Section: 4 | Physical Properties of the Rare-Earth Metals |

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PHYSICAL PROPERTIES OF THE RARE-EARTH METALS

K. A. Gschneidner

These tables contain physical and structural property data for the rare-earth metals, which are important in many applications, including magnetic materials. They are often in short supply due to international trade considerations.

Atomic Structure Properties of Rare-Earth Metal Ions

Table 1 contains atomic structure data for the trivalent ions of the rare-earth elements. Column definitions for Table 1 are as follows.

Table 1 Column heading	Definition
Rare-earth metal	Name of the rare-earth metal
Symbol	Symbol of the rare-earth metal
Atomic no.	Atomic number
Atomic wt.	Standard atomic weight; see also "Standard Atomic Weights" table in Section 1
No. 4f elec. R³⁺ ion	Number of 4f electrons in the trivalent ion of the element
S	Spin quantum number of the R³⁺ (trivalent) ion
L	Azimuthal quantum number of the R³⁺ (trivalent) ion
J	Total angular momentum quantum number of the R³⁺ (trivalent) ion
Spect. ground st.	The spectroscopic symbol for the ground state of the R³⁺ (trivalent) ion

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TABLE 1. Atomic Structure Data for Rare-Earth Metal Ions (Trivalent)

Rare-earth metal	Symbol	Atomic no.	Atomic wt.^a	No. 4f elec. R³⁺ion	S^b	L^b	J^b	Spect. ground st.
Scandium	Sc	21	44.955908	0
Yttrium	Y	39	88.90584	0
Lanthanum	La	57	138.90547	0
Cerium	Ce	58	140.116	1	1/2	3	5/2	²F_5/2
Praseodymium	Pr	59	140.90766	2	1	5	4	³H₄
Neodymium	Nd	60	144.242	3	3/2	6	9/2	⁴I_9/2
Promethium	Pm	61	145^c	4	2	6	4	⁵I₄
Samarium	Sm	62	150.36	5	5/2	5	5/2	⁶H_5/2
Europium	Eu	63	151.964	6	3	3	0	⁷F₀
Gadolinium	Gd	64	157.25	7	7/2	0	7/2	⁸S_7/2
Terbium	Tb	65	158.925354	8	3	3	6	⁷F₆
Dysprosium	Dy	66	162.500	9	5/2	5	15/2	⁶H_15/2
Holmium	Ho	67	164.9303218	10	2	6	8	⁵I₈
Erbium	Er	68	167.259	11	3/2	6	15/2	⁴I_15/2
Thulium	Tm	69	168.93422	12	1	5	6	³H₆
Ytterbium	Yb	70	173.045	13	1/2	3	7/2	²F_7/2
Lutetium	Lu	71	174.9668	14

^a2019 Standard Atomic Weights.
^bIn R³⁺ ion.
^cMass number of longest-lived isotope.

Note: For additional information, see Goldschmidt, Z.B., in Handbook on the Physics and Chemistry of Rare Earths, Vol. 1, Gschneidner, K.A., Jr. and Eyring, L., Eds., North-Holland Physics, Amsterdam, 1978; DeLaeter, J.R., and Heumann, K.G., J. Phys. Chem. Ref. Data 20, 1313, 1991; Pure Appl. Chem. 66, 2423, 1994.

Crystallographic Data

Tables 2 and 3 contain crystallographic data for the rare-earth metals at 297 K or below and high temperatures, respectively. Column definitions for Tables 2 and 3 are as follows.

Table 2 Column heading	Definition
Rare-earth metal	Symbol of the rare-earth metal
Crystal structure	Crystal structure symbol, as defined in the table below
a₀	Primary lattice vector, in Å
b₀	Secondary lattice vector, in Å
c₀	Tertiary lattice vector, in Å
r_metal(CN12)	Ionic radius of the metallic atom with 12 nearest neighbors (coordination number = 12), in Å
V_A	Volume of one mole of the metal at standard conditions; in units of cm³ mol^-1
ρ	Density (mass per unit volume); in units of g cm^-3

Table 3 Column heading	Definition
Rare-earth metal	Symbol of the rare-earth metal
Crystal structure	Crystal structure symbol, as defined in the table below
Lattice parameter	Lattice vector, in Å
t_meas	Measurement temperature, in °C
r_metal(CN8)	Ionic radius of the metallic atom with 8 nearest neighbors (coordination number = 8), in Å
r_metal(CN12)	Ionic radius of the metallic atom with 12 nearest neighbors (coordination number = 12), in Å
V_A	Volume of one mole of the metal at standard conditions; in units of cm³ mol^-1
ρ	Density (mass per unit volume); in units of g cm^-3

Crystal structure symbol	Definition
hcp	Hexagonal close-packed; P6₃/mmc, hP2, A3, Mg-type
dhcp	Double-c hexagonal close-packed; P6₃/mmc, hP4, A3´, αLa-type
fcc	Face-centered cubic; Fm3¯m, cF4, A1, Cu-type
rhomb	Rhombohedral; R3¯m, hR3, αSm-type
bcc	Body-centered cubic; Im3¯m, cI2, A2, W-type
ortho	Orthorhombic; Cmcm, oC4, α´ Dy-type

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TABLE 2. Crystallographic Data for the Rare-Earth Metals at 24 °C (297 K) or Below

Rare-earth metal	Crystal structure	a_o/Å	b_o/Å	c_o/Å	r_metal(CN12)/Å	V_A/cm³mol^-1	ρ/g cm^-3
Continued on next page...
αSc	hcp	3.3088		5.2680	1.6406	15.039	2.989
αY	hcp	3.6482		5.7318	1.8012	19.893	4.469
αLa	dhcp	3.7740		12.171	1.8791	22.602	6.146
αCe^a	fcc	4.85^a			1.72^a	17.2^a	8.16^a
βCe	dhcp	3.6810		11.857	1.8321	20.947	6.689
γCe^b	fcc	5.1610			1.8247	20.696	6.770
αPr	dhcp	3.6721		11.8326	1.8279	20.803	6.773
αNd	dhcp	3.6582		11.7966	1.8214	20.583	7.008
αPm	dhcp	3.65		11.65	1.811	20.24	7.264
αSm	rhomb^c	3.6290^c		26.207	1.8041	20.000	7.520
Eu	bcc	4.5827			2.0418	28.979	5.244
αGd	hcp	3.6336		5.7810	1.8013	19.903	7.901
α′Tb^d	ortho	3.605^d	6.244^d	5.706^d	1.784^d	19.34^d	8.219^d
αTb	hcp	3.6055		5.6966	1.7833	19.310	8.230
α′Dy^e	ortho	3.595^e	6.184^e	5.678^e	1.774^e	19.00^e	8.551^e
αDy	hcp	3.5915		5.6501	1.7740	19.004	8.551
Ho	hcp	3.5778		5.6178	1.7661	18.752	8.795
Er	hcp	3.5592		5.5850	1.7566	18.449	9.066
Tm	hcp	3.5375		5.5540	1.7462	18.124	9.321

^aAt 77 K (–196 °C).
^bEquilibrium room temperature (standard state) phase.
^cRhombohedral is the primitive cell. Lattice parameters given are for the nonprimitive hexagonal cell.
^dAt 220 K (–53 °C).
^eAt 86 K (–187 °C).
^fAt 23 °C.

Note: For additional information, see Gschneidner, K.A., Jr. and Calderwood, F.W., in Handbook on the Physics and Chemistry of Rare Earths, Vol. 8, Gschneidner, K.A., Jr. and Eyring, L., Eds., North-Holland Physics, Amsterdam, 1986; Gschneidner, K.A., Jr., Pecharsky, V.K., Cho, Jaephil and Martin, S.W., Scripta Mater., 34, 1717, 1996. [https://doi.org/10.1016/1359-6462(96)00035-8]

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