omron-sinicx/MaterialBENCH huggingface dataset:
Question: Chromium has four naturally occurring isotopes: 4.34% of 50Cr, with an atomic weight of 49.9460 amu; 83.79% of 52Cr, with an atomic weight of 51.9405 amu; 9.50% of 53Cr, with an atomic weight of 52.9407 amu; and 2.37% of 54Cr, with an atomic weight of 53.9389 amu. On the basis of these data, chose the average atomic weight of Cr from the following four choices: (a) 52.00,(b) 52.06, (c) 52.19, and (d) 52.94.
Answer: (a)
Question: Sodium chloride (NaCl) exhibits predominantly ionic bonding. Choose the set of inert gasses whose electron structure is identical to the Na+ and Cl- ions respectively from the following four choices: (a) Ar, Ar, (b) Ne, Ar, (c) Ar, Ne, and (d) Ne, Ne.
Answer: (b)
Question: Chose to what group in the periodic table (new IUPAC) would an element with atomic number 114 belong, from the following four choices: (a) 12, (b) 16, (c) 14, and (d) 10.
Answer: (c)
Question: Write down the electron configuration of fluorine in the style such as 1s22s2. Choose from the following four choices: (a) 1s22s22p63s23p6, (b) 1s22s22p5, (c) 1s22s22p63s23p63d24s2, and (d) 1s22s22p63s23p64s1.
Answer: (b)
Question: What electron subshell is being filled for the actinide series? Choose from the following four choices: (a) 3d, (b) 4f, (c) 6d, and (d) 5f.
Answer: (d)
Question: What type of bonding would be expected for aluminum phosphide (AlP)? Choose from the following four choices: (a) metallic, (b) ionic, (c) covalent, and (d) hydrogen.











Answer: (b)
Question: Chose the atomic packing factor for the FCC crystal structure from the following four choices: (a) 0.74, (b) 0.68, (c) 0.34, and (d) 0.52.
Answer: (a)
Question: Copper has an atomic radius of 0.128 nm, an FCC crystal structure, and an atomic weight of 63.5 g/mol. Choose its theoretical density (g/cm^3) from the following four choices: (a) 11.2, (b) 16.3, (c) 8.89, and (d) 20.6.
Answer: (c)
Question: For cubic crystals, as values of the planar indices h, k, and l increase, how the distance between adjacent and parallel planes (i.e., the interplanar spacing) changes? Choose from the following four choices: (a) increase, (b) decrease, (c) no change, and (d) case-by-case.
Answer: (b)
Question: The diffraction from BCC iron, whose lattice parameter is 0.2866 nm, is measured with monochromatic radiation having a wavelength of 0.1790 nm. Choose the diffraction angle (degrees) for the (220) set of planes (assuming the order of reflection is 1) from the following four choices: (a) 52.4, (b) 65.5, (c) 77.3, and (d) 124.
Answer: (d)
Question: For the body-centered cubic crystal structure, how the unit cell edge length a is related with the atomic radius R? Choose from the following four choices: (a) a=4R/√2, (b) a=2R/√3, (c) a=2R, and (d) a=4R/√3.
Answer: (d)
Question: A hypothetical metal has the simple cubic crystal structure. If its atomic weight is 70.4 g/mol and the atomic radius is 0.126 nm. Choose its density from the following four choices: (a) 7.31, (b) 2.58, (c) 14.6, and (d) 4.74.
Answer: (a)
Question: Iodine has an orthorhombic unit cell for which the a, b, and c lattice parameters are 0.479, 0.725, and 0.978 nm, respectively. If the atomic packing factor and atomic radius are 0.547 and 0.177 nm, respectively, determine the number of atoms in each unit cell. Choose from the following four choices: (a) 4, (b) 12, (c) 6, and (d) 8.
Answer: (d)
Question: For tetragonal crystals, list the indices of directions that are equivalent to the [110] direction. Choose from the following four choices: (a) [001], [00-1],[100],[-100], (b) [010],[0-10], (c) [011],[0-1-1], and (d) [-1-10], [-110], [1-10].
Answer: (d)
Question: List the indices of the direction that results from the intersection of each of the following pairs of planes within a cubic crystal: the (10-1) and (001) planes. Choose from the following four choices: (a) [10-1] or [001], (b) [010] or [0-10], (c) [010] or [110], and (d) [0-10] or [00-1].
Answer: (b)
Question: Derive linear density expression for FCC [100] direction in terms of the atomic radius R. Choose from the following four choices: (a) 1/2R, (b) √2/4R, (c) 1/(R√6/(4/3)), and (d) 1/(2R√2).
Answer: (d)
Question: Calculate a planar density value (m^-2) for (110) plane for vanadium. Choose from the following four choices: (a) 1.01 x 10^19, (b) 1.522 x 10^19 , (c) 1.24 x 10^19, and (d) 8.28 x 10^8.
Answer: (b)
Question: Calculate the expected 2-theta diffraction angle (degrees) for the first-order reflection from the (113) set of planes for FCC platinum when monochromatic radiation of wavelength 0.1542 nm is used. Choose from the following four choices: (a) 52.016, (b) 81.38, (c) 105.61, and (d) 64.97.
Answer: (b)
Question: The metal rubidium has a BCC crystal structure. If the angle of diffraction for the (321) set of planes occurs at 27.00 degrees (first-order reflection) when monochromatic x-radiation having a wavelength of 0.0711 nm is used, calculate the atomic radius (nm) for the rubidium atom. Choose from the following four choices: (a) 0.127, (b) 0.247, (c) 0.202, and (d) 0.104.
Answer: (b)
Question: Calculate the equilibrium number of vacancies per cubic meter for copper at 1000℃. The energy for vacancy formation is 0.9 eV/atom; the atomic weight and density (at 1000℃) for copper are 63.5 g/mol and 8.4 g/cm3, respectively. Choose from the following four choices: (a) 2.2x10^25, (b) 8.9x10^9, (c) 1.2x10^27, and (d) 2.2x10^19.
Answer: (a)
Question: The surface energy of a single crystal depends on crystallographic orientation. How does this surface energy change with an increase in planar density? Choose from the following four choices: (a) increase, (b) decrease, (c) no change, and (d) case-by-case.
Answer: (a)
Question: Calculate the fraction of atom sites that are vacant for lead at its melting temperature of 327 ℃ (600 K). Assume an energy for vacancy formation of 0.55 eV/atom. Choose from the following four choices: (a) 7.51x10^-6, (b) 1.42x10^-29, (c) 1.62x10^-9, and (d) 2.41x10^-5.
Answer: (d)
Question: Calculate the activation energy (eV/atom) for vacancy formation in aluminum, given that the equilibrium number of vacancies at 500℃ (773 K) is 7.57 x 10^23m^-3.The atomic weight and density (at 500℃) for aluminum are, respectively, 26.98 g/mol and 2.62 g/cm^3. Choose the answer from the following four choices: (a) 0.12, (b) 1.1, (c) 0.75, and (d) 0.49.
Answer: (c)
Question: For both FCC and BCC crystal structures, there are two different types of interstitial sites. In each case, one site is larger than the other and is normally occupied by impurity atoms. For FCC, this larger one is located at the center of each edge of the unit cell; it is termed an octahedral interstitial site. On the other hand, with BCC the larger site type is found at 0 positions—that is, lying on {100} faces and situated midway between two unit cell edges on this face and one-quarter of the distance between the other two unit cell edges; it is termed a tetrahedral interstitial site. For FCC crystal structure, derive an expression for the radius r of an impurity atom that will just fit into one of these sites in terms of the atomic radius R of the host atom. Choose the answer from the following four choices: (a) r=(√2-1)R, (b) r=(√3-1)R, (c) r=(1/2)R, and (d) r=((√3-1)/2)R.

Answer: (a)
Question: What is the composition (Zn at%, Cu at%) of an alloy that consists of 30 wt% Zn and 70 wt% Cu? Choose the answer from the following four choices: (a) Zn: 70.6at%, Cu: 29.4at%, (b) Zn: 29.4at%, Cu: 70.6at%, (c) Zn: 30.6at%, Cu: 69.4at% , and (d) Zn: 30.3at%, Cu: 69.7at%.
Answer: (b)
Question: What is the composition (Sn at%, Pb at%) of an alloy that contains 98 g tin and 65 g lead? Choose the answer from the following four choices: (a) Sn: 27.5at%, Pb: 72.5at%, (b) Sn: 80.9at%, Pb: 19.1at%, (c) Sn: 46.3at%, Pb: 53.7at%, and (d) Sn: 72.5at%, Pb: 27.5at%.
Answer: (d)
Question: Calculate the number of atoms per cubic meter in aluminum. Choose the answer from the following four choices: (a) 6.00x10^30, (b) 6.05x10^22, (c) 6.00x10^24, and (d) 6.05x10^28.
Answer: (d)
Question: Calculate the unit cell edge length (nm) for an 85 wt% Fe–15 wt% V alloy. All of the vanadium is in solid solution, and at room temperature the crystal structure for this alloy is BCC. Choose the answer from the following four choices: (a) 0.289, (b) 0.303, (c) 0.354, and (d) 0.205.
Answer: (a)
Question: Gold forms a substitutional solid solution with silver. Compute the number of gold atoms per cubic centimeter for a silver–gold alloy that contains 10 wt% Au and 90 wt% Ag. The densities of pure gold and silver are 19.32 and 10.49 g/cm3, respectively. Choose the answer from the following four choices: (a) 3.36x10^21, (b) 5.86x10^22, (c) 9.89x10^21, and (d) 2.09x10^21.
Answer: (a)
Question: For a given material, would you expect the surface energy to be greater than, the same as, or less than the grain boundary energy? The grain boundary energy of a small angle grain boundary is greater or less than for a high angle one? Answer two questions by separating with comma. Choose the answer from the following four choices: (a) greater, greater, (b) greater, less, (c) the same, less, and (d) less, greater.

Answer: (b)
Question: Aluminum–lithium alloys have been developed by the aircraft industry to reduce the weight and to improve the performance of its aircraft. A commercial aircraft skin material having a density of 2.55 g/cm3 is desired. Calculate the concentration of Li (in wt%) that is required. Choose the answer from the following four choices: (a) 1.54, (b) 1.03, (c) 25.8, and (d) 17.3.
Answer: (a)
Question: A 15 mm-thick plate of iron is exposed to a carburizing (carbon-rich) atmosphere on one side and a decarburizing (carbon-deficient) atmosphere on the other side at 700 ℃. If a condition of steady state is achieved, calculate the diffusion flux of carbon (kg/m^2s) through the plate if the concentrations of carbon at positions of 5 and 10 mm beneath the carburizing surface are 1.2 and 0.8 kg/m3, respectively. Assume a diffusion coefficient of 3x 10^-11 m2/s at this temperature. Choose the answer from the following four choices: (a) 2.4x10^- 9, (b) 8.0x10^-10, (c) 4.0x10^-9, and (d) 1.6x10^-9.

Answer: (a)
Question: The diffusion coefficients for copper in aluminum at 500 and 600℃ are 4.8 x 10^-14 and 5.3x10^-13 m2/s, respectively. Determine the approximate time (h) at 500℃ that will produce the same diffusion result (in terms of concentration of Cu at some specific point in Al) as a 10-h heat treatment at 600℃. Choose the answer from the following four choices: (a) 90.6, (b) 24, (c) 22, and (d) 110.4.

Answer: (d)
Question: Boron atoms are to be diffused into a silicon wafer using both predeposition and drive-in heat treatments; the background concentration of B in this silicon material is known to be 1 x 10^20 atoms/m3. The predeposition treatment is to be conducted at 900℃ for 30 minutes; the surface concentration of B is to be maintained at a constant level of 3 x 10^26 atoms/m3. Drive-in diffusion will be carried out at 1100℃ for a period of 2 h. For the diffusion coefficient of B in Si, values of Qd and D0 are 3.87 eV/atom and 2.4 x 10^-3 m2/s, respectively. Calculate the value of xj (μm) for the drive-in diffusion treatment. Choose the answer from the following four choices: (a) 1.08, (b) 1.22, (c) 1.27, and (d) 2.16.

Answer: (d)
Question: The purification of hydrogen gas is considered by diffusion through a palladium sheet. Calculate the number of kilograms of hydrogen that pass per hour (kg/h) through a 5-mm-thick sheet of palladium having an area of 0.20 m^2 at 500 ℃. Assume a diffusion coefficient of 1.0 x 10^-8 m2/s, that the concentrations at the high- and low-pressure sides of the plate are 2.4 and 0.6 kg of hydrogen per cubic meter of palladium, and that steady-state conditions have been attained. Choose the answer from the following four choices: (a) 7.2x10^-7, (b) 6.5x10^-2, (c) 2.6x10^-3, and (d) 1.8x10^-5.

Answer: (c)
Question: For a steel alloy it has been determined that a carburizing heat treatment of 10-h duration will raise the carbon concentration to 0.45 wt% at a point 2.5 mm from the surface. Estimate the time (h) necessary to achieve the same concentration at a 5.0-mm position for an identical steel and at the same carburizing temperature. Choose the answer from the following four choices: (a) 20, (b) 40, (c) 14, and (d) 57.

Answer: (b)
Question: The diffusion coefficients for iron in nickel are given at two temperatures: 
T (K)  D (m2/s)
1273  9.4 x 10^-16
1473  2.4 x 10^-14
Calculate the value of the activation energy Qd (kJ/mol). Choose the answer from the following four choices: (a) 252.4, (b) 109.7, (c) 106.4, and (d) 46.2.

Answer: (a)
Question: Carbon is allowed to diffuse through a steel plate 15 mm thick.The concentrations of carbon at the two faces are 0.65 and 0.30 kg C/m3 Fe, which are maintained constant. If the preexponential and activation energy are 6.2 x 10^-7 m2/s and 80,000 J/mol, respectively, calculate the temperature (K) at which the diffusion flux is 1.43 x 10^-9 kg/m2 s. Choose the answer from the following four choices: (a) 4160, (b) 1044, (c) 68, and (d) 3294.

Answer: (b)
Question: A diffusion couple is prepared using two hypothetical metals A and B. After a 30-h heat treatment at 1000 K (and subsequently cooling to room temperature) the concentration of A in B is 3.2 wt% at the 15.5-mm position within metal B. If another heat treatment is conducted on an identical diffusion couple, only at 800 K for 30 h, at what position (mm) will the composition be 3.2 wt% A? Assume that the preexponential and activation energy for the diffusion coefficient are 1.8 x 10^-5 m2/s and 152,000 J/mol, respectively.  Choose the answer from the following four choices: (a) 1.6, (b) 2.5, (c) 6.2, and (d) 0.33.

Answer: (a)
Question: A piece of copper originally 305 mm long is pulled in tension with a stress of 276 MPa. If the deformation is entirely elastic, what will be the resultant elongation (mm)? Choose the answer from the following four choices: (a) 0.77, (b) 1.1, (c) 0.0025, and (d) 1.3.
Answer: (a)
Question: A tensile stress is to be applied along the long axis of a cylindrical brass rod that has a diameter of 10 mm. Determine the magnitude of the load (N) required to produce a 2.5 x 10^-3 mm change in diameter if the deformation is entirely elastic. Choose the answer from the following four choices: (a) 22000, (b) 650, (c) 2600, and (d) 5600.
Answer: (d)
Question: Of those metals listed in the table below, which is the stiffest? Choose the answer from the following four choices: (a) A, (b) B, (c) C, and (d) D.
Table
Material  Yield Strength(MPa)  Tensile Strength(MPa)  Strain at Fracture  Fracture Strength(MPa)  Elastic Modulus(GPa)
A  310  340  0.23  265  210
B  100  120  0.40  105  150
C  415  550  0.15  500  310
D  700  850  0.14  720  210
E  Fractures before yielding 650 350

Answer: (c)
Question: A cylindrical specimen of steel having an original diameter of 12.8 mm is tensile-tested to fracture and found to have an engineering fracture strength of 460 MPa. If its cross-sectional diameter at fracture is 10.7 mm, calculate the ductility in terms of percent reduction in area. Choose the answer from the following four choices: (a) 16, (b) 0.065, (c) 30, and (d) 139.
Answer: (c)
Question: Of those metals listed in the table below, which is the hardest? Choose the answer from the following four choices: (a) B, (b) C, (c) D, and (d) E.
Table
Material  Yield Strength(MPa)  Tensile Strength(MPa)  Strain at Fracture  Fracture Strength(MPa)  Elastic Modulus(GPa)
A  310  340  0.23  265  210
B  100  120  0.40  105  150
C  415  550  0.15  500  310
D  700  850  0.14  720  210
E  Fractures before yielding 650 350

Answer: (c)
Question: The following tensile strengths were measured for four specimens of the same steel alloy:
 Sample Number Tensile Strength(MPa)
1 520
2 512
3 515
4 522
Calculate the standard deviation (MPa). Choose the answer from the following four choices: (a)  517 (b) 4, (c) 16, and (d) 23.

Answer: (b)
Question: A tensile-testing apparatus is to be constructed that must withstand a maximum load of 220,000 N. The design calls for two cylindrical support posts, each of which is to support half of the maximum load. Furthermore, plain-carbon (1045) steel ground and polished shafting rounds are to be used; the minimum yield and tensile strengths of this alloy are 310 MPa and 565 MPa, respectively. Specify a suitable diameter (mm) for these support posts when factor of safety is 5. Choose the answer from the following four choices: (a) 35.2, (b) 47.5, (c) 23.8, and (d) 67.2.

Answer: (b)
Question: A cylindrical specimen of a titanium alloy having an elastic modulus of 107 GPa and an original diameter of 3.8 mm will experience only elastic deformation when a tensile load of 2000 N is applied. Calculate the maximum length (mm) of the specimen before deformation if the maximum allowable elongation is 0.42 mm. Choose the answer from the following four choices: (a) 1018, (b) 81.1, (c) 255, and (d) 606.

Answer: (c)
Question: For a bronze alloy, the stress at which plastic deformation begins is 275 MPa, and the modulus of elasticity is 115 GPa. What is the maximum load (N) that may be applied to a specimen with a cross-sectional area of 325 mm2 without plastic deformation? Choose the answer from the following four choices: (a) 777, (b) 10.3 x 10^6, (c) 89.4x10^3, and (d) 777 x 10^6.
Answer: (c)
Question: Consider a cylindrical specimen of a steel alloy 10.0 mm in diameter and 75 mm long that is pulled in tension. When the steel is elastic upto 320 MPa with the elastic modulus of 200 GPa, calculate its elongation (mm) when a load of 20,000 N is applied. Choose the answer from the following four choices: (a) 0.024, (b) 0.004, (c) 0.3, and (d) 0.1.
Answer: (d)
Question: A cylindrical bar of steel 10 mm in diameter is to be deformed elastically by application of a force along the bar axis. Using the following data: Modulus of Elasticity = 207 GPa, Shear Modulus = 83 GPa, Poisson’s ratio = 0.30, determine the force (N) that will produce an elastic reduction of 3 x 10^-3 mm in the diameter. Choose the answer from the following four choices: (a) 1462, (b) 6516, (c) 196, and (d) 16250.

Answer: (d)
Question: A cylindrical specimen of an alloy 8 mm in diameter is stressed elastically in tension. A force of 15,700 N produces a reduction in specimen diameter of 5 x 10^-3 mm. Calculate Poisson’s ratio for this material if its modulus of elasticity is 140 GPa. Choose the answer from the following four choices: (a) 0.06, (b) 1.12, (c) 3.6, and (d) 0.28.
Answer: (d)
Question: Consider a cylindrical specimen of some hypothetical metal alloy that has a diameter of 8.0 mm. A tensile force of 1000 N produces an elastic reduction in diameter of 2.8 x 10^-4 mm. Calculate the modulus of elasticity (GPa) for this alloy, given that Poisson’s ratio is 0.30. Choose the answer from the following four choices: (a) 42.7, (b) 1900, (c) 171, and (d) 474.
Answer: (c)
Question: A cylindrical rod 380 mm long, having a diameter of 10.0 mm, is to be subjected to a tensile load. If the rod is to experience neither plastic deformation nor an elongation of more than 0.9 mm when the applied load is 24,500 N, which of the four metals or alloys listed in the following table are possible candidates? Choose the answer from the following four choices: (a) Aluminum alloy, (b) Brass alloy, (c) Copper, and (d) Steel alloy.
Material Modulus of Elasticity(GPa) Yield Strength(MPa) Poisson’s Ratio
Aluminum alloy 70 255 420
Brass alloy 100 345 420
Copper 110 250 290
Steel alloy 207 450 550

Answer: (d)
Question: A tensile test is performed on a metal specimen, and it is found that a true plastic strain of 0.20 is produced when a true stress of 575 MPa is applied; for the same metal, the value of linear coefficient between true stress and n-th power of true strain is 860 MPa. Calculate the true strain that results from the application of a true stress of 600 MPa. Choose the answer from the following four choices: (a) 1.86, (b) 0.167, (c) 0.237, and (d) 0.026.

Answer: (c)
Question: The following true stresses produce the corresponding true plastic strains for a brass alloy: What true stress (MPa) is necessary to produce a true plastic strain of 0.25? Choose the answer from the following four choices: (a) 440, (b) 910, (c) 131, and (d) 271.
True Stress(MPa) True Strain
345.4 0.10
414.4 0.20

Answer: (a)
Question: Which of the following is the slip system for the simple cubic crystal structure? Choose the answer from the following four choices: (a) {100}<010>, (b) {110}<110>, (c) {100}<110>, and (d) {110}<111>.
Answer: (a)
Question: Consider a single crystal of BCC iron oriented such that a tensile stress is applied along a [010] direction.
Calculate the resolved shear stress (MPa) along a (110) plane and in a direction when a tensile stress of 52 MPa is applied. Choose the answer from the following four choices: (a) 26, (b) 21, (c) 17, and (d) 42.

Answer: (b)
Question: Burgers vectors for FCC and BCC crystal structures are of the form b = a/2 <uvw> where a is the unit cell edge length. Also, because the magnitudes of these Burgers vectors may be determined from the following equation:
|b| = a/2 (u^2 + v^2 + w^2)^(1/2)
calculate values of |b| (nm) for aluminum. Atomic radii of aluminium 0.1431 nm. Choose the answer from the following four choices: (a) 0.2337, (b) 0.2862, (c) 0.3505, and (d) 0.4957.

Answer: (b)
Question: Sometimes cosφcosλis termed the Schmid factor. Calculate the magnitude of the Schmid factor for an FCC single crystal oriented with its [100] direction parallel to the loading axis. Choose the answer from the following four choices: (a) 0.5, (b) 0.408, (c) 0.354, and (d) 0.707.
Answer: (b)
Question: A single crystal of aluminum is oriented for a tensile test such that its slip plane normal makes an angle of 28.1 ° with the tensile axis. Three possible slip directions make angles of 62.4 °, 72.0 ° , and 81.1 ° with the same tensile axis. If plastic deformation begins at a tensile stress of 1.95 MPa, determine the critical resolved shear stress (MPa) for aluminum. Choose the answer from the following four choices: (a) 0.21, (b) 0.26, (c) 0.53, and (d) 0.8.

Answer: (d)
Question: Consider a single crystal of silver oriented such that a tensile stress is applied along a [001] direction. If slip occurs on a (111) plane and in a direction, and is initiated at an applied tensile stress of 1.1 MPa, compute the critical resolved shear stress (MPa). Choose the answer from the following four choices: (a) 0.32, (b) 0.55, (c) 0.39, and (d) 0.45.

Answer: (d)
Question: which grain boundaried are more effective in interfering with the slip process: small-angle grain boundaries or high-angle grain boundaries? Choose the answer from the following four choices: (a) small-angle, (b) high-angle, (c) same, and (d) case-by-case.

Answer: (b)
Question: The lower yield point for an iron that has an average grain diameter of 5 x 10^-2 mm is 135 MPa. At a grain diameter of 8 x 10^-3 mm, the yield point increases to 260 MPa. At what grain diameter (mm) will the lower yield point be 205 MPa? Choose the answer from the following four choices: (a) 1.48 x 10^-2, (b) 8.23, (c) 1.95, and (d) 4.67.
Answer: (a)
Question: The average grain diameter for a brass material was measured as a function of time at 650 C, which is shown in the following table at two different times:
Time(min)  Grain Diameter(mm)
30  3.9 x 10^-2
90  6.6 x 10^-2
What grain diameter (mm) would you predict after 150 min at 650 C? Choose the answer from the following four choices: (a) 0.084, (b) 0.053, (c) 0.099, and (d) 0.048.

Answer: (a)
Question: Determine whether it is possible to cold work steel so as to give a minimum Brinell hardness of 225, and at the same time have a ductility of at least 12%EL. Choose the answer from the following four choices: (a) both possible, (b) both not possible, (c) hardness: possible, ductility: not possible, and (d) hardness: not possible, ductility: possible.
Answer: (a)