List of top Mechanical Metallurgy Questions asked in GATE MT

During carburizing of a steel, the surface concentration is kept constant at 1.4 wt.% carbon. Diffusivity of carbon for the steel at \(950^{\circ}\text{C}\) is \(6.25 \times 10^{-11}\) m\(^2\)/s. At \(950^{\circ}\text{C}\), the time required to carburize the steel with an initial composition of 0.2 wt.% carbon to 0.8859 wt.% carbon at a depth of 0.2 mm is _______ seconds (approximate to the nearest integer).
Use the nearest value of the error function from the table given below for your calculation.
\[ \begin{array}{cc} z & \text{erf}(z) \\ 0.3 & 0.3268 \\ 0.4 & 0.4284 \\ 0.5 & 0.5205 \end{array} \]

A given volume of liquid is undercooled just below the melting temperature to form a spherical solid nucleus (consider homogeneous nucleation). The Gibbs free energy of solidification (\(\Delta G_v\)) is \((-0.5 \times 10^{8})\) J/m\(^3\). The solid-liquid interfacial energy (\(\gamma\)) is isotropic and its value is \(0.1\) J/m\(^2\).
The critical nucleus size for a stable nucleus is _______ nm (answer in integer).

A metal having body-centered cubic structure is analyzed through X-ray diffraction using monochromatic X-ray of wavelength 0.154 nm. The diffraction angle (\(2\theta\)) corresponding to \(\{2\,0\,0\}\) plane is \(60^{\circ}\) (for first order reflection).
The atomic radius of this element (rounded off to three decimal places) is ______ nm.

A cylindrical single crystal of copper having 10 mm diameter is deformed under a uniaxial tensile load of 2200 N. The angle between the normal to the slip plane and the tensile loading axis is \(\alpha\), whereas the angle between slip direction and the tensile axis is \(\beta\). The slip direction is in the plane defined by the stress axis and the normal to the slip plane.
If \(\alpha=\beta\), the critical resolved shear stress (CRSS), rounded off to one decimal place, is ______ MPa.

For an equilibrium phase diagram of a binary A-B alloy at a constant pressure as shown in the figure, the degree of freedom at 'X' is (answer in integer) ______.

The figure shows a binary A-B alloy phase diagram with composition (wt.%B) on the x-axis and temperature on the y-axis. A liquidus curve runs from pure A down to pure B and a solidus curve runs below it; the region above the liquidus is labelled Liquid and the region below the solidus is labelled Solid. Point X lies inside the lens shaped region between the liquidus and the solidus curves, that is, in the two-phase (liquid + solid) region.