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Lattice Centering and Coordination Number02:33

Lattice Centering and Coordination Number

11.4K
The structure of a crystalline solid, whether a metal or not, is best described by considering its simplest repeating unit, which is referred to as its unit cell. The unit cell consists of lattice points that represent the locations of atoms or ions. The entire structure then consists of this unit cell repeating in three dimensions. The three different types of unit cells present in the cubic lattice are illustrated in Figure 1.
Types of Unit Cells
Imagine taking a large number of identical...
11.4K
Titration Calculations: Strong Acid - Strong Base02:28

Titration Calculations: Strong Acid - Strong Base

33.8K
Calculating pH for Titration Solutions: Strong Acid/Strong Base
A titration is carried out for 25.00 mL of 0.100 M HCl (strong acid) with 0.100 M of a strong base NaOH. The pH at different volumes of added base solution can be calculated as follows:
(a) Titrant volume = 0 mL. The solution pH is due to the acid ionization of HCl. Because this is a strong acid, the ionization is complete and the hydronium ion molarity is 0.100 M. The pH of the solution is then:
33.8K
Trends in Lattice Energy: Ion Size and Charge02:54

Trends in Lattice Energy: Ion Size and Charge

26.6K
An ionic compound is stable because of the electrostatic attraction between its positive and negative ions. The lattice energy of a compound is a measure of the strength of this attraction. The lattice energy (ΔHlattice) of an ionic compound is defined as the energy required to separate one mole of the solid into its component gaseous ions. For the ionic solid sodium chloride, the lattice energy is the enthalpy change of the process:
26.6K
Strong Acid and Base Solutions03:22

Strong Acid and Base Solutions

35.3K
A strong acid is a compound that dissociates completely in an aqueous solution and produces a concentration of hydronium ions equal to the initial concentration of acid. For example, 0.20 M hydrobromic acid will dissociate completely in water and produces 0.20 M of hydronium ions and 0.20 M of bromide ions.
35.3K
Titration of a Strong Acid with a Strong Base01:23

Titration of a Strong Acid with a Strong Base

10.2K
During the titration of a strong acid with a strong base, pH calculations are primarily based on the concentration of residual hydronium or hydroxide ions. Initially, a strong acid like hydrochloric acid fully dissociates, creating hydronium and chloride ions, resulting in a low pH. The addition of a strong base like sodium hydroxide alters the concentration of hydronium ions by neutralizing them. As more base is added, the pH gradually increases. At the equivalence point, all hydronium ions...
10.2K
Bewley Lattice Diagram01:12

Bewley Lattice Diagram

1.5K
The Bewley lattice diagram, developed by L. V. Bewley, effectively organizes the reflections occurring during transmission-line transients. It visually represents how voltage waves propagate and reflect within a transmission line, making it easier to understand the complex interactions that occur.
1.5K

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Updated: Jan 23, 2026

Transaxillary First Rib Resection for Treatment of the Thoracic Outlet Syndrome
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Rib-Reinforced Ultralight and Ultra-Strong Shell Lattices.

Winston Wai Shing Ma1, Lei Zhang2, Junhao Ding3

  • 1Department of Mechanical Engineering, Hong Kong Polytechnic University, Kowloon, Hong Kong, China.

Advanced Science (Weinheim, Baden-Wurttemberg, Germany)
|January 22, 2026
PubMed
Summary
This summary is machine-generated.

Researchers developed novel ribbed shell lattices to improve strength in ultralight materials. This design enhances load-bearing capacity and prevents buckling failure in lightweight applications.

Keywords:
buckling‐resistant designcurvature directionsribbed shell latticestriply periodic minimal surfacesultralight and ultra‐strong lattices

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Area of Science:

  • Materials Science
  • Mechanical Engineering
  • Additive Manufacturing

Background:

  • Shell lattices offer unique geometric and mechanical properties for lightweight applications.
  • Low relative densities (RDs) in shell lattices lead to reduced strength due to yielding-to-buckling failure modes.
  • Optimizing ultralight and ultra-strong shell lattices is challenging.

Purpose of the Study:

  • To propose a novel design of rib-reinforced shell lattices, termed ribbed shell lattices.
  • To enhance the strength of ultralight triply periodic minimal surface (TPMS) shell lattices.
  • To investigate the effect of rib placement on mechanical properties.

Main Methods:

  • Revealing intrinsic relations between curvature and stress directions in TPMS thin shell lattices.
  • Orchestrating two groups of ribs along representative curvature directions: line of asymptotes (LOA) and line of principal curvatures (LOC).
  • Physical realization and numerical simulations to validate the design.

Main Results:

  • Incorporating ribs along LOAs and LOCs passing through shell umbilical points enhanced strength by 112.3% at an RD of approximately 1.28%.
  • Ribs redistribute stress, strengthen thin shells, and suppress buckling deformation, particularly at umbilical regions.
  • Continuous ribs provide additional load paths, improving load-bearing efficiency.

Conclusions:

  • Rib-reinforced shell lattices offer a practical design strategy for enhancing the strength of ultralight TPMS structures.
  • The proposed method effectively addresses micro-architecture buckling failure in shell lattices.
  • This advancement facilitates the development of stronger and more efficient lightweight materials.