Micropillar compression deformation of single crystals of α-Nb₅Si₃ with the tetragonal D8_l structure

Figures & data

Table 1. The largest Schmid factors for some slip systems in α-Nb₅Si₃ single crystals with the [021], [010], [001] and [$\bar{1}$10] orientations

Slip system	b (nm)	[021]	[010]	[001]	[$\bar{1}$10]
(001)<100>	0.657	0.497	0	0	0
{010}<100>		0	0	0	0.500
{011}<100>		0.240	0	0	0.438
{1$\bar{1}$0}<111>	0.754	0.447	0.308	0	0
{01$\bar{1}$}<111>		0.276	0.381	0.381	0.381
{11$\bar{2}$}<111>		0.170	0.243	0.485	0.485
(001)<110>	0.929	0.352	0	0	0
{1$\bar{1}$0}<110>		0.275	0.500	0	0
{1$\bar{1}$2}<110>		0.433	0.394	0	0
{010}[001]	1.188	0.497	0	0	0
{110}[001]		0.352	0	0	0

Figure 1. Typical stress-strain curves obtained for micropillar specimens of α-Nb₅Si₃ single crystals with the loading axis orientations of (a) [021], (b) [010], (c) [001] and (d) [$\bar{1}$10]. Insets are magnified curves just before failure. A pair of straight gray lines with the elastic slope are indicated as a guide for the eyes in each of the insets. Arrows in the insets indicate the yield points determined as either the elastic limit or the stress for the first strain burst

Figure 2. Deformation microstructures of micropillar specimens of α-Nb₅Si₃ single crystals with orientations of (a) [021] (L = 3.1 μm), (b) [010] (L = 2.4 μm), (c) [001] (L = 0.75 μm) and (d) [$\bar{1}$10] (L = 1.4 μm). All images were taken along the oblique direction 30° from the loading axis

Figure 3. (a) A load-displacement curve obtained in a micro-cantilever bend test of a micro-beam specimen having a chevron-notch parallel to (001). (b) An SEM secondary electron image of the fracture surface of the fractured micro-beam specimen

Table 2. Summary of first-principles DFT calculations of generalized stacking fault energy and the critical shear stress τ_crit for instantaneous nucleation of new dislocations for (001)<010>, {110}<1$\bar{1}$0> and {0$\bar{1}$1}<111> slip in α-Nb₅Si₃ and Mo₅SiB₂ [17]. The isotropic elastic constants of G = 127.9 GPa, ν = 0.229 for α-Nb₅Si₃ [31] and G = 127.9 GPa, ν = 0.229 for Mo₅SiB₂ [41] were used for the calculations of the τ_crit values

								Critical shear stress τcrit for spontaneous dislocation nucleation (GPa)
Material	Slip system	Slip plane	Slip direction	Unstable stacking fault energy, γusf (J/m^2)	Theoretical shear strength, τth (GPa)	Stable stacking fault energy, γsf (J/m^2)	Surface energy (J/m^2)	Full loop	Half loop	Quarter loop	Room-temperature bulk CRSS (τbulk) from micropillar compression data (GPa)
α-Nb5Si3	(001)<010>	(001)a	<010>	2.67	23.6	2.14	2.60	9.3	6.1	3.5	1.1 ± 0.1
		(001)b		2.87	27.6	2.04	2.90
	{110}<1$\bar{1}$0>	{110}a	<1$\bar{1}$0>	3.23	25.4	2.67	2.51	9.3	5.8	3.2	2.1 ± 0.1
		{110}b		3.99	40.7	1.86	2.79
	{0$\bar{1}$1}<111>	{0$\bar{1}$1}a	<1$\bar{1}$$\bar{1}$>	3.68	27.2	-	2.62
			<$\bar{1}$$\bar{1}$$\bar{1}$>	3.05	20.5	2.36		9.3	6.0	3.4	1.0 ± 0.1
		{0$\bar{1}$1}b	<1$\bar{1}$$\bar{1}$>	3.79	22.4	-	2.61
			<$\bar{1}$$\bar{1}$$\bar{1}$>	4.05	27.2	-
		{0$\bar{1}$1}c	<1$\bar{1}$$\bar{1}$>	3.38	27.2	-	2.56
			<$\bar{1}$$\bar{1}$$\bar{1}$>	3.19	24.3	2.43
Mo5SiB2	(001)<010>	(001)a	<010>	2.88	29.5	2.38	2.77	11.4	7.5	4.2	2.7 ± 0.1
		(001)b		3.31	34.0	2.83	3.54
	{110}<1$\bar{1}$0>	{110}a	<1$\bar{1}$0>	2.97	24.1	2.06	3.20	11.3	7.3	4.0	1.9 ± 0.1
		{110}b		3.96	43.8	1.69	3.10
	{0$\bar{1}$1}<111>	{0$\bar{1}$1}a	<1$\bar{1}$$\bar{1}$>	3.84	34.1	-	3.22				2.1 ± 0.1
			<$\bar{1}$$\bar{1}$$\bar{1}$>	3.75	26.4	-		11.4	7.6	4.2
		{0$\bar{1}$1}b	<1$\bar{1}$$\bar{1}$>	3.84	36.8	-	3.09
			<$\bar{1}$$\bar{1}$$\bar{1}$>	3.86	31.2	-
		{0$\bar{1}$1}c	<1$\bar{1}$$\bar{1}$>	4.48	31.2	-	3.22
			<$\bar{1}$$\bar{1}$$\bar{1}$>	3.86	29.2	-

Figure 4. The calculated GSFE curves and their derivatives for three slip systems, (a) (001)<100>, (b) {110}<1$\bar{1}$0> and (c) {0$\bar{1}$1}<111> in α-Nb₅Si₃. (d) and (e) indicate the glide planes selected for the GSFE calculations

Figure 5. Specimen size (edge length L) dependence of CRSS for (001)<100>, {110}<1$\bar{1}$0> and {0$\bar{1}$1}<111> slip. The shaded area (L = 20 − 30 μm) corresponds to the size range, where the CRSS values for micropillar specimens coincide with those obtained for bulk single crystals of many fcc and bcc metals

Figure 6. Orientation dependence of the operative slip systems under uniaxial loading calculated with (a) the estimated bulk CRSS values and (b) those for micropillar specimens with L ~ 2 μm for the three slip systems, (001)<100>, {110}<1$\bar{1}$0> and {0$\bar{1}$1}<111> in α-Nb₅Si_3.

Figure 7. Relationship among the power-law exponent (n), estimated bulk CRSS (τ_bulk) and theoretical shear strength (τ_th). (a) n – τ_bulk, (b) τ_bulk – τ_th and (c) n – τ_th. Error bars for τ_bulk correspond to the values calculated using the fitted power-law equations for L = 20 μm (upper limit) and 30 μm (lower limit)

Figure A1. Schematic illustration of (a) a chevron-notched micro-beam specimen for single cantilever bend test and (b) the shape of a chevron-notch

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