Elastic properties of the elements (data page)

Elastic properties describe the reversible deformation (elastic response) of a material to an applied stress. They are a subset of the material properties that provide a quantitative description of the characteristics of a material, like its strength.

Material properties are most often characterized by a set of numerical parameters called moduli. The elastic properties can be well-characterized by the Young's modulus, Poisson's ratio, Bulk modulus, and Shear modulus or they may be described by the Lamé parameters.

Young's modulus

Young's modulus E(GPa)

number	symbol	name	use	WEL [1]	CRC [2]
3	Li	lithium	4.9	4.9
4	Be	beryllium	287	287
11	Na	sodium	10	10
12	Mg	magnesium	45	45
13	Al	aluminium	70	70
14	Si	silicon	130–188	130–188
20	Ca	calcium	20	20
21	Sc	scandium	74.4	74	74.4
22	Ti	titanium	116	116
23	V	vanadium	128	128
24	Cr	chromium	279	279
25	Mn	manganese	198	198
26	Fe	iron	211	211
27	Co	cobalt	209	209
28	Ni	nickel	200	200
29	Cu	copper	130	130
30	Zn	zinc	108	108
33	As	arsenic	8	8
34	Se	selenium	10	10
37	Rb	rubidium	2.4	2.4
39	Y	yttrium	63.5	64	63.5
40	Zr	zirconium	68	68
41	Nb	niobium	105	105
42	Mo	molybdenum	329	329
44	Ru	ruthenium	447	447
45	Rh	rhodium	275	275 (possibly incorrect [3] )
46	Pd	palladium	121	121
47	Ag	silver	83	83
48	Cd	cadmium	50	50
49	In	indium	11	11
50	Sn	tin	50	50
51	Sb	antimony	55	55
52	Te	tellurium	43	43
55	Cs	caesium	1.7	1.7
56	Ba	barium	13	13
57	La	lanthanum	(α form) 36.6	37	(α form) 36.6
58	Ce	cerium	(γ form) 33.6	34	(γ form) 33.6
59	Pr	praseodymium	(α form) 37.3	37	(α form) 37.3
60	Nd	neodymium	(α form) 41.4	41	(α form) 41.4
61	Pm	promethium	(α form) est. 46	46	(α form) est. 46
62	Sm	samarium	(α form) 49.7	50	(α form) 49.7
63	Eu	europium	18.2	18	18.2
64	Gd	gadolinium	(α form) 54.8	55	(α form) 54.8
65	Tb	terbium	(α form) 55.7	56	(α form) 55.7
66	Dy	dysprosium	(α form) 61.4	61	(α form) 61.4
67	Ho	holmium	64.8	65	64.8
68	Er	erbium	69.9	70	69.9
69	Tm	thulium	74.0	74	74.0
70	Yb	ytterbium	(β form) 23.9	24	(β form) 23.9
71	Lu	lutetium	68.6	69	68.6
72	Hf	hafnium	78	78
73	Ta	tantalum	186	186
74	W	tungsten	411	411
75	Re	rhenium	463	463
77	Ir	iridium	528	528
78	Pt	platinum	168	168
79	Au	gold	78	78
81	Tl	thallium	8	8
82	Pb	lead	16	16
83	Bi	bismuth	32	32
90	Th	thorium	79	79
92	U	uranium	208	208
94	Pu	plutonium	96	96

Poisson's ratio

Poisson's ratio ${\displaystyle \nu }$(dimensionless)

number	symbol	name	use	WEL [1]	CRC [2]
4	Be	beryllium	0.032	0.032
12	Mg	magnesium	0.29	0.29
13	Al	aluminium	0.35	0.35
20	Ca	calcium	0.31	0.31
21	Sc	scandium	0.279	0.28	0.279
22	Ti	titanium	0.32	0.32
23	V	vanadium	0.37	0.37
24	Cr	chromium	0.21	0.21
26	Fe	iron	0.29	0.29
27	Co	cobalt	0.31	0.31
28	Ni	nickel	0.31	0.31
29	Cu	copper	0.34	0.34
30	Zn	zinc	0.25	0.25
34	Se	selenium	0.33	0.33
38	Sr	strontium	0.28	0.28
39	Y	yttrium	0.243	0.24	0.243
40	Zr	zirconium	0.34	0.34
41	Nb	niobium	0.40	0.40
42	Mo	molybdenum	0.31	0.31
44	Ru	ruthenium	0.30	0.30
45	Rh	rhodium	0.26	0.26
46	Pd	palladium	0.39	0.39
47	Ag	silver	0.37	0.37
48	Cd	cadmium	0.30	0.30
50	Sn	tin	0.36	0.36
57	La	lanthanum	(α form) 0.280	0.28	(α form) 0.280
58	Ce	cerium	(γ form) 0.24	0.24	(γ form) 0.24
59	Pr	praseodymium	(α form) 0.281	0.28	(α form) 0.281
60	Nd	neodymium	(α form) 0.281	0.28	(α form) 0.281
61	Pm	promethium	(α form) est. 0.28	0.28	(α form) est. 0.28
62	Sm	samarium	(α form) 0.274	0.27	(α form) 0.274
63	Eu	europium	0.152	0.15	0.152
64	Gd	gadolinium	(α form) 0.259	0.26	(α form) 0.259
65	Tb	terbium	(α form) 0.261	0.26	(α form) 0.261
66	Dy	dysprosium	(α form) 0.247	0.25	(α form) 0.247
67	Ho	holmium	0.231	0.23	0.231
68	Er	erbium	0.237	0.24	0.237
69	Tm	thulium	0.213	0.21	0.213
70	Yb	ytterbium	(β form) 0.207	0.21	(β form) 0.207
71	Lu	lutetium	0.261	0.26	0.261
72	Hf	hafnium	0.37	0.37
73	Ta	tantalum	0.34	0.34
74	W	tungsten	0.28	0.28
75	Re	rhenium	0.30	0.30
76	Os	osmium	0.25	0.25
77	Ir	iridium	0.26	0.26
78	Pt	platinum	0.38	0.38
79	Au	gold	0.44	0.44
81	Tl	thallium	0.45	0.45
82	Pb	lead	0.44	0.44
83	Bi	bismuth	0.33	0.33
90	Th	thorium	0.27	0.27
92	U	uranium	0.23	0.23
94	Pu	plutonium	0.21	0.21

Bulk modulus

Bulk modulus K(GPa)

number	symbol	name	use	WEL [1]	CRC [2]	other
3	Li	lithium	11	11
4	Be	beryllium	130	130
5	B	boron	(β form) 185	320		β 185(7) GPa, α 224(15) GPa [4]
6	C	carbon	33	33
11	Na	sodium	6.3	6.3
12	Mg	magnesium	45	45
13	Al	aluminium	76	76
14	Si	silicon	100	100
15	P	phosphorus	11	11
16	S	sulfur	7.7	7.7
17	Cl	chlorine		(liquid) 1.1
19	K	potassium	3.1	3.1
20	Ca	calcium	17	17
21	Sc	scandium	56.6	57	56.6
22	Ti	titanium	110	110
23	V	vanadium	160	160
24	Cr	chromium	160	160
25	Mn	manganese	120	120
26	Fe	iron	170	170
27	Co	cobalt	180	180
28	Ni	nickel	180	180
29	Cu	copper	140	140
30	Zn	zinc	70	70
31	Ga	gallium	56			56 average [5]
32	Ge	germanium	75.8			75.8 [6]
33	As	arsenic	22	22
34	Se	selenium	8.3	8.3
35	Br	bromine		1.9
37	Rb	rubidium	2.5	2.5
39	Y	yttrium	41.2	41	41.2
41	Nb	niobium	170	170
42	Mo	molybdenum	230	230
44	Ru	ruthenium	220	220
45	Rh	rhodium	380	380 (possibly incorrect [3] )
46	Pd	palladium	180	180
47	Ag	silver	100	100
48	Cd	cadmium	42	42
50	Sn	tin	58	58
51	Sb	antimony	42	42
52	Te	tellurium	65	65
53	I	iodine	7.7	7.7
55	Cs	caesium	1.6	1.6
56	Ba	barium	9.6	9.6
57	La	lanthanum	(α form) 27.9	28	(α form) 27.9
58	Ce	cerium	(γ form) 21.5	22	(γ form) 21.5
59	Pr	praseodymium	(α form) 28.8	29	(α form) 28.8
60	Nd	neodymium	(α form) 31.8	32	(α form) 31.8
61	Pm	promethium	(α form) est. 33	33	(α form) est. 33
62	Sm	samarium	(α form) 37.8	38	(α form) 37.8
63	Eu	europium	8.3	8.3	8.3
64	Gd	gadolinium	(α form) 37.9	38	(α form) 37.9
65	Tb	terbium	(α form) 38.7	38.7	(α form) 38.7
66	Dy	dysprosium	(α form) 40.5	41	(α form) 40.5
67	Ho	holmium	40.2	40	40.2
68	Er	erbium	44.4	44	44.4
69	Tm	thulium	44.5	45	44.5
70	Yb	ytterbium	(β form) 30.5	31	(β form) 30.5
71	Lu	lutetium	47.6	48	47.6
72	Hf	hafnium	110	110
73	Ta	tantalum	200	200
74	W	tungsten	310	310
75	Re	rhenium	370	370
76	Os	osmium	462			462 [7]
77	Ir	iridium	320	320
78	Pt	platinum	230	230
79	Au	gold	180	180
80	Hg	mercury		25
81	Tl	thallium	43	43
82	Pb	lead	46	46
83	Bi	bismuth	31	31
90	Th	thorium	54	54
92	U	uranium	100	100

Shear modulus

Shear modulus G(GPa)

number	symbol	name	use	WEL [1]	CRC [2]
3	Li	lithium	4.2	4.2
4	Be	beryllium	132	132
11	Na	sodium	3.3	3.3
12	Mg	magnesium	17	17
13	Al	aluminium	26	26
19	K	potassium	1.3	1.3
20	Ca	calcium	7.4	7.4
21	Sc	scandium	29.1	29	29.1
22	Ti	titanium	44	44
23	V	vanadium	47	47
24	Cr	chromium	115	115
25	Mn	manganese	81	81
26	Fe	iron	82	82
27	Co	cobalt	75	75
28	Ni	nickel	76	76
29	Cu	copper	48	48
30	Zn	zinc	43	43
34	Se	selenium	3.7	3.7
38	Sr	strontium	6.1	6.1
39	Y	yttrium	25.6	26	25.6
40	Zr	zirconium	33	33
41	Nb	niobium	38	38
42	Mo	molybdenum	120	120
44	Ru	ruthenium	173	173
45	Rh	rhodium	150	150
46	Pd	palladium	44	44
47	Ag	silver	30	30
48	Cd	cadmium	19	19
50	Sn	tin	18	18
51	Sb	antimony	20	20
52	Te	tellurium	16	16
56	Ba	barium	4.9	4.9
57	La	lanthanum	(α form) 14.3	14	(α form) 14.3
58	Ce	cerium	(γ form) 13.5	14	(γ form) 13.5
59	Pr	praseodymium	(α form) 14.8	15	(α form) 14.8
60	Nd	neodymium	(α form) 16.3	16	(α form) 16.3
61	Pm	promethium	(α form) est. 18	18	(α form) est. 18
62	Sm	samarium	(α form) 19.5	20	(α form) 19.5
63	Eu	europium	7.9	7.9	7.9
64	Gd	gadolinium	(α form) 21.8	22	(α form) 21.8
65	Tb	terbium	(α form) 22.1	22	(α form) 22.1
66	Dy	dysprosium	(α form) 24.7	25	(α form) 24.7
67	Ho	holmium	26.3	26	26.3
68	Er	erbium	28.3	28	28.3
69	Tm	thulium	30.5	31	30.5
70	Yb	ytterbium	(β form) 9.9	9.9	(β form) 9.9
71	Lu	lutetium	27.2	27	27.2
72	Hf	hafnium	30	30
73	Ta	tantalum	69	69
74	W	tungsten	161	161
75	Re	rhenium	178	178
76	Os	osmium	222	222
77	Ir	iridium	210	210
78	Pt	platinum	61	61
79	Au	gold	27	27
81	Tl	thallium	2.8	2.8
82	Pb	lead	5.6	5.6
83	Bi	bismuth	12	12
90	Th	thorium	31	31
92	U	uranium	111	111
94	Pu	plutonium	43	43

References

1. Values from WebElements presumably are also at room temperature. As quoted at http://www.webelements.com/ from these sources:
   • A.M. James and M.P. Lord in Macmillan's Chemical and Physical Data, Macmillan, London, UK, 1992.
   • G.W.C. Kaye and T. H. Laby in Tables of physical and chemical constants, Longman, London, UK, 15th edition, 1993.
   • G.V. Samsonov (Ed.) in Handbook of the physicochemical properties of the elements, IFI-Plenum, New York, USA, 1968.
   • D.R. Lide, (Ed.) in Chemical Rubber Company handbook of chemistry and physics, CRC Press, Boca Raton, Florida, USA, 79th edition, 1998.
2. Values from CRC refer to room temperature. As quoted in an online version of:
   • David R. Lide (ed), CRC Handbook of Chemistry and Physics, 84th Edition. CRC Press. Boca Raton, Florida, 2003; Section 4, Properties of the Elements and Inorganic Compounds; Physical Properties of the Rare Earth Metals
   which further refers to:
   • Scott, T., 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, 591.
3. Cardarelli, François (2018). Materials Handbook. p. 567. doi:10.1007/978-3-319-38925-7_4.
4. Nelmes, R. J.; Loveday, J. S.; Allan, D. R.; Besson, J. M.; Hamel, G.; Grima, P.; Hull, S. (1993). "Neutron- and x-ray-diffraction measurements of the bulk modulus of boron" . Physical Review B. 47 (13): 7668–7673. Bibcode:1993PhRvB..47.7668N. doi:10.1103/PhysRevB.47.7668. PMID   10004773.
5. "Materials Science Articles | Latest Science Articles | Scientific Development". AZoM.com. Retrieved 30 December 2022.
6. "Germanium (Ge) bulk modulus". Group IV Elements, IV-IV and III-V Compounds. Part a - Lattice Properties. Landolt-Börnstein - Group III Condensed Matter. 2001. pp. 1–6. doi:10.1007/10551045_235. ISBN   3-540-64070-3.
7. H. Cynn; J. E. Klepeis; C.-S. Yoo; D. A. Young (2002). "Osmium has the Lowest Experimentally Determined Compressibility". Physical Review Letters. 88, 135701 (13): 135701. Bibcode:2002PhRvL..88m5701C. doi:10.1103/PhysRevLett.88.135701. PMID   11955108. Archived from the original on 2006-01-10.