comparison between the calculated and the measured 4f promotion energies, A-, for transferring a 4f electron of the lanthanide metals to the conduction band at E,. The solid symbols for the heavy rare earth metals refer to the promotion of minority spin 4f electrons [74 B 21. The calculation was made by [72 H l] using the rcnormalized atom method.

2.1.3.2 Cerium

Ce

0 0.5

CP

1 1.5 2.0 GPO 2.5

P-

Fig. 10. Ce. Low pressure - low temperature region of pseudo-equilibrium phase diagram. The dashed lint in the p-Ce phase region is the extension of the u-y phase boundary to lower temperatures and pressures. CP denotes the critical point [78 K 11.

H. Drulis, M. Drulis

Landolt-BBmsfein New Scricr 111119dl

Ref.

p.

1831 2.1.3.2 Ce figures 49

- Foner , H =lO kOe

8

A

Fig. 11. p-Ce. Magnetic ordering in hexagonal Ce.

The magnetic moment pee = 0.62 ur, is directed along the c axis, with the magnetic unit cell parameter a being twice as large as the crystallographic one. The stacking sequence of the ferrimagnetic planes is + - + - along the c axis [61 W I].

Fig. 13. p-Ce. (a) Reciprocal of the magnetic susceptibility (Foner and Faraday results). The ac susceptibility data shown here are values averaged from the rapidly cooled and warmed results. (b) shows the details near the Neel temperature [76 B 11.

3 6 9 12 15 K 18

T-

Fig. 12. @Ce. ac magnetic susceptibility of a quenched sample vs. temperature near the magnetic ordering tem- perature as a function of magnetic field. The full line presents the Foner susceptibility data measured at 10 kOe [76 B 11.

0 80 160 240 K

a l-

320 9.0

I 9 403 cm3

‘5 8.0 1.5

4 6 8 IO 12 14 K 16

b T-

Land&-B&-n&n

New Series III/l9dl

H. Drulis, M. Drulis

50 2.1.3.2 Ce: figures [Ref.

p.

183

4.8 .lP

cm3 9

15 30 65 60 75 90 105 120 135 K 150

I-

Fig. 14. a-Ce. Magnetic susceptibility vs. temperature from 2 to 150 K. Almost a Pauli paramagnet. The slow rise with temperature above 60K is probably due to changes in position or shape of the 4f band with temperature. The low-temperature rise has not been explained satisfactorily [75 K 1-j.

58 I I" 4 I

160

.lrF I

cm! p-Ce -

mol I

Ibp=lOkbor 1 1 1 1 I

or I 1 I I I I I I I

0

^{50 100 150 200} 250 K 300

T-

Fig. 15. a-Ce, p-Ce. (a) Temperature dependence of the differential magnetic susceptibility, X,,,=da,/dH,of a-Ce at 8 kOe and 10 kbar. A correction for a small con- centration of paramagnetic impurities is indicated by the dashed line. (b) emphasizes the weak temperature de- pendence of xrn in the nonmagnetic a phase by a comparison with the fl phase [71 M 11.

I I I I

0 4 8 12 16 kbor

a

6 m"

cm3

I

iiT \

2 2

0 IO 20 30 40 50 kbor 60

b P-

Fig. 16. Ce. (a) Pressure dependence of the magnetic susceptibility of Ce at room temperature showing the y-+a phase transition. Open and solid circles indicate different experimental runs. (b) shows the linear extrapol- ation of the measurements in the a phase to the a+’

phase boundary. The extrapolated susceptibility at 50 kbar is comparable with the susceptibilities of the quadrivalent transition metals Hf and Th [71 M 11.

H. Drulis, M. Drulis

Land&-BBmstein New Series III/19dl

Ref.

p.

1831 2.1.3.2 Ce: figures 51

15 .lO" I

n a-

Ce

5

0 200 400 600 800 1000 1200 K 14 T-

I 10 20 30 40 50 60 meV 70

no2 -

Fig. 18. cl-Ce, y-Ce. Inelastic neutron scattering at 300 K from Ce metal (a) below and (b) above the first order ‘y-cl phase transition at p = 1 atm., 6 kbar and 8 kbar. The background scattering from the pressure cell has been substracted from the data. The small sharp peak near 6 meV has been attributed to a phonon transition. The 4f electron contributions give rise to linewidths only [77 R I].

Fig. 17. cl-Ce. Inverse paramagnetic susceptibility as a function of temperature. The solid line represents behavior of interacting Ce3+ ions with 0 = -50 K [61 C I]. T,: melting point.

3 meV

2 Y-Ce

I -

I T= 293 K

800

II = 2.98 w-' 600

I H5

,

-5 0 0 5 5 10 10 15 meV 20 15 meV 20 hUJ-

Fig. 19. y-Ce. Energy spectra of neutrons scattered from y-Ce at 293K for two different scattering vectors. The solid curve is the calculated total neutron cross section for crystal field transition, while the dashed-dotted curve gives the calculated total intensity including dynamical exchange interaction. The dashed curve is the phonon contribution to the intensity. The position of the inelastic crystal field peak gives the ground state I, doublet with Is quartet separated by 67 K. AE is the instrumental energy resolution [74 M I].

&andolt-BBmstein

New Series IWl9dl

H. Drulis, M. Drulis

52 2.1.3.2 Ce: figures [Ref. p. 183

0 15 30 45 60 K2 75 0 5 10 15 20 25 K 30

T2- I-

Fig. 20. a-Cc. Low-temperature (T<9 K) heat capacity of a43 [75 K 11.

Fig. 21. p-Ce. Heat capacity showing the electronic, lattice, magnetic and Schottky contributions. The magne- tic contribution is interpreted as evidence for separate ordering at 12.45 and 13.7 K for the two types of site symmetry, the lower-temperature peak being associated with ordering on the cubic sites and the higher- temperature peak with ordering on the hexagonal sites [78 s 1-J.

13 J md K

12 11

I IO z 9 8

7 6

12 13 14 15 16 K 17

T-

Fig. 22. B-Ce. Heat capacity, C,, vs. temperature from 12 to 17 K. Open symbols and dashed line: [74 K 11, solid symbols and full line [76T 1-J. The diffcrcnccs arc due to the presence of a-Ce in the [74 K l] sample. To calculate the Schottky contribution the excitation encrgics used correspond to 98 and 113 K for the two doublets on hexagonal sites and 206 K for the quartet on cubic sites.

The calculation is given by the full line.

-T

2.5 K 2.0 1.8 1.6 1.6 1.3 1.2 1.1 1.0 5.2

2 4.0 5

3.6

400 500 600 700 800 .@K-’ 1000

l/1 -

Fig. 23. p-Ce. Logarithm of the magnetic heat capacity, C map, vs. the reciprocal of the temperature, l/T, in the very low temperature range. C,,, denotes the total heat capacity corrected for lattice, electronic, and Schottky contributions, cf. Fig. 21. The solid line is a least-squares fit, cm,,= f(T)exp[-E$k,‘T’l, to the data below T= 1.33 K yielding a spin-wave energy gap E$k,=1.41(2)K and f(T)=162,8(25)mJmol-‘K-l [76T 11. Open symbols: [74K 11, solid symbols:

[76T I].

H. Drulis, M. Drulis

Ref.

p.

1831 2.1.3.2 Ce: figures 53

1.5

1.4

I 1.3 0

B 1.2 a , i: 1.1

1.0

I I

0.9 II

0 2 4 6 8 10 12 I’+ 16 18 kbor 20

P-

Fig. 24. cl-Ce, y-Ce. Variation of the specific heat, C,, of cerium with pressure at 300 K. The systematic scatter of some points from the curve is related to the history of the sample [78 B 21.

60

.lO-4 I

K-’

Ce

_{I i I}

0 3 6 9 12 15 kbor 18

Fig. 25. cl-Ce, y-Ce. Variation of the temperature coeffi- cient, fi, of electrical resistance with pressure at 300K [78B2].

50 FQcm 40

0 50 100 150 200 250 K 300

T-

o

50 100 150 200 250 K 300

T-

Fig. 26. Ce. Electrical resistivities of initially allotropically pure B-Ce and y-Ce, cooled down over a two-day period and warmed up over a Ii-day period as a function of temperature. The data reflect that both B-Ce and y-Ce transform to a-Ce at zz 50 and g 100 K, respectively. The B-Ce, not transformed to ~1, orders at z 13 K [76 B I].

Fig. 27. B-Ce. Anomalous electrical resistivity, which was obtained by subtracting the phonon and residual electri- cal resistivities from the observed resistivity, as a function of temperature. The solid line is the theoretical resistivity based on the model of Kondo scattering in the presence of strong spin correlation (i.e. magnetic ordering) [76 L 21.

Land&BBmstein

New Series IIIIl9dl

H. Drulis, M. Drubs

54 2.1.3.2 Ce: figures [Ref.

p.

183

0.4 1

\

Ce \

0.38- P=O H =2145(5) kOe \

+- Ce3+

0.35 \

\

1 _._-

Fig. 28. a-Ce, y-Ce. Paramagnetic enhancement ]gN]jI vs.

T obtained by the PAD method using 13“Ce as probe nuclei in Ce metal at zero pressure and an applied :

0.29 magnetic held of 21.45 kOe. /I is the ratio of the effective

maenetic field at the ‘34Ce site and the applied magnetic z 0.26 field, while g,= -0.187 is the g-factor of the 10’ isomeric

state of 13JCe. The data points are numbered to show the 0.23 sequence of temperatures used in the experimental run,

thus indicating the hysteresis of the yea transition. Open

circles give the results of preliminary measurements. The 0.20 solid line represents a fit based on the Curie-Weiss law for

y-Ce, and the dashed lines show the enhancement for Ce

ions of integer valence [84 B 1). 0.17

0 50 100 150 200 250 300 K

..,’

. EELS

i. .

IL

-pch

>-

3dq1f2 3dq 41’ 3dq 4fn

I I , 3dw

3dq4f2 3dq4f’ 3dq4f0

I I 1 W/2

I I I I I

880 890 900 910 920 ev 930

Fig. 29.a-Ce, y-Ce. EELS and XPS 3d core-level spectra of a-Cc and y-Ce on a common energy scale (the elastic peak in EELS is aligned with the Fermi energy of the XPS spectrum). The corresponding final states are indicated.

For EELS the 3dp4f2 and for XPS the 3dp4f1 final state multiplet structure was taken [83 W 11.

‘0

H. Drulis, M. Drulis

Land&-B6mstein New Series III/19dl

Ref. p. 1831 2.1.3.3 Pr: figures 55 2.1.3.3 Praseodymium

Pr3+: 4f2

T=r

r, ^+A

Fig. 30. Pr. Crystal-field level scheme for Pr in cubic environment with the Fr singlet the ground state. The arrows indicate nonvanishing magnetic-dipole matrix elements [72 B 11.

9” 11” 13” 15” 17” 19” 21” 23” 25” 27” 29” 31” 33” 35”

Fig. 31. Pr. Elastic neutron scattering powder pattern for fee Pr at 4.5 K in the region of the (111) peak [72 B I].

In-3 60 I -!nL

VU

2 min 59

I ⁵⁸

-z co 2

51

0 5 IO 15 20 K 25

Fig. 32. Pr. Temperature dependence of the neutron diffraction (111) integrated intensity in fee Pr. The dashed line indicates the high temnerature value of the intensitv

[72Bl]. - - .

Landolt-BBmstein

New Series III/19dl

H. Drulis, M. Drulis

56 2.1.3.3 Pr: figures [Ref. p. 183

20:

m:' a

17:

15:

SC

25

0 a

c .ld jcJ

mol

I : IoE2

1

c 3 6 9 12 kOe

H-

Fig. 33. Pr. Molar magnetization CT,,, vs. magnetic tield at 1.43 K for dhcp and fee Pr [69 B 21.

/ _fee

5 Xl3 Gcm3

mol

I 3

62

b I-

0 IO 20 30 LO K

100 150 200 250 K 300 I-

Fig. 34. Pr. (a) Inverse magnetic molar susceptibility vs.

temperature from 1.43 to 300K and (b) molar magnetiz- ation vs. tempcraturc for dhcp and fee Pr in an applied magnetic tield of 14.24 kOe [69 B 21.

Fig. 35. Molecular licld calculations of the magnetization of fee Pr as function of the exchange field for x = - 0.877 and AE(T,--T,)/k,=69K at T=O [72C2].

1.0 1-IB 0.8

I 0.6 c 4"

0.4

0.2

4 6 8 10 kOe ’

H er -

0 2

H. Drubs, M. Drulis

Land&Bbmstein NW Series 111/19dl

Ref.

p.

1831 2.1.3.3 Pr: figures 57

2001 I I I IO

100 78K

3 0 - 0”

300

IA IQ=1.08-11

200 I

t 1

^{0 300}

I I

0 2

0 2

100 \o

-c-o78K Ob

3 5 7 9 meV 11

ha---,

Fig. 36. Inelastic r, -r, excitation scans in fee Pr at several temperatures for momentum transfers (a) Q=0.6k’ and (b) Q=l.0k1[72B1].

K fee Pr I 1 I I I I

na

100, I I I I I I I

K/ I I I I I L1

80,,

1 I

^{60 I I I}

Ob

0 0.3 0.6 0.9 1.2 1.5 1.8 2.1

9a/n -

Fig. 37. Dispersion curves calculated for (a) longitudinal and (b) transverse magnetic excitons at T = 0 in fee Pr with x = -0.877, AE(T, 1 T,)/k, = 69 K, and pPr =0.75 pB [72C2].

Land&-Biirnstein

New Series III/19dl

H. Drulis, M. Drulis

58 2.1.3.3 Pr: figures [Ref. p. 183

Pr

dhcp

p=o /

\ \

-0.15 -0.12 -0.09 -0.06 -0.03

q-

$73)

Fig. 38. Neutron diffraction scans for dhcp Pr. The results at 40mK correspond to a scan precisely through a maenetic peak, but only approximately in the direction indkatcd. The solid lines show the sum of two Gaussian functions fitted to the data [82 M 11.

2500

2000

I 1500 : A 5 :1000

500

0

-0.20 -0.17 - -0.11 4

q-

,qo3)

+-w-M JG=ZZ -

H. Drulis, M. Drulis

LandoIl-BBmstein New Series III/19dl

Ref. p. 1831 2.1.3.3 Pr: figures 59

12

.I0

I I t 3o dhcp Pr I ’ I

1 i"-Oi ( / [

II!

41 )r

;10-

3[

I 20 4:

IO

C

(903) central peak

I I I

t ²⁰⁰

(gO3) satellite peak I

0 0

J 0

0.25 0.50 0.75 1.00 1.25 4.00 K 4.25 T-

Fig. 39. Pr. Intensity of the two Gaussian peaks in the (qO3) scans of Fig. 38 for dhcp Pr vs. temperature for (a) the “central” peak and (b) the “satellite” peak, suitably normalized to the intensity of the (103) nuclear peak (solid symbols). The results of [81 M2] are shown for com- parison (open symbols). The sharp satellite peak which emerges from the central peak and continues to grow with decreasing temperature is a manifestation of magnetic ordering at g 40 mK [82 M 11.

0.6

r

PB

I \

I

0.4 L a” 0.2

0 1 2 3 4 !I K b

a T-

0.57 Pe I 0.55 d 0.53 0.51

0 0.1 0.2 0.3 0.4 0.5 K 0.6

b T-

Fig. 40. Effective moments deduced from the integrated intensity of the neutron satellites in single crystals without magnetic field at very low temperature for (a) dhcp Pr and Pr -2.5at% Nd, and (b) dhcp Pr -25at% Nd below 0.6 K [82 M I].

1

0 2 4 6 8 K 10

T-

Fig. 41. Temperature dependence of the peak intensity of the (QOQ3) magnetic satellite reflection observed in dhcp Pr when a uniaxial stress of 800 bar is applied along the [1210] a direction. The dashed line shows the mean-field extrapolation used to determine T,=7.5K. The direc- tion of the elastic scans is indicated [78 M I].

Land&-Biimstein

New Series IWl9dl

H. Drulis, M. Drulis

60 2.1.3.3 Pr

figures

[Ref. p. 183

2.0 I

I+ dhcp Pr

1.5

I

I = 1.5 K 1.2

a’

Q 0.8

0 0.i 0.8 1.2 1.6 kbar 2.0

P-

Fig.42. Experimental measurements of the first har- monic of the magnetization in dhcp Pr at 1.5 K, deduced from the neutron scattering intensities of the (QOl) diffraction peaks, as a function of the uniaxial pressure in the o direction. The dashed line is the result obtained using the effective S= 1 model, whcrcas the solid line includes the effects of all the J=4 levels [87 J l]

r

16 K 12

I 8 LF

I I

Fig. 43. TN in dhcp Pr calculated as a function of the unianial pressure in the o direction, using the mcan-ficld- model of [79 H 23. Circles show the results obtained from neutron-diffraction mcasuremcnts of [82 M 2, 83 M 2, 87 J 11.

1S pa 0.t

! ot Q

0.1

0.;

O.O!\

I I a 50.02:

Q -0.051

c (3h,D,Ll) (h.0.2itli -

0 0.2 0.1 0.6 0.8 A- 1.0

sine/1 -

Fig. 44. (a) Induced magnetic form factor for dhcp Pr metal in a held of poH= 1.57T applied along the (120) a direction at 4.2K. The solid and dashed curves are calculated for the hexagonal sites only, including the effects of the crystalline clcctric field. They correspond to diffcrcnt values of the angle, 47, bctwccn the (100) direction and the direction of the scattering vector in the (hOI) plane. (b) shows the diffcrcnce, Af=j(O”)-j(v), for the form factors calculated for cp=45” and 90’ (dashed curves), and the dipole form factor, fdip (solid curve) [79 L 21.

H. Drulis, M. Drulis

Land&-Bdmstein New Series 111’19dl

Ref.

p.

1833 2.1.3.3 Pr: figures 61

2.5 lb 2.0

I 1.5 a" L

1.0

0.5

0 2.5 Pe 2.0

I 1.5 L 4"

1.0

0.5

0:

I%

0.E

1 L 0.4 a"

0.2

c HII b

I I

I I

^{T=B2 K}

4 8 12 16 T 20

POH-

Fig. 45. Magnetization as a function of magnetic field at different temperatures measured along (a) the a axis, (b) the b axis and(c) the c axis of a dhcp Pr single crystal. The full curves only connect the data points [79 H I].

2.0 I

PB

dhco Pr e =

900

1.6

0 20 40 60 kOe 80

H-

Fig. 46. Magnetization curves of single-crystal line and polycrystal line dhcp Pr at 4.2K. 0 denotes the angle between the magnetic field and the hexagonal c axis of the single crystal. When Hlc the magnetic moment has tendency to saturate in high magnetic fields while in the field H 11 c the magnetic moment is small and almost linear up to 80 kOe. The close agreement between the broken line calculated and the experimental one for the polycry- stalline sample suggests no essential difference in magneti- zation between the single crystal and the polycrystal [76S2].

5 40-j

!a kOe

I 3

=

*2

20 40 60 80 K 100

T-

Fig. 47. Initial magnetic susceptibility per atom, XII =(dWdH),+, for a single crystal of dhcp Pr in a magnetic field parallel to the c axis as a function of temperature [76 S 21.

Land&Bh-nstein

New Series III/lYdl

H. Drulis, M. Drulis

62 2.1.3.3 Pr: figures [Ref. p. 183

I I

E lk

9

dhcp Pr I

lo >z

^{HII c}

;o T= 4.2 K

,l > K C’ .

P*

.D

*. so .’

. *O

10 20 30 1

1.

LO

Fig. 48. High-field magnetization of dhcp Pr, as a func- tion of internal magnetic field along the c axis. Arrows indicate results for increasing and decreasing fields. The schematic field dcpcndcncc of the low-lying crystal field levels for the hexagonal sites is also indicated. The magnetic field reduces the energy of the I-1) state relative to the ground state and at the critical field at which they cross a magnetic moment of 0.8u, per hexagonal-site atom develops discontinuously [73 M 1, 76ClJ

12

12, / I , I I I 1

.10-’

.10-'

Cd

Cd "'x, Hz 320 oe "'x, Hz 320 oe

dhcp Pr dhcp Pr 9

9 . . . .

1. I

I

I

8.

8.

L

0

0 10 10 20 20 30 30 40 40 K K 50 50 T-

T-

Fig. 49. Variation of the magnetic susceptibility, xg, with Fig. 49. Variation of the magnetic susceptibility, xg, with tempcraturc for dhcp Pr in 320 Oc and 47 kOc. The tempcraturc for dhcp Pr in 320 Oc and 47 kOc. The arrows refer to the hump seen at 23 K which reflects the arrows refer to the hump seen at 23 K which reflects the antifcrromagnctic ordering of the hexagonal sites antifcrromagnctic ordering of the hexagonal sites [83A 11.

[83A 11.

Fig. 50. Plot of l/x vs. Tin Pr. A discontinuous deviation from Curie behavior is seen at 33 K (arrow) for the data taken in H=47 kOc. The straight line is a Curie law tit made in the interval 35 < T<45 K [83 A 11.

H. Drulis, M. Drulis

Land&-BCmstein New Serier 111119dl

Ref.

p.

1831 2.1.3.3 Pr: figures

₆₃

0

^{20 40 60 K 80}

a l-

cubic hexagonal

sites

-p1;4>+cc\+ 2) 250

K t

- - 150

t

’ I

125 ^{100 - 13,>}

- -s”

-.

25 t

- l+1>

0.85 13, >+0.5 IO > -

OL -lo>

b

Fig. 51. (a) Experimental results for the temperature dependence of the reciprocal magnetic susceptibility per atom in dhcp Pr along the c axis and the a direction, respectively [71 J I]. The solid lines indicate the behavior calculated by [72 R I] using the crystal field energy level scheme shown in (b).

30 .103 9 cm3

0 50 100 150 200 250 K 300

T-

1.50, I I

0.50

0 5 10 15 20 25 K

l-

Fig. 52. Reciprocal of the magnetic susceptibility, l/x,, of dhcp Pr plotted against temperature down to 1.3K.

Above lOOK, x obeys Curie law with peff=3.56 pB/Pr [57 L I].

Land&-Bknstein

New Series 111/19dl

H. Drulis, M. Dralis

64 2.1.3.3 Pr: figures [Ref. p. 183

2.0 JO-“0

bar 1.5 b ," 1.0 ,x 2” 0.5

0 L 8 12 16 20 24 K

l-

Fig. 54. Relative stress dependence of the magnetic sus- ceptibilities parallel and perpendicular the hexagonal c axis, x,, and xl, for a single crystal of dhcp Pr. u, and rro denote stresses applied along the c axis and a direction, respectively. The results indicate that internal strains may be responsible for the ordering phenomena in polycry- stalline Pr [75 0 1).

0

303 500 700 900 1100 1300 K 15

l-

Fig. 53. Temperature dependence of the reciprocal mag- netic susceptibility, 1/x8, of Pr over the high-temperature range from 300 to 15OOK. Tr : dhcpsbcc transition temperature, ‘&: melting point [61 A2]. The circles indicate results for different samples.

- :“”

320:

500

25C

I

dhcp Pr -+-.-

(0.2 , 0 ,-0.2.3 1 1=5.2K

8

I

p= 800 bor

AElh -

Fig. 55. Constant-Q neutron groups measured at the reciprocal-space position (0.2, 0, -0.2, 3) in dhcp Pr, under uniaxial pressure in the [lZlO] a direction. The sample temperature was 5.2 K in each case. The lines are guides to the eye. The three clear peaks at zero applied stress are identified as two excitations and an elastic peak due to incoherent scattering [78 M 11.

H. Drulis, M. Drulis

Landolt436mstein New Swim III,/lVdl

Ref.

p.

1831 2.1.3.3 Pr: figures 65

rn,“v dhcp Pr

1 13,> 1

I I

Fig. 56. Crystal-field splittings of the lowest levels of Pr3+

on the hexagonal sites in dhcp Pr. The energies relative to the ground state are calculated, using the parameters given by [79 H 23, as function of an uniaxial pressure in the a direction. The state-vector designation of the levels is the one at small values of the pressure [87 J I].

3.0 meV 2.1 2.4

I 2.1 ccl l.E

5 10 15 20 25 30 K 35

J

l-

Fig. 59. Temperature dependence of selected magnetic excitations in dhcp Pr taken from inelastic neutron scattering data in the temperature range up to 35 K for the hexagonal sites. The full lines are calculated in the RPA- approximation. As temperature is lowered the modes soften but not all the way to zero [75 H I].

0 0.1 0.2 0.3 0.4 0.5

r 4400 - M

Fig. 57. Dispersion relation of the optical excitations in the antiferromagnetic phase of dhcp Pr at 5.5 K under an applied uniaxial pressure of 1280 bar along an a direction.

The TM direction considered is the one which is per- pendicular to the pressure axis. The circles mark the peak positions obtained in inelastic neutron scattering experi- ments [82 M 21, with closed and open circles indicating the longitudinal and transverse branches, respectively. Q denotes the wavevector of the magnetic soft mode. The full lines are the calculated RPA energies of the excita- tions. The dashed lines indicate longitudinal excitations of weaker intensities, while the dashed-dotted lines are the experimental dispersion relations in unstressed Pr at T=6.4K [79H2].

For Fig. 58, see next page.

Land&-BBmstein

New Series 111/19dl

H. Drulis, M. Drulis

66 2.1.3.3 Pr: figures [Ref. p. 183

0 0.2 0.1 0.6 0.8 1.6 1.4 1.2 1.0 0.8 0.6 0.1 0.2 0 0.1 0.2 0.3 a-’ 0.5 a

b L- M K

Fig. 58. (a) Magnetic excitations in dhcp Pr. The upper set of excitations (open squares) corresponds to crystal field transitions on the cubic sites while the lower set (solid circles: acoustic modes, solid squares: optic modes) corresponds to transitions on the hexagonal sites, plotted in the double-zone representation in the TA direction. The temperature and magnetic held depen- dence H/lb of this branch is also shown. The open circles indicate an additional mode of unknown origin. In (b) the intra- and intersublattice exchange constants for the two sublattices of the hexagonal sites, J(q) and J’(q), respectively, deduced from the results presented in (a) are given [71 R 11.

r A

r’

2.101

2.101 I

lo4 lo4

dhcp Pr

mJ AL- mot K

mot K I

4

102

1021 I

0

0 5 5 10 10 15 15 20 20 K K 25 25 T-

T-

Fig. 60. Specific heat of dhcp Pr metal in the temperature range between 3 and 25 K [67 L 11.

Fig. 60. Specific heat of dhcp Pr metal in the temperature range between 3 and 25 K [67 L 11.

H. Drulis, M. Drulis

Land&-BBmstein New Series 111/19dl

Ref. p. 1833 2.1.3.3 Pr: figures 67

cubic 1.50

hexagonal sites

z EO-

1.25 K

I

200 - 1.00

0.25 50- =

0 - o--

1 2 4 6810 2 4 6 8 IO’K 2.102

T-

Fig. 61. Crystal field levels and magnetic heat capacity of dhcp Pr as a function of temperature calculated by [72 R I]. Two very closely separated lines represent a doublet. The experimental data points are derived from [Sl P I]; the full line is a least-squares fit to them.

L J mol K

2

10-l 8 6.10-2

2.10-2 4 6 8 10-l 2 4 6 Kl

T-

Fig. 62. Specific heat of Pr vs. temperature. Open circles:

[69 H I]; full circles: [64 L I]; triangles: [64T I]. The arrow indicates the temperature below which C- CN

=(24.4 T+4.53 T3) mJ/molK, T in K, is smaller than 1% of C, where CN is the nuclear contribution to C. The solid curve represents the best fit to the present data assuming a sinusoidal hypertine magnetic field for only half of the 141Pr ions in the lattice (cf. Table 5). The broken curve is the best fit assuming a constant hyperfine field and a’= 0.0470 K, P = 0.0013 K [69 H I].

150 mJ mol K2

125

I 100

Q 75 3

50

25 0

I I

dhcp Pr poH= 0 ::

1 2 3 4 5 K 6

a 1' . . Ps

I 1.0 E Q 0.F:

T-

I .:.

I' . . . P rms . . ,.O'.. ,"

'. 0'

. . '. P' . .,.-

I '. :

;: y<' ,:' '..

I

;..>' '0. '. y . .

:y '. '.

.3 . . . *

b

0 1 2 3 4 T

k’oH -

Fig. 63. (a) Heat capacity, C,,/T, vs. temperature for dhcp Pr in various magnetic fields applied along the b direc- tion. (b) Root-mean-square induced electronic magnetic moment, ~~~~~ and conduction electron heat capacity coefficient, y, vs. magnetic field applied along the b direction [Sl F I]. The broken line shows the average Pr magnetic moment induced by magnetic fields along the a direction [71 L 21.

1

^21.0

_3.L

nol K2 18.5

1 x 16.0

Land&-Biimstein

New Series III/l9dl

H. Drulis, M. Drulis