omron-sinicx/MaterialBENCH huggingface dataset:
Problem: 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, calculate the average atomic weight of Cr.
Answer: 52.00
Problem: Sodium chloride (NaCl) exhibits predominantly ionic bonding. The Na+ and Cl- ions have electron structures that are identical to which two inert gases, respectively?
Answer: Ne, Ar
Problem: To what group in the periodic table (new IUPAC) would an element with atomic number 114 belong?
Answer: 14
Problem: Write down the electron configuration of fluorine in the style such as 1s22s2.
Answer: 1s22s22p5
Problem: What electron subshell is being filled for the actinide series?
Answer: 5f
Problem: What type of bonding would be expected for aluminum phosphide (AlP)?
Answer: ionic
Problem: Calculate the atomic packing factor for the FCC crystal structure. 
Answer: 0.74
Problem: Copper has an atomic radius of 0.128 nm, an FCC crystal structure, and an atomic weight of 63.5 g/mol. Calculate its theoretical density (g/cm^3).
Answer: 8.89
Problem: 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, calculate its density (g/cm^3).
Answer: 7.31
Problem: 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, calculate the number of atoms in each unit cell.
Answer: 8
Problem: For tetragonal crystals, list the indices of directions that are equivalent to the [110] direction.
Answer: [-1-10], [-110], [1-10]
Problem: 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.
Answer: [010] or [0-10]
Problem: Derive linear density expressions for FCC [100] direction in terms of the atomic radius R.
Answer: 1/(2R√2)
Problem: Calculate a planar density value (m^-2) for (110) plane for vanadium.
Answer: 1.522 x 10^19
Problem: 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.
Answer: 81.38
Problem: 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.
Answer: 0.247
Problem: 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.
Answer: 2.2x10^25
Problem: The surface energy of a single crystal depends on crystallographic orientation. How does this surface energy change with an increase in planar density?
Answer: increase
Problem: 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.
Answer: 2.41x10^-5
Problem: 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.
Answer: 0.75
Problem: 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. ForFCC 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.
Answer: r=(√2-1)R
Problem: What is the composition (Zn at%, Cu at%) of an alloy that consists of 30 wt% Zn and 70 wt% Cu?
Answer: Zn:29.4at%, Cu:70.6at%
Problem: What is the composition (Sn at%, Pb at%) of an alloy that contains 98 g tin and 65 g lead?
Answer: Sn: 72.5at%, Pb: 27.5at%
Problem: Calculate the number of atoms per cubic meter in aluminum.
Answer: 6.05x10^28
Problem: 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.
Answer: 0.289
Problem: Gold forms a substitutional solid solution with silver. Calculate 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.
Answer: 3.36x10^21
Problem: 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. 
Answer: greater, less
Problem: 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.
Answer: 1.54
Problem: 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.
Answer: 2.4x10^- 9
Problem: The diffusion coefficients for copper in aluminum at 500 and 600℃ are 4.8 x 10^-14 and 5.3x10^-13 m2/s, respectively. Calculate 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℃.
Answer: 110.4
Problem: 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.
Answer: 2.16
Problem: 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.
Answer: 2.6x10^-3
Problem: 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.
Answer: 40
Problem: 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 values of the activation energy Qd (kJ/mol).
Answer: 252.4
Problem: 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.
Answer: 1044
Problem: 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.
Answer: 1.6
Problem: 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)?
Answer: 0.77
Problem: A tensile stress is to be applied along the long axis of a cylindrical brass rod that has a diameter of 10 mm. Calculate 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.
Answer: 5600
Problem: 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.
Answer: 30
Problem: 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).
Answer: 4.6
Problem: 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.
Answer: 47.5
Problem: 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.
Answer: 255
Problem: 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?
Answer: 89.4x10^3
Problem: 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 up to 320 MPa with the elastic modulus of 200 GPa, calculate its elongation (mm) when a load of 20,000 N is applied.
Answer: 0.1
Problem: 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, calculate the force (N) that will produce an elastic reduction of 3 x 10^-3 mm in the diameter.
Answer: 16250
Problem: 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.
Answer: 0.28
Problem: 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.
Answer: 171
Problem: 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.
Answer: 0.237
Problem: 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?
True Stress(MPa) True Strain
345.4 0.10
414.4 0.20
Answer: 440
Problem: 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.
Answer: 21
Problem: 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.
Answer: 0.2862
Problem: 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.
Answer: 0.408
Problem: 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.
Answer: 0.8
Problem: 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, calculate the critical resolved shear stress (MPa).
Answer: 0.45
Problem: 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?
Answer: 1.48 x 10^-2
Problem: 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
Calculate grain diameter (mm) predict after 150 min at 650 C.
Answer: 0.084
Problem: A relatively large plate of a glass is subjected to a tensile stress of 40 MPa. If the specific surface energy and modulus of elasticity for this glass are 0.3 J/m2 and 69 GPa, respectively, calculate the maximum length of a surface flaw (μm) that is possible without fracture.
Answer: 8.2
Problem: What is the magnitude of the maximum stress (MPa) that exists at the tip of an internal crack having a radius of curvature of 2.5 x 10^-4 mm  and a crack length of 2.5 x 10^-2 mm when a tensile stress of 170 MPa is applied?
Answer: 2404
Problem: If the specific surface energy for soda-lime glass is 0.30 J/m2, using data: Flexural Strength = 69 MPa; Modulus of Elasticity = 69 GPa, calculate the critical stress (MPa) required for the propagation of a surface crack of length 0.05 mm.
Answer: 16.2
Problem: A structural component in the form of a wide plate is to be fabricated from a steel alloy that has a plane strain fracture toughness of 77.0 MPa√m and a yield strength of 1400 MPa.The flaw size resolution limit of the flaw detection apparatus is 4.0 mm. If the design stress is one-half of the yield strength and the value of Y (a dimentionless parameter that depends on both crack and specimen sizes and geometries to express fracture toughness) is 1.0, determine whether a critical flaw for this plate is subject to detection by reasoning with the flaw size.
Answer: Is not subject to detection because flaw size < 4.0 mm
Problem: Following is tabulated data that were gathered from a series of Charpy impact tests on a ductile cast iron.
Temperature (℃) Impact Energy (J )
  25 124
  50 123
  75 115
  85 100
 100 73
 110 52
 125 26
 150 9
 175 6
Determine a ductile-to-brittle transition temperature (℃) as that temperature corresponding to the average of the maximum and minimum impact energies.
Answer: 105
Problem: The fatigue data for a brass alloy are given as follows:
Stress Amplitude(MPa) Cycles to Failure
310   2x10^5
223   1x10^6
191   3x10^6
168   1x10^7
153   3x10^7
143   1x10^8
134   3x10^8
127   1x10^9
Calculate the fatigue strength (MPa) at 5 x 10^5 cycles.
Answer: 250
Problem: The following creep data were taken on an aluminum alloy at 400 C and a constant stress of 25 MPa. Determine the steady-state or minimum creep rate (min^-1). Note: The initial and instantaneous strain is not included.
Time (min) Strain
0 0.000 
2 0.025 
4 0.043 
6 0.065 
8 0.078 
10 0.092 
12 0.109 
14 0.120
16 0.135
18 0.153
20 0.172
22 0.193
24 0.218
26 0.255
28 0.307
Answer: 7.0 x 10^-3
Problem: Steady-state creep data taken for a stainless steel at a stress level of 70 MPa are given as follows:
έ(s^-1)   T(K)
1.0x10^-5   977
2.5x10^-3   1089
If it is known that the value of the stress exponent n for this alloy is 7.0, calculate the steady-state creep rate (s^-1) at 1250 K and a stress level of 50 MPa.
Answer: 0.12
Problem: Calculate the minimum cation-to-anion radius ratio for the coordination number 3.
Answer: 0.155
Problem: Based on the crystal structure of sodium chloride and the ionic radii for Na+ and Cl- as 0.102 and 0.181 nm, respectively, calculate the theoretical density (g/cm^3) of this material.
Answer: 2.14
Problem: Calculate the number of Schottky defects per cubic meter in potassium chloride at 500 ℃. The energy required to form each Schottky defect is 2.6 eV, whereas the density for KCl (at 500 ℃) is 1.955 g/cm3.
Answer: 5.31 x 10^19
Problem: At which coordination number the minimum cation-to-anion radius ratio is 0.225?
Answer: 4
Problem: On the basis of ionic charge and ionic radii, Cs+ 0.170 nm and I- 0.220 nm, predict crystal structure of CsI
Answer: Cesium chloride
Problem: The zinc blende crystal structure is one that may be generated from close-packed planes of anions. 
Will the stacking sequence for this structure be FCC or HCP? Will cations fill tetrahedral or octahedral positions?  Answer the two questions, by connecting comma. 
Answer: FCC, tetrahedral
Problem: Iron sulfide (FeS) may form a crystal structure that consists of an HCP arrangement of S2  ions.
Which type of interstitial site will the Fe2  ions occupy?
What fraction of these available interstitial sites will be occupied by Fe2  ions?
 Answer the two questions, by connecting comma.
Answer: octahedral, all
Problem: Magnesium oxide has the rock salt crystal structure and a density of 3.58 g/cm3.
Calculate the unit cell edge length (nm).
Answer: 0.421
Problem: Using the ionic radii Cs+ 0.170 nm and Cl- 0.181 nm, calculate the theoretical density (g/cm^3) of CsCl.
Answer: 4.2
Problem: Calculate the atomic packing factor for cesium chloride using the ionic radii Cs  0.170 nm Cl  0.181 nm, and assuming that the ions touch along the cube diagonals.
Answer: 0.68
Problem: Suppose that Li2O is added as an impurity to CaO. If the Li+ substitutes for Ca2+, what kind of vacancies would you expect to form? How many of these vacancies are created for every Li+ added?
Answer: O2  vacancy;one O2  vacancy for every two Li  added
Problem: A three-point bending test was performed on an aluminum oxide specimen having a circular cross section of radius 3.5 mm; the specimen fractured at a load of 950 N when the distance between the support points was 50 mm. Another test is to be performed on a specimen of this same material, but one that has a square cross section of 12 mm length on each edge. At what load (N) would you expect this specimen to fracture if the support point separation is 40 mm?
Answer: 1.0 x 10^4
Problem: The modulus of elasticity for beryllium oxide (BeO) having 5 vol% porosity is 310 GPa.
Calculate the modulus of elasticity (GPa) for the nonporous material.
Answer: 342
Problem: A continuous and aligned glass fiber–reinforced composite consists of 40 vol% of glass fibers having a modulus of elasticity of 69 GPa and 60 vol% of a polyester resin that, when hardened, displays a modulus of 3.4 GPa.
Calculate the modulus of elasticity (GPa) of this composite in the longitudinal direction.
Answer: 30
Problem: For a glass fiber–epoxy matrix combination, the critical fiber length–fiber diameter ratio is 50. Using the data on the glass below: specific gravity = 2.58, tensile strength = 3.45 GPa, specific strength = 1.34 GPa, modulus of elasticity = 72.5 GPa, specific modulus = 28.1 GPa, calculate the fiber-matrix bond strength (MPa).
Answer: 34.5
Problem: Assume a continuous and aligned fiber–reinforced composite is to be produced consisting of 30 vol% aramid fibers and 70 vol% of a polycarbonate matrix, where the modulus of elasticity and tensile strength of armid fire are 131 GPa and 3600 MPa, those of polycarbonate are 2.4 GPa and 65 MPa. It has a cross-sectional area of 320 mm2 and is subjected to a longitudinal load of 44,500 N.
Calculate the fiber–matrix load ratio.
Answer: 23.4
Problem: Calculate the longitudinal strength (MPa) of an aligned carbon fiber–epoxy matrix composite having a 0.25 volume fraction of fibers, assuming the following: (1) an average fiber diameter of 10 x 10^-3 mm, (2) an average fiber length of 5 mm, (3) a fiber fracture strength of 2.5 GPa, (4) a fiber-matrix bond strength of 80 MPa, (5) a matrix stress at fiber failure of 10.0 MPa, and (6) a matrix tensile strength of 75 MPa.
Answer: 633
Problem: Calculate the longitudinal tensile strength (MPa) of an aligned glass fiber–epoxy matrix composite in which the average fiber diameter and length are 0.010 mm and 2.5 mm, respectively, and the volume fraction of fibers is 0.40. Assume that (1) the fiber-matrix bond strength is 75 MPa, (2) the fracture strength of the fibers is 3500 MPa, and (3) the matrix stress at fiber failure is 8.0 MPa.
Answer: 1340
Problem: One-half of an electrochemical cell consists of a pure nickel electrode in a solution of Ni2+ ions; the other half is a cadmium electrode immersed in a Cd2+ solution.
Calculate the cell potential (V) at 25 ℃ if the Cd2+ and Ni2+ concentrations are 1 M.
Answer: 0.153
Problem: Calculate the voltage (V) at 25ºC of an electrochemical cell consisting of pure cadmium immersed in a 2 x 10^(-3) M solution of Cd2+ ions, and pure iron in a 0.4 M solution of Fe2+ ions.
Answer: 0.031
Problem: A piece of corroded steel plate was found in a submerged ocean vessel. It was estimated that the original area of the plate was 10 in.2 and that approximately 2.6 kg had corroded away during the submersion. Assuming a corrosion penetration rate of 200 mpy for this alloy in seawater, estimate the time of submersion in years. The density of steel is 7.9 g/cm3.
Answer: 10
Problem: For Sn, calculate the Pilling–Bedworth ratio using metal density of 7.30 (g/cm3), and the density of metal oxide SnO2 is 6.95 (g/cm3). Also, on the basis of this value, specify whether you would expect the oxide scale that forms on the surface to be protective.
Answer: 1.33, protective
Problem: For intrinsic gallium arsenide, the room-temperature electrical conductivity is 10^-6 (Ω∙m)^-1; the electron and hole mobilities are, respectively, 0.85 and 0.04 m2/V∙s. Calculate the intrinsic carrier concentration (m^-3) at room temperature.
Answer: 7.0 x 10^12